语音压缩感知关键技术研究
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摘要
语音是人类最方便直接的交流方式，在数字化的时代，如何对语音信号建模以获得更少的采样但又不影响语音的质量，是当前语音信号处理领域中的研究热点。压缩感知（Compressed Sensing，CS）是基于信号在某个域的稀疏性建立的线性、非自适应采样的新理论，表明具有稀疏性的压缩感知能获得更好的压缩性能，信号的稀疏性或可压缩性是实现压缩重构的必要条件之一。由于语音信号具有可压缩性，能够采用低于Nyquist采样的速率无失真地采样信号，基于压缩感知进行低速率无失真地采样给语音信号的采样、存储、传输和处理都带来了很大方便。所以CS理论与语音信号处理领域的结合，意味着对传统的基于奈奎斯特均匀采样定律下的语音分析方法的颠覆。用CS理论中的观测来代替传统的Nyquist采样值，将导致信号特征根本性的变化，进而影响整个语音信号处理各种应用的理论和技术体系。将CS应用于语音信号领域，来探求语音信号处理的各种新方法具有很好的现实意义，而研究语音压缩感知中的各种关键技术是其走向实用的基础。本论文的主要工作和创新如下：
（1）根据语音信号在离散余弦（DCT）基下的稀疏性描述了基于正交基的语音压缩感知的框架。基于此框架，对随机观测矩阵进行选择，并采用基追踪（BP）和正交匹配追踪（OMP）算法对已压缩采样的语音信号进行重构，提出一系列结论：CS观测矩阵的维数（其决定了压缩比）、每帧语音信号选取的帧长的大小、分帧时采用的窗函数及帧移，都对重构性能有影响。
（2）基于语音信号帧内样值间的相关性和冗余域的稀疏性，采用离散余弦转换矩阵及基追踪方法对压缩感知采样语音进行重构时，针对语音稀疏性不够好导致大压缩下采样后重构效果差的缺点，本文提出采用过完备线性预测字典做转换矩阵，用基追踪重构算法对压缩感知采样语音进行高质量重构。该方法预先由训练语音的预测系数聚类构造过完备字典，不需要测试语音的预测系数；基于过完备线性预测字典重构信号性能良好。对利用基追踪重构的语音进行了主客观评价，得出结论：同样的观测数目下，基于过完备线性预测字典，比基于离散余弦变换矩阵压缩感知采样语音重构信噪比高出3~8dB。
（3）针对含白噪语音信号压缩采样后采用基追踪方法重构性能差的问题，在设计更具鲁棒性的重构算法方面提出自适应基追踪去噪方法，该方法根据原含噪信号的信噪比自适应选择重构最佳参数，从而在重构语音的同时提高原信号信噪比。并在此基础上提出自适应基追踪去噪并后置去噪方法。随后又提出前置去噪后基追踪重构方法，针对前置去噪提出了一种基于数据驱动字典和过完备稀疏表示的自适应语音增强方法，含噪语音增强之后再采用基追踪实现含白噪语音的压缩感知。基于这三种方法实现含噪语音信号的压缩感知，并对其性能进行比较。针对观测含有噪声的压缩感知问题，提出采用对观测噪声鲁棒性较好的ABPDN重构算法，当语音观测含有噪声时，采用ABPDN算法重构信号性能优于采用BP算法重构信号性能。
（4）针对语音信号在小波域的压缩感知问题，在系数总长度不超过原信号长度的前提下，推导了Sym小波分解合成的矩阵形式，提出了语音信号多尺度压缩感知（MCS）系统框架。论文进一步分析语音信号在小波基下不同级的稀疏性，提出了一种自适应多尺度压缩感知（AMCS）方法，并将这两种方法应用于语音压缩重构中，对重构语音进行了主客观评价和说话人识别验证，得出结论：基于AMCS的压缩重构，比非自适应的MCS重构语音的性能好。
Speech is the most convenient way for human to communicate with each other. In thedigital era, how to model the speech signal in order to obtain fewer samples without affectingthe quality of the speech, is the research focus in the field of speech signal processing.Compressed sensing (CS) based on the sparsity of the signal is a new theory of linear andnon-adaptive sampling. Compressed sensing shows that the sparser of the signal, the better thecompression performance is. The sparsity or compressibility of the signal is a necessarycondition for achieving good performance of compression reconstruction. As the speech signalis compressible, it can be sampled at the lower rate than the Nyquist sampling rate withoutdistortion, which has brought great convenience to the signal sampling, storage, transmissionand processing. The combination of CS theory and speech signal processing means thesubversion to traditional speech analysis methods based on the Nyquist sampling theory. Withobservations in the CS theory to replace traditional speech sample value is bound to the signalcharacteristics fundamental change, thereby affecting the entire speech signal processing theoryand technology systems of a variety of applications. The CS is used in the field of speech signalto explore new ways of the speech signal processing, which has a good practical significance.Research on the key issues of compressed speech sensing is the foundation to practicalapplication. In this thesis, the main work and innovation are as follows:
(1) According to the sparsity of speech signals in the discrete cosine transform basis (DCT),the CS framework of speech signal is described and CS random observation matrix andreconstruction algorithm are selected firstly, and then Via basis pursuit (BP) and orthogonalmatching pursuit (OMP), it is demonstrated that the performance of reconstruction is correlatedwith the dimensions of measurement matrix, the length of frames, the shift of frames and theshape of the window.
(2) Using the correlation of speech signals and the sparsity on the residual, we propose anew algorithm of compressed sensing of speech signals based on overcomplete linear prediction(OLP) dictionary from codebook constructed by the linear prediction coefficients of trainingsignals. The proposed method not only improves the performance of reconstructed speechsignals based on Gaussian measurement matrix and basis pursuit, but also does not need to know prediction coefficients of testing signals. We compare OLP with discrete cosine transform(DCT) by applying both methods to compressed speech sensing, and the reconstructed speechsignal is evaluated by the objective and subjective evaluations. The experimental results showthat the performance of compressed speech signal sensing based on OLP is3~8dB higher thanDCT with the same number of measurements.
(3) To deal with the problem that the reconstruction performance of compressed sensing ofspeech reconstructed by basis pursuit (BP) is degraded by white Gaussian noise interference, anadaptive basis pursuit de-noising (ABPDN) method is proposed for compressed sensing of noisyspeech. This method adaptively selects the prime regularization parameter according to the SNRof original speech signal and enhancement is achieved as it is applied to compressed sensing ofnoisy speech. And then an adaptive basis pursuit denoising tracked post-denoising method is putforward. Finally, pre-denoised tracked reconstruction method is proposed, which employs anadaptive speech enhancement method based on overcompletely sparse representation in adata-driven dictionary and basis pursuit. The performances of the three methods by the objectiveand subjective evaluations are compared. For compressed speech sensing of the measurementwith noise, an adaptive basis pursuit de-noising method is proposed. The reconstructionperformance of speech signal based on ABPDN is superior to BP.
(4) For compressed sensing of the speech signal in the wavelet domain, a matrix form ofSym wavelet decomposition and synthesis is deduced, keeping the length of the coefficient nomore than the length of original speech signals, and then we propose a framework of speechmultiscale compressed sensing (MCS) and an adaptive multiscale compressed sensing (AMCS)method by analyzing sparsity of different wavelet levels of speech signals.We compare AMCSwith MCS by applying both methods to speech compression and reconstruction, and thereconstructed speech signal evaluated by the objective and subjective evaluation is applied tospeaker recognition. The experimental results show that the reconstruction performance ofspeech signal based on AMCS is superior to MCS.
（1）根据语音信号在离散余弦（DCT）基下的稀疏性描述了基于正交基的语音压缩感知的框架。基于此框架，对随机观测矩阵进行选择，并采用基追踪（BP）和正交匹配追踪（OMP）算法对已压缩采样的语音信号进行重构，提出一系列结论：CS观测矩阵的维数（其决定了压缩比）、每帧语音信号选取的帧长的大小、分帧时采用的窗函数及帧移，都对重构性能有影响。
（2）基于语音信号帧内样值间的相关性和冗余域的稀疏性，采用离散余弦转换矩阵及基追踪方法对压缩感知采样语音进行重构时，针对语音稀疏性不够好导致大压缩下采样后重构效果差的缺点，本文提出采用过完备线性预测字典做转换矩阵，用基追踪重构算法对压缩感知采样语音进行高质量重构。该方法预先由训练语音的预测系数聚类构造过完备字典，不需要测试语音的预测系数；基于过完备线性预测字典重构信号性能良好。对利用基追踪重构的语音进行了主客观评价，得出结论：同样的观测数目下，基于过完备线性预测字典，比基于离散余弦变换矩阵压缩感知采样语音重构信噪比高出3~8dB。
（3）针对含白噪语音信号压缩采样后采用基追踪方法重构性能差的问题，在设计更具鲁棒性的重构算法方面提出自适应基追踪去噪方法，该方法根据原含噪信号的信噪比自适应选择重构最佳参数，从而在重构语音的同时提高原信号信噪比。并在此基础上提出自适应基追踪去噪并后置去噪方法。随后又提出前置去噪后基追踪重构方法，针对前置去噪提出了一种基于数据驱动字典和过完备稀疏表示的自适应语音增强方法，含噪语音增强之后再采用基追踪实现含白噪语音的压缩感知。基于这三种方法实现含噪语音信号的压缩感知，并对其性能进行比较。针对观测含有噪声的压缩感知问题，提出采用对观测噪声鲁棒性较好的ABPDN重构算法，当语音观测含有噪声时，采用ABPDN算法重构信号性能优于采用BP算法重构信号性能。
（4）针对语音信号在小波域的压缩感知问题，在系数总长度不超过原信号长度的前提下，推导了Sym小波分解合成的矩阵形式，提出了语音信号多尺度压缩感知（MCS）系统框架。论文进一步分析语音信号在小波基下不同级的稀疏性，提出了一种自适应多尺度压缩感知（AMCS）方法，并将这两种方法应用于语音压缩重构中，对重构语音进行了主客观评价和说话人识别验证，得出结论：基于AMCS的压缩重构，比非自适应的MCS重构语音的性能好。
Speech is the most convenient way for human to communicate with each other. In thedigital era, how to model the speech signal in order to obtain fewer samples without affectingthe quality of the speech, is the research focus in the field of speech signal processing.Compressed sensing (CS) based on the sparsity of the signal is a new theory of linear andnon-adaptive sampling. Compressed sensing shows that the sparser of the signal, the better thecompression performance is. The sparsity or compressibility of the signal is a necessarycondition for achieving good performance of compression reconstruction. As the speech signalis compressible, it can be sampled at the lower rate than the Nyquist sampling rate withoutdistortion, which has brought great convenience to the signal sampling, storage, transmissionand processing. The combination of CS theory and speech signal processing means thesubversion to traditional speech analysis methods based on the Nyquist sampling theory. Withobservations in the CS theory to replace traditional speech sample value is bound to the signalcharacteristics fundamental change, thereby affecting the entire speech signal processing theoryand technology systems of a variety of applications. The CS is used in the field of speech signalto explore new ways of the speech signal processing, which has a good practical significance.Research on the key issues of compressed speech sensing is the foundation to practicalapplication. In this thesis, the main work and innovation are as follows:
(1) According to the sparsity of speech signals in the discrete cosine transform basis (DCT),the CS framework of speech signal is described and CS random observation matrix andreconstruction algorithm are selected firstly, and then Via basis pursuit (BP) and orthogonalmatching pursuit (OMP), it is demonstrated that the performance of reconstruction is correlatedwith the dimensions of measurement matrix, the length of frames, the shift of frames and theshape of the window.
(2) Using the correlation of speech signals and the sparsity on the residual, we propose anew algorithm of compressed sensing of speech signals based on overcomplete linear prediction(OLP) dictionary from codebook constructed by the linear prediction coefficients of trainingsignals. The proposed method not only improves the performance of reconstructed speechsignals based on Gaussian measurement matrix and basis pursuit, but also does not need to know prediction coefficients of testing signals. We compare OLP with discrete cosine transform(DCT) by applying both methods to compressed speech sensing, and the reconstructed speechsignal is evaluated by the objective and subjective evaluations. The experimental results showthat the performance of compressed speech signal sensing based on OLP is3~8dB higher thanDCT with the same number of measurements.
(3) To deal with the problem that the reconstruction performance of compressed sensing ofspeech reconstructed by basis pursuit (BP) is degraded by white Gaussian noise interference, anadaptive basis pursuit de-noising (ABPDN) method is proposed for compressed sensing of noisyspeech. This method adaptively selects the prime regularization parameter according to the SNRof original speech signal and enhancement is achieved as it is applied to compressed sensing ofnoisy speech. And then an adaptive basis pursuit denoising tracked post-denoising method is putforward. Finally, pre-denoised tracked reconstruction method is proposed, which employs anadaptive speech enhancement method based on overcompletely sparse representation in adata-driven dictionary and basis pursuit. The performances of the three methods by the objectiveand subjective evaluations are compared. For compressed speech sensing of the measurementwith noise, an adaptive basis pursuit de-noising method is proposed. The reconstructionperformance of speech signal based on ABPDN is superior to BP.
(4) For compressed sensing of the speech signal in the wavelet domain, a matrix form ofSym wavelet decomposition and synthesis is deduced, keeping the length of the coefficient nomore than the length of original speech signals, and then we propose a framework of speechmultiscale compressed sensing (MCS) and an adaptive multiscale compressed sensing (AMCS)method by analyzing sparsity of different wavelet levels of speech signals.We compare AMCSwith MCS by applying both methods to speech compression and reconstruction, and thereconstructed speech signal evaluated by the objective and subjective evaluation is applied tospeaker recognition. The experimental results show that the reconstruction performance ofspeech signal based on AMCS is superior to MCS.
引文
[1] Donoho D L. Compressed sensing [J]. IEEE Transactions on Information Theory.2006,52(4):1289-1306.
[2] Baraniuk R G. Compressive sensing [J]. IEEE Signal Processing Magazine.2007,24(4):118-120.
[3] Tsaig Y, Donoho D L. Extensions of compressed sensing [J]. Signal Processing.2006,86(3):549-571.
[4] Candes E, Braun N, Wakin M. Sparse signal and image recovery from compressive samples[C]. Arlington, VA, United states: Inst. of Elec. and Elec. Eng. Computer Society,2007.
[5] Candes E J, Wakin M B. An introduction to compressive sampling: A sensing/samplingparadigm that goes against the common knowledge in data acquisition [J]. IEEE SignalProcessing Magazine.2008,25(2):21-30.
[6] Jin J, Gu Y, Mei S. An introduction to compressive sampling and its applications [J]. DianziYu Xinxi Xuebao/Journal of Electronics and Information Technology.2010,32(2):470-475.
[7] Candes E J, Romberg J, Tao T. Robust uncertainty principles: Exact signal reconstructionfrom highly incomplete frequency information [J]. IEEE Transactions on Information Theory.2006,52(2):489-509.
[8] Calderbank R, Howard S, Jafarpour S. Construction of a large class of deterministic sensingmatrices that satisfy a statistical isometry property [J]. IEEE Journal on Selected Topics inSignal Processing.2010,4(2):358-374.
[9] Rauhut H, Schnass K, Vandergheynst P. Compressed sensing and redundant dictionaries [J].IEEE Transactions on Information Theory.2008,54(5):2210-2219.
[10] Candes E J, Eldar Y C, Needell D, et al. Compressed sensing with coherent and redundantdictionaries[J]. Applied and Computational Harmonic Analysis,2011,31(1):59-73.
[11] Duarte M F, Sarvotham S, Baron D, et al. Distributed compressed sensing of jointly sparsesignals[C]. Pacific Grove, CA, United states: Inst. of Elec. and Elec. Eng. Computer Society,2005.
[12] Ji S, Xue Y, Carin L. Bayesian compressive sensing [J]. IEEE Transactions on SignalProcessing.2008,56(6):2346-2356.
[13] Laska J N, Wen Z W, Yin W T, Baraniuk R G. Trust, but verify: Fast and accurate signalrecovery from1-Bit compressive measurements [J]. IEEE Transactions on Signal Processing.2011,59(11):5289-5301.
[14] Baraniuk R G，Cevher,V，Duarte M F，Hegde C. Model-based compressive sensing [J].IEEETransactions on Information Theory.2010,56(4):1982-2001
[15] Duarte M F, Baraniuk R G. Spectral Compressive Sensing. Preprint submitted to Appl.Comput. Harmon. Anal. August1,2012.
[16] Peyré G. Best Basis Compressed Sensing [J]. IEEE Transactions on Signal Processing.2010,58(5):2613-2622.
[17] Levin A, Fergus R, Durand F, Freeman B. Image and depth from a conventional camera with acoded aperture[C]. San Diego, CA, United states: Association for Computing Machinery,2007.
[18] Sheikh M A, Milenkovic O, Baraniuk R G. Designing compressive sensing DNA microarrays
[C]. St. Thomas, United states virgin islands: Inst. of Elec. and Elec. Eng. Computer Society,2007.
[19] Dai W, Milenkovic O, Sheikh M A, et al. Probe design for compressive sensing DNAmicroarrays [C]. Philadelphia, PA, United states: Inst. of Elec. and Elec. Eng. ComputerSociety,2008.
[20] Ma J W. Improved Iterative Curvelet Thresholding for Compressed Sensing and Measurement[J]. IEEE Transactions on Instrumentation and Measurement.2011,60(1):126-136.
[21] Mallat S G, Zhang Z F. Matching pursuits with time-frequency dictionaries [J]. IEEETransactions on Signal Processing.1993,41(12):3397-3415.
[22] Mallat S G, Zhang Z F. Adaptive time-frequency transform [C]. IEEE International Conferenceon Acoustics, Speech and Signal Processing.1993, v3, p111.241-243.
[23] Davis G, Mallat S G, Zhang Z F. Adaptive time-frequency decompositions [J]. OpticalEngineering.1994,33(7):2183-2191.
[24] Davis G, Mallat S G, Zhang Z F. Adaptive time-frequency decompositions with matchingpursuit [C]. Orlando, FL, United states: Publ by Society of Photo-Optical InstrumentationEngineers,1994.
[25] Zhang X, Durand L, Senhadji L, et al. Application of the matching pursuit method for theanalysis and synthesis of the phonocardiogram [C]. Amsterdam, Neth: IEEE,1996.
[26] Neff R, Zakhor A. Very low bit-rate video coding based on matching pursuits [J]. IEEETransactions on Circuits and Systems for Video Technology.1997,7(1):158-171.
[27] Peng C K, Huang C L, Huang W L. Very-low-bit rate coding using matching pursuit andcodebook adaptation [C]. Vancouver, BC, Canada: Institute of Electrical and ElectronicsEngineers Computer Society,2000.
[28] Chen S S, Donoho D L, Saunders M A. Atomic decomposition by basis pursuit [J]. SIAMReview.2001,43(1):129-159.
[29] Shen Y, Ai H M, Kuo C C J. Matching pursuit decomposition of speech signals for compactrepresentation [C]. Boston, MA, United states: SPIE,2002.
[30] Daubechies I. Time-frequency localization operators: A geometric phase space approach [J].IEEE Transactions on Information Theory.1988,34(4):605-612.
[31] Coifman R R, Wickerhauser M V. Entropy-based algorithms for best basis selection [J]. IEEETransactions on Information Theory.1992,38(2):713-718.
[32] Aroutchelvame S M, Raahemifar K. An efficient architecture for entropy-based best-basisalgorithm [C]. Atlanta, GA, United states: IEEE Computer Society,2006.
[33] Donoho D L, Huo X. Uncertainty principles and ideal atomic decomposition [J]. IEEETransactions on Information Theory.2001,47(7):2845-2862.
[34]郭海燕.基于稀疏分解的单通道混合语音分离算法研究[D].南京:南京邮电大学博士论文,2010.
[35] Ni X, Li Q, Meng F, et al. Image denoising method based on curvelet transform and totalvariation [J]. Guangxue Xuebao/Acta Optica Sinica.2009,29(9):2390-2394.
[36] Berg A P, Mikhael W B. Survey of mixed transform techniques for speech and image coding[J]. Proceedings-IEEE International Symposium on Circuits and Systems.1999,4:106-109.
[37] Cotter S F, Rao B D. Sparse channel estimation via matching pursuit with application toequalization [J]. IEEE Transactions on Communications.2002,50(3):374-377.
[38] Elad M, Bruckstein A M. A generalized uncertainty principle and sparse representation in pairsof bases [J]. IEEE Transactions on Information Theory.2002,48(9):2558-2567.
[39] Feuer A, Nemirovski A. On sparse representation in pairs of bases [J]. IEEE Transactions onInformation Theory.2003,49(6):1579-1581.
[40] Malioutov D M, Cetin M, Willsky A S. Optimal sparse representations in generalovercomplete bases [C]. Montreal, Que, Canada: Institute of Electrical and ElectronicsEngineers Inc.,2004.
[41] Adelino R and Silva F D. Atomic decomposition with evolutionary pursuit [J]. Digital SignalProcessing: A Review Journal.2003,13(2):317-337.
[42] Granai L, Vandergheynst P. Sparse decomposition over multi-component redundantdictionaries [C]. Siena, Italy: Institute of Electrical and Electronics Engineers Inc.,2004.
[43] Monaci G, Jost P, Vandergheynst P. Image compression with learnt tree-structured dictionaries
[C]. Siena, Italy: Institute of Electrical and Electronics Engineers Inc.,2004.
[44] Monaci G, Escoda O D, Vandergheynst P. Analysis of multimodal signals using redundantrepresentations [C]. Genova, Italy: Institute of Electrical and Electronics Engineers ComputerSociety,2005.
[45] Yang R, Ren M. Learning overcomplete dictionaries with application to image denoising [C].Chengdu, China: IEEE Computer Society,2010.
[46]刘丹华，石光明，周佳社.一种冗余字典下的信号稀疏分解新方法[J].西安电子科技大学学报.2008,35(02):228:232.
[47] Tai S L. Image representation using2D Gabor wavelets [J]. IEEE Transactions on PatternAnalysis and Machine Intelligence.1996,18(10):959-971.
[48] Aharon M, Elad M, Bruckstein A. K-SVD: An algorithm for designing overcompletedictionaries for sparse representation [J]. IEEE Transactions on Signal Processing.2006,54(11):4311-4322.
[49] Zhang Q, Li B. Discriminative K-SVD for dictionary learning in face recognition [C]. SanFrancisco, CA, United states: IEEE Computer Society,2010.
[50] Gowreesunker B V, Tewfik A H. Learning sparse representation using iterative subspaceidentification [J]. IEEE Transactions on Signal Processing.2010,58(6):3055-3065.
[51] Zhang C M, Yin Z K, Chen X D, Xiao M X. Signal overcomplete representation and sparsedecomposition based on redundant dictionaries [J]. Chinese Science Bulletin.2005,50(23):2672–2677.
[52] Lesage S, Gribonval R, Bimbot F and Benaroya L. Learning Unions of Orthonormal Baseswith Thresholded Singular Value Decomposition [C]. Proceedings.(ICASSP '05). IEEEInternational Conference on Acoustics, Speech, and Signal Processing,2005., Philadelphia,Pennsylvania, USA:, pp.293-296.
[53] Ravelli E, Richard G and Daudet L.Union of MDCT Bases for Audio Coding [J]. IEEETransactions on Audio, Speech, and Language Processing.2008,16(8):1361-1372.
[54] Yaghoobi M, Daudet L and Davies M E. Parametric Dictionary Design for Sparse Coding [J].IEEE Transactions on Signal Processing,2009,57(12):4800-4810.
[55] Tropp J. Greed is Good: Algorithmic Results for Sparse Approximation [J]. IEEE Transactionson Information Theory,2004,50(10):2231-2242.
[56] Gilbert A, Muthukrishnan S and Strauss M. Approximation of functions over redundantdictionaries using coherence [C]. Proc.14th Annu. ACM-SIAM Symp. on Discrete algorithms,Baltimore, MD,2003.
[57] Tropp J, Dhillon I, Heath R and Strohmer T. Designing structured tight frames via analternating projection method [J]. IEEE Transactions on Information Theory.2005,51(1):188-209.
[58] Sustik M, Tropp J, Dhillon I and Heath R. On the existence of equiangular tight frames [J].Linear Algebra and Its Applications,2007,426(2-3):619–635.
[59] Yaghoobi M, Daudet L and Davies M E. Structured and incoherent parametric dictionarydesign [C].2010IEEE International Conference on Acoustics, Speech and Signal Processing,Dallas, TX, USA:2010, pp.5486-5489.
[60] Engan K, Skretting K and Hus y J H. A family of iterative LS-based dictionary learningalgorithms, ILS-DLA, for sparse signal representation [J]. Digital Signal Process.2007,17(1):32–49.
[61] Rubinstein R, Zibulevsky M and Elad M. Efficient implementation of the k-svd algorithmusing batch orthogonal matching pursuit [R]. Technical Report CS-2008-08, Technion,2008.
[62] Skretting K and Engan K. Recursive Least Squares Dictionary Learning Algorithm [J]. IEEETransactions on Signal Processing,2010,58(4):2121-2130.
[63] Candes E, Romberg J. Sparsity and incoherence in compressive sampling [J]. Inverse Problems.2007,23(3):969-985.
[64] Candes E J, Tao T. Decoding by linear programming [J]. IEEE Transactions on InformationTheory.2005,51(12):4203-4215.
[65]Candes E J, Tao T. Near-optimal signal recovery from random projections: Universal encodingstrategies?[J].IEEE Transactions on Information Theory,52(12),2006:5406-5425.
[66] Taghavi M H, Siegel P H. Adaptive linear programming decoding [C]. Seattle, WA, Unitedstates: Institute of Electrical and Electronics Engineers Inc.,2006.
[67] Taghavi M H, Shokrollahi A, Siegel P H. Efficient implementation of linear programmingdecoding [C]. Monticello, IL, United states: Inst. of Elec. and Elec. Eng. Computer Society,2008.
[68] Taghavi M H, Siegel P H. Adaptive methods for linear programming decoding [J]. IEEETransactions on Information Theory.2008,54(12):5396-5410.
[69] Yang K, Wang X, Feldman J. A new linear programming approach to decoding linear blockcodes [J]. IEEE Transactions on Information Theory.2008,54(3):1061-1072.
[70] Rosnes E. On linear programming decoding on a quantized additive white Gaussian noisechannel [C]. Cirencester, United kingdom: Springer Verlag,2009.
[71] Fang H, Zhang Q, Wei S. Method of image reconstruction based on sub-Gaussian randomprojection [J]. Jisuanji Yanjiu yu Fazhan/Computer Research and Development.2008,45(8):1402-1407.
[72] Gilbert A C, Guha S, Indyk P, et al. Near-optimal sparse Fourier representations via sampling
[C]. Montreal, Que., Canada: Association for Computing Machinery,2002.
[73] Bajwa W U, Haupt J D, Raz G M, et al. Toeplitz-structured compressed sensing matrices [C].Madison, WI, United states: Inst. of Elec. and Elec. Eng. Computer Society,2007.
[74] Yu L, Barbot J P, Zheng G, et al. Toeplitz-structured chaotic sensing matrix for compressivesensing [C]. Newcastle upon Tyne, United kingdom: IEEE Computer Society,2010.
[75] Sebert F, Zou Y M, Ying L. Toeplitz block matrices in compressed sensing and theirapplications in imaging [C]. Shenzhen, China: Inst. of Elec. and Elec. Eng. Computer Society,2008.
[76] Do T T, Tran T D, Gan L. Fast compressive sampling with structurally random matrices [C].Las Vegas, NV, United states: Institute of Electrical and Electronics Engineers Inc.,2008.
[77] Wang M. Raw SAR data compression by structurally random matrix based compressivesampling [C]. Xian, China: IEEE Computer Society,2009.
[78] Elad M. Optimized projections for compressed sensing [J]. IEEE Transactions on SignalProcessing.2007,55(12):5695-5702.
[79] Xu J, Pi Y, Cao Z. Optimized projection matrix for compressive sensing [J]. Eurasip Journalon Advances in Signal Processing.2010.
[80] Wang Z, Arce G R, Paredes J L. Colored random projections for compressed sensing [C].Honolulu, HI, United states: Institute of Electrical and Electronics Engineers Inc.,2007.
[81] Babacan S D, Molina R, Katsaggelos A K. Fast Bayesian compressive sensing using Laplacepriors [C]. Taipei, Taiwan: Institute of Electrical and Electronics Engineers Inc.,2009.
[82] Babacan S D, Molina R, Katsaggelos A K. Bayesian compressive sensing using laplace priors[J]. IEEE Transactions on Image Processing.2010,19(1):53-63.
[83] Tzagkarakis G, Tsakalides P. Bayesian compressed sensing imaging using a gaussian scalemixture [C]. Dallas, TX, United states: Institute of Electrical and Electronics Engineers Inc.,2010.
[84]石光明，刘丹华，高大化，等.压缩感知理论及其研究进展[J].电子学报.2009,37(5):1070-1081.
[85] Tropp J A, Gilbert A C. Signal recovery from random measurements via orthogonal matchingpursuit [J]. IEEE Transactions on Information Theory.2007,53(12):4655-4666.
[86] Donoho D L, Tsaig Y, Drori I,etc. Sparse solution of underdetermined linear equations bystagewise rthogonal matching pursuit [J]. IEEE Transactions on Information Theory,2012,58(2):1094-1121.
[87] Needell D, Vershynin R. Signal recovery from incomplete and inaccurate measurements viaregularized orthogonal matching pursuit [J]. IEEE Journal on Selected Topics in SignalProcessing.2010,4(2):310-316.
[88] Fan N. Super-Resolution using Regularized Orthogonal Matching Pursuit based on compressedsensing theory in the wavelet domain [C]. Tianjin, China: IEEE Computer Society,2009.
[89] Needell D, Tropp J A. CoSaMP: Iterative signal recovery from incomplete and inaccuratesamples [J]. Applied and Computation Harmonic Analysis,2009,26:301-321.
[90] Dai W, Milenkovic O. Subspace pursuit for compressive sensing signal reconstruction [J].IEEE Transactions on Information Theory,2009,55(5):2230-2249.
[91] Do T T, Gan L, Nguyen N. etc. Sparsity adaptive matching pursuit algorithm for practicalcompressed sensing [C]. Asilomar Conference on Signals, Systems, and Computers, PacificGrove, California,2008,10:581-587.
[92] Candes E, Braun N, Wakin M. Sparse signal and image recovery from compressive samples
[C]. Arlington, VA, United states: Inst. of Elec. and Elec. Eng. Computer Society,2007.
[93] Saligrama V, Manqi Z. Thresholded basis pursuit: LP algorithm for oder-wise optimal supportrecovery for sparse and approximately sparse signals from noisy random measurements [J].IEEE Transactions on Information Theory.2011,57(3):1567-1586.
[94] Kim S, Koh K, Lustig M, et al. An interior-point method for large-scale1-regularized leastsquares [J]. IEEE Journal on Selected Topics in Signal Processing.2007,1(4):606-617.
[95] Koh K, Kim S, Boyd S. An efficient method, for large-scale l1-regularized convex lossminimization [C]. San Diego, CA, United states: Inst. of Elec. and Elec. Eng. ComputerSociety,2007.
[96] Figueiredo M A T, Nowak R D, Wright S J. Gradient projection for sparse reconstruction:Application to compressed sensing and other inverse problems [J]. IEEE Journal on SelectedTopics in Signal Processing.2007,1(4):586-597.
[97] Harmany Z, Thompson D, Willett R, et al. Gradient projection for linearly constrained convexoptimization in sparse signal recovery [C]. Hong Kong, Hong kong: IEEE Computer Society,2010.
[98] Jin J, Gu Y, Mei S. A stochastic gradient approach on compressive sensing signalreconstruction based on adaptive filtering framework [J]. IEEE Journal on Selected Topics inSignal Processing.2010,4(2):409-420.
[99] Broughton R L, Coope I D, Renaud P F, et al. A box constrained gradient projection algorithmfor compressed sensing [J]. Signal Processing.2011,91(8):1985-1992.
[100] Fornasier M, Pitolli F. Adaptive iterative thresholding algorithms formagnetoencephalography(MEG)[J]. Journal of Computational and Applied Mathematics.2008,221(2):386-395.
[101] Fornasier M, Rauhut H. Iterative thresholding algorithms [J]. Applied and ComputationalHarmonic Analysis.2008,25(2):187-208.
[102] Bredies K. An iterative thresholding-like algorithm for inverse problems with sparsityconstraints in Banach space [J]. Journal of Inverse and Ill-Posed Problems.2009,17(1):19-26.
[103] Khoramian S. An iterative thresholding algorithm for linear inverse problems withmulti-constraints and its applications [J]. Applied and Computational Harmonic Analysis.2012,32(1):109-130.
[104] Blumensath T, Yaghoobi M, Davies M E. Iterative hard thresholding and L0regularisation
[C]. Honolulu, HI, United states: Institute of Electrical and Electronics Engineers Inc.,2007.
[105] Gribonval R, Nielsen M. Highly sparse representations from dictionaries are unique andindependent of the sparseness measure [J]. Applied and Computational Harmonic Analysis.2007,22(3):335-355.
[106] Chartrand R. Exact reconstruction of sparse signals via nonconvex minimization [J]. IEEESignal Processing Letters.2007,14(10):707-710.
[107] Gilbert A C, Muthukrishnan S, Strauss M. Improved time bounds for near-optimal sparseFourier representations [C]. San Diego, CA, United states: SPIE,2005.
[108] Gilbert A C, Strauss M J, Tropp J A, et al. One sketch for all: Fast algorithms for compressedsensing [C]. San Diego, CA, United states: Association for Computing Machinery,2007.
[109]李树涛,魏丹.压缩传感综述[J].自动化学报,2009,35(11):1369-1377.
[110] Tropp J A. Greed is good: Algorithmic results for sparse approximation [J]. IEEETransactions on Information Theory.2004,50(10):2231-2242.
[111] Do T T, Gan L, Nguyen N, et al. Sparsity adaptive matching pursuit algorithm for practicalcompressed sensing [C]. Pacific Grove, CA, United states: IEEE Computer Society,2008.
[112] Sun G L, Zhang Y, Lv L Q, et al. Research on iterative thresholding matching pursuit basedon adaptive sparsity [J]. Journal of Computational Information Systems.2011,7(1):34-41.
[113] Candès E, Tao T. The Dantzig selector: Statistical estimation when p is much larger than n [J].Annals of Statistics,2007,35(6):2313-2351.
[114]Boyd S, Vandenberghe L. convex optimization [M]. Cambridge: Cambridge University Press,2004.
[115] Figueiredo M A T, Nowak R D, Wright S J. Gradient projection for sparse reconstruction:Application to compressed sensing and other inverse problems [J]. IEEE Journal on SelectedTopics in Signal Processing.2007,1(4):586-597.
[116] Harmany Z, Thompson D, Willett R, et al. Gradient projection for linearly constrained convexoptimization in sparse signal recovery [C]. Hong Kong, Hong kong: IEEE Computer Society,2010.
[117]郭海燕，王天荆，杨震. DCT域的语音信号自适应压缩感知[J].仪器仪表学报.2010,31(6):1262-1268.
[118]孙林慧，杨震，叶蕾.基于自适应多尺度压缩感知的语音压缩与重构[J].电子学报.2011,39(1):40-45.
[119]郭海燕，杨震.基于近似KLT域的语音信号压缩感知[J].电子与信息学报.2009,31(12):2948-2952.
[120] Xu T T, Yang Z, Shao X. Adaptive compressed sensing of speech signal based on data-drivendictionary [C].200915th Asia-Pacific Conference on Communications, APCC2009.2009,257-260.
[121] Sreenivas T V, Kleijn W B. Compressive sensing for sparsely excited speech signals [C].Acoustics, Speech and Signal Processing,2009. ICASSP2009. IEEE InternationalConference on,2009:4125–4128.
[122]季云云，杨震.基于自相关观测的语音信号压缩感知[J].信号处理.2011,127(2):207-214.
[123] Gemmeke J F, Hamme H V, Cranen B, et al. Compressive Sensing for Missing DataImputation in Noise Robust Speech Recognition [J]. Selected Topics in Signal Processing,IEEE Journal of.2010,4(2):272-287.
[124] Gemmeke J F, Cranen B. Using sparse representations for missing data imputation in noiserobust speech recognition [C]. European Signal Processing Conf.(EUSIPCO), Lausanne，Switzerland，August2008.
[125] Giacobello D, Christensen M G, Murthi M N, et al. Retrieving sparse patterns using acompressed sensing framework: applications to speech coding based on sparse linearprediction [J]. Signal Processing Letters, IEEE.2010,17(1):103-106.
[126]叶蕾，杨震，郭海燕.基于小波变换和压缩感知的低速率语音编码方案[J].仪器仪表学报.2010,31(7):1569-1575.
[127] Goyal V K, Fletcher A K, Rangan S. Compressive Sampling and Lossy Compression [J].Signal Processing Magazine, IEEE.2008,25(2):48-56.
[128] Griffin A, Hirvonen T, Tzagkarakis C, et al. Single-channel and Multi-channel SinusoidalAudio Coding Using Compressed Sensing [J]. Audio, Speech, and Language Processing,IEEE Transactions on.2011,19(5):1382-1395.
[129] Griffin A, Hirvonen T, Mouchtaris A, et al. Encoding the sinusoidal model of an audio signalusing compressed sensing [C].2009IEEE International Conference on Multimedia and Expo(ICME).2009:153-156.
[130] Xu T, Yang Z, Shao X. Novel speech secure communication system based on informationhiding and compressed sensing [C]. Porto, Portugal: IEEE Computer Society,2009.
[131] Ma H, Xiong J, Xu Y, et al. Packet loss concealment for speech transmission based oncompressed sensing [C]. IET International Communication Conference on Wireless Mobileand Computing,2009:327-330.
[132] Xu T, Wang W. A block-based compressed sensing method for underdetermined blind speechseparation incorporating binary mask [C]. Dallas, TX, United states: Institute of Electricaland Electronics Engineers Inc.,2010.
[133] Griffin A, Tsakalides P. Compressed sensing of audio signals using multiple sensors [C]. inProc.16th European Signal Processing Conference (EUSIPCO '08)，Lausanne，Switzerland，2008.
[134] Blumensath T, Davies M E.Gradient pursuits [J]. IEEE Trans. on Signal Processing，2008，56(6):2370–2382.
[135] Vaidyanathan P P. Theory Of Linear Prediction [M]. San Rafael, United States: Morgan&Claypool Publishers,2007.
[136] Benesty J, Makino S, Chen J. Speech enhancement [M]. Berlin, Germany: Springer,2005.
[137] Tashev I, Lovitt A, Acero A. Unified Framework for Single Channel Speech Enhancement [C].IEEE Pacific Rim Conference on Communications, Computers and Signal Processing,2009:883-888.
[138] Hao J, Attias H, Nagarajan S, et al. Speech enhancement, gain, and noise spectrum adaptationusing approximate bayesian estimation [J]. IEEE Transactions on Audio, Speech andLanguage Processing.2009,17(1):24-37.
[139] Yoshioka T, Nakatani T, Okuno H G. Noisy speech enhancement based on prior knowledgeabout spectral envelope and harmonic structure [C].2010IEEE International Conference onAcoustics Speech and Signal Processing (ICASSP),2010:4270-4273.
[140] Tantibundhit C, Pernkopf F, Kubin G. Joint time–frequency segmentation algorithm fortransient speech decomposition and speech enhancement [J]. IEEE Transactions on Audio,Speech, and Language Processing,2010,18(6):1417-1428.
[141] Mallat S. A Wavelet Tour of Signal Processing [M].2nd ed. New York: Academic Press,1998.
[142] Hansen P C, O’Leary D P, The use of the L-curve in the regularization of discrete ill-posedproblems [J]. SIAM Journal on Scientific Computing,1993,14(6):1487–1503.
[143]叶蕾, et al.基于压缩感知观测序列倒谱距离的语音端点检测算法[J].信号处理,2011,27(1):67-72.
[144] Coifman R R and Donoho D L. Translation-Invariant De-noising [J]. New York: Springer-Verlag,1995:125-150.
[145] Donoho D, Johnstone I M. Ideal spatial adaptation by wavelet shrinkage [J]. Biomet rika,1994,81(3):425-455.
[146] Zhang L H, Rong G F. A kind of modified speech enhancement algorithm based on waveletpackage transformation [C]. Proceedings of the2008International Conference on WaveletAnalysis and Pattern Recognition, Hong Kong,30-31Aug.2008:421-425.
[147]李映,等.基于信号稀疏表示的形态成分分析:进展和展望[J].电子学报,2009,37(1):146-152.
[148]王大凯,等.小波分析及其在信号处理中的应用[M].北京:电子工业出版社,2006.
[149]鲍长春.高质量的4kb/s散布脉冲CELP语音编码算法[J].电子学报,2003,31(2):1-5.
[2] Baraniuk R G. Compressive sensing [J]. IEEE Signal Processing Magazine.2007,24(4):118-120.
[3] Tsaig Y, Donoho D L. Extensions of compressed sensing [J]. Signal Processing.2006,86(3):549-571.
[4] Candes E, Braun N, Wakin M. Sparse signal and image recovery from compressive samples[C]. Arlington, VA, United states: Inst. of Elec. and Elec. Eng. Computer Society,2007.
[5] Candes E J, Wakin M B. An introduction to compressive sampling: A sensing/samplingparadigm that goes against the common knowledge in data acquisition [J]. IEEE SignalProcessing Magazine.2008,25(2):21-30.
[6] Jin J, Gu Y, Mei S. An introduction to compressive sampling and its applications [J]. DianziYu Xinxi Xuebao/Journal of Electronics and Information Technology.2010,32(2):470-475.
[7] Candes E J, Romberg J, Tao T. Robust uncertainty principles: Exact signal reconstructionfrom highly incomplete frequency information [J]. IEEE Transactions on Information Theory.2006,52(2):489-509.
[8] Calderbank R, Howard S, Jafarpour S. Construction of a large class of deterministic sensingmatrices that satisfy a statistical isometry property [J]. IEEE Journal on Selected Topics inSignal Processing.2010,4(2):358-374.
[9] Rauhut H, Schnass K, Vandergheynst P. Compressed sensing and redundant dictionaries [J].IEEE Transactions on Information Theory.2008,54(5):2210-2219.
[10] Candes E J, Eldar Y C, Needell D, et al. Compressed sensing with coherent and redundantdictionaries[J]. Applied and Computational Harmonic Analysis,2011,31(1):59-73.
[11] Duarte M F, Sarvotham S, Baron D, et al. Distributed compressed sensing of jointly sparsesignals[C]. Pacific Grove, CA, United states: Inst. of Elec. and Elec. Eng. Computer Society,2005.
[12] Ji S, Xue Y, Carin L. Bayesian compressive sensing [J]. IEEE Transactions on SignalProcessing.2008,56(6):2346-2356.
[13] Laska J N, Wen Z W, Yin W T, Baraniuk R G. Trust, but verify: Fast and accurate signalrecovery from1-Bit compressive measurements [J]. IEEE Transactions on Signal Processing.2011,59(11):5289-5301.
[14] Baraniuk R G，Cevher,V，Duarte M F，Hegde C. Model-based compressive sensing [J].IEEETransactions on Information Theory.2010,56(4):1982-2001
[15] Duarte M F, Baraniuk R G. Spectral Compressive Sensing. Preprint submitted to Appl.Comput. Harmon. Anal. August1,2012.
[16] Peyré G. Best Basis Compressed Sensing [J]. IEEE Transactions on Signal Processing.2010,58(5):2613-2622.
[17] Levin A, Fergus R, Durand F, Freeman B. Image and depth from a conventional camera with acoded aperture[C]. San Diego, CA, United states: Association for Computing Machinery,2007.
[18] Sheikh M A, Milenkovic O, Baraniuk R G. Designing compressive sensing DNA microarrays
[C]. St. Thomas, United states virgin islands: Inst. of Elec. and Elec. Eng. Computer Society,2007.
[19] Dai W, Milenkovic O, Sheikh M A, et al. Probe design for compressive sensing DNAmicroarrays [C]. Philadelphia, PA, United states: Inst. of Elec. and Elec. Eng. ComputerSociety,2008.
[20] Ma J W. Improved Iterative Curvelet Thresholding for Compressed Sensing and Measurement[J]. IEEE Transactions on Instrumentation and Measurement.2011,60(1):126-136.
[21] Mallat S G, Zhang Z F. Matching pursuits with time-frequency dictionaries [J]. IEEETransactions on Signal Processing.1993,41(12):3397-3415.
[22] Mallat S G, Zhang Z F. Adaptive time-frequency transform [C]. IEEE International Conferenceon Acoustics, Speech and Signal Processing.1993, v3, p111.241-243.
[23] Davis G, Mallat S G, Zhang Z F. Adaptive time-frequency decompositions [J]. OpticalEngineering.1994,33(7):2183-2191.
[24] Davis G, Mallat S G, Zhang Z F. Adaptive time-frequency decompositions with matchingpursuit [C]. Orlando, FL, United states: Publ by Society of Photo-Optical InstrumentationEngineers,1994.
[25] Zhang X, Durand L, Senhadji L, et al. Application of the matching pursuit method for theanalysis and synthesis of the phonocardiogram [C]. Amsterdam, Neth: IEEE,1996.
[26] Neff R, Zakhor A. Very low bit-rate video coding based on matching pursuits [J]. IEEETransactions on Circuits and Systems for Video Technology.1997,7(1):158-171.
[27] Peng C K, Huang C L, Huang W L. Very-low-bit rate coding using matching pursuit andcodebook adaptation [C]. Vancouver, BC, Canada: Institute of Electrical and ElectronicsEngineers Computer Society,2000.
[28] Chen S S, Donoho D L, Saunders M A. Atomic decomposition by basis pursuit [J]. SIAMReview.2001,43(1):129-159.
[29] Shen Y, Ai H M, Kuo C C J. Matching pursuit decomposition of speech signals for compactrepresentation [C]. Boston, MA, United states: SPIE,2002.
[30] Daubechies I. Time-frequency localization operators: A geometric phase space approach [J].IEEE Transactions on Information Theory.1988,34(4):605-612.
[31] Coifman R R, Wickerhauser M V. Entropy-based algorithms for best basis selection [J]. IEEETransactions on Information Theory.1992,38(2):713-718.
[32] Aroutchelvame S M, Raahemifar K. An efficient architecture for entropy-based best-basisalgorithm [C]. Atlanta, GA, United states: IEEE Computer Society,2006.
[33] Donoho D L, Huo X. Uncertainty principles and ideal atomic decomposition [J]. IEEETransactions on Information Theory.2001,47(7):2845-2862.
[34]郭海燕.基于稀疏分解的单通道混合语音分离算法研究[D].南京:南京邮电大学博士论文,2010.
[35] Ni X, Li Q, Meng F, et al. Image denoising method based on curvelet transform and totalvariation [J]. Guangxue Xuebao/Acta Optica Sinica.2009,29(9):2390-2394.
[36] Berg A P, Mikhael W B. Survey of mixed transform techniques for speech and image coding[J]. Proceedings-IEEE International Symposium on Circuits and Systems.1999,4:106-109.
[37] Cotter S F, Rao B D. Sparse channel estimation via matching pursuit with application toequalization [J]. IEEE Transactions on Communications.2002,50(3):374-377.
[38] Elad M, Bruckstein A M. A generalized uncertainty principle and sparse representation in pairsof bases [J]. IEEE Transactions on Information Theory.2002,48(9):2558-2567.
[39] Feuer A, Nemirovski A. On sparse representation in pairs of bases [J]. IEEE Transactions onInformation Theory.2003,49(6):1579-1581.
[40] Malioutov D M, Cetin M, Willsky A S. Optimal sparse representations in generalovercomplete bases [C]. Montreal, Que, Canada: Institute of Electrical and ElectronicsEngineers Inc.,2004.
[41] Adelino R and Silva F D. Atomic decomposition with evolutionary pursuit [J]. Digital SignalProcessing: A Review Journal.2003,13(2):317-337.
[42] Granai L, Vandergheynst P. Sparse decomposition over multi-component redundantdictionaries [C]. Siena, Italy: Institute of Electrical and Electronics Engineers Inc.,2004.
[43] Monaci G, Jost P, Vandergheynst P. Image compression with learnt tree-structured dictionaries
[C]. Siena, Italy: Institute of Electrical and Electronics Engineers Inc.,2004.
[44] Monaci G, Escoda O D, Vandergheynst P. Analysis of multimodal signals using redundantrepresentations [C]. Genova, Italy: Institute of Electrical and Electronics Engineers ComputerSociety,2005.
[45] Yang R, Ren M. Learning overcomplete dictionaries with application to image denoising [C].Chengdu, China: IEEE Computer Society,2010.
[46]刘丹华，石光明，周佳社.一种冗余字典下的信号稀疏分解新方法[J].西安电子科技大学学报.2008,35(02):228:232.
[47] Tai S L. Image representation using2D Gabor wavelets [J]. IEEE Transactions on PatternAnalysis and Machine Intelligence.1996,18(10):959-971.
[48] Aharon M, Elad M, Bruckstein A. K-SVD: An algorithm for designing overcompletedictionaries for sparse representation [J]. IEEE Transactions on Signal Processing.2006,54(11):4311-4322.
[49] Zhang Q, Li B. Discriminative K-SVD for dictionary learning in face recognition [C]. SanFrancisco, CA, United states: IEEE Computer Society,2010.
[50] Gowreesunker B V, Tewfik A H. Learning sparse representation using iterative subspaceidentification [J]. IEEE Transactions on Signal Processing.2010,58(6):3055-3065.
[51] Zhang C M, Yin Z K, Chen X D, Xiao M X. Signal overcomplete representation and sparsedecomposition based on redundant dictionaries [J]. Chinese Science Bulletin.2005,50(23):2672–2677.
[52] Lesage S, Gribonval R, Bimbot F and Benaroya L. Learning Unions of Orthonormal Baseswith Thresholded Singular Value Decomposition [C]. Proceedings.(ICASSP '05). IEEEInternational Conference on Acoustics, Speech, and Signal Processing,2005., Philadelphia,Pennsylvania, USA:, pp.293-296.
[53] Ravelli E, Richard G and Daudet L.Union of MDCT Bases for Audio Coding [J]. IEEETransactions on Audio, Speech, and Language Processing.2008,16(8):1361-1372.
[54] Yaghoobi M, Daudet L and Davies M E. Parametric Dictionary Design for Sparse Coding [J].IEEE Transactions on Signal Processing,2009,57(12):4800-4810.
[55] Tropp J. Greed is Good: Algorithmic Results for Sparse Approximation [J]. IEEE Transactionson Information Theory,2004,50(10):2231-2242.
[56] Gilbert A, Muthukrishnan S and Strauss M. Approximation of functions over redundantdictionaries using coherence [C]. Proc.14th Annu. ACM-SIAM Symp. on Discrete algorithms,Baltimore, MD,2003.
[57] Tropp J, Dhillon I, Heath R and Strohmer T. Designing structured tight frames via analternating projection method [J]. IEEE Transactions on Information Theory.2005,51(1):188-209.
[58] Sustik M, Tropp J, Dhillon I and Heath R. On the existence of equiangular tight frames [J].Linear Algebra and Its Applications,2007,426(2-3):619–635.
[59] Yaghoobi M, Daudet L and Davies M E. Structured and incoherent parametric dictionarydesign [C].2010IEEE International Conference on Acoustics, Speech and Signal Processing,Dallas, TX, USA:2010, pp.5486-5489.
[60] Engan K, Skretting K and Hus y J H. A family of iterative LS-based dictionary learningalgorithms, ILS-DLA, for sparse signal representation [J]. Digital Signal Process.2007,17(1):32–49.
[61] Rubinstein R, Zibulevsky M and Elad M. Efficient implementation of the k-svd algorithmusing batch orthogonal matching pursuit [R]. Technical Report CS-2008-08, Technion,2008.
[62] Skretting K and Engan K. Recursive Least Squares Dictionary Learning Algorithm [J]. IEEETransactions on Signal Processing,2010,58(4):2121-2130.
[63] Candes E, Romberg J. Sparsity and incoherence in compressive sampling [J]. Inverse Problems.2007,23(3):969-985.
[64] Candes E J, Tao T. Decoding by linear programming [J]. IEEE Transactions on InformationTheory.2005,51(12):4203-4215.
[65]Candes E J, Tao T. Near-optimal signal recovery from random projections: Universal encodingstrategies?[J].IEEE Transactions on Information Theory,52(12),2006:5406-5425.
[66] Taghavi M H, Siegel P H. Adaptive linear programming decoding [C]. Seattle, WA, Unitedstates: Institute of Electrical and Electronics Engineers Inc.,2006.
[67] Taghavi M H, Shokrollahi A, Siegel P H. Efficient implementation of linear programmingdecoding [C]. Monticello, IL, United states: Inst. of Elec. and Elec. Eng. Computer Society,2008.
[68] Taghavi M H, Siegel P H. Adaptive methods for linear programming decoding [J]. IEEETransactions on Information Theory.2008,54(12):5396-5410.
[69] Yang K, Wang X, Feldman J. A new linear programming approach to decoding linear blockcodes [J]. IEEE Transactions on Information Theory.2008,54(3):1061-1072.
[70] Rosnes E. On linear programming decoding on a quantized additive white Gaussian noisechannel [C]. Cirencester, United kingdom: Springer Verlag,2009.
[71] Fang H, Zhang Q, Wei S. Method of image reconstruction based on sub-Gaussian randomprojection [J]. Jisuanji Yanjiu yu Fazhan/Computer Research and Development.2008,45(8):1402-1407.
[72] Gilbert A C, Guha S, Indyk P, et al. Near-optimal sparse Fourier representations via sampling
[C]. Montreal, Que., Canada: Association for Computing Machinery,2002.
[73] Bajwa W U, Haupt J D, Raz G M, et al. Toeplitz-structured compressed sensing matrices [C].Madison, WI, United states: Inst. of Elec. and Elec. Eng. Computer Society,2007.
[74] Yu L, Barbot J P, Zheng G, et al. Toeplitz-structured chaotic sensing matrix for compressivesensing [C]. Newcastle upon Tyne, United kingdom: IEEE Computer Society,2010.
[75] Sebert F, Zou Y M, Ying L. Toeplitz block matrices in compressed sensing and theirapplications in imaging [C]. Shenzhen, China: Inst. of Elec. and Elec. Eng. Computer Society,2008.
[76] Do T T, Tran T D, Gan L. Fast compressive sampling with structurally random matrices [C].Las Vegas, NV, United states: Institute of Electrical and Electronics Engineers Inc.,2008.
[77] Wang M. Raw SAR data compression by structurally random matrix based compressivesampling [C]. Xian, China: IEEE Computer Society,2009.
[78] Elad M. Optimized projections for compressed sensing [J]. IEEE Transactions on SignalProcessing.2007,55(12):5695-5702.
[79] Xu J, Pi Y, Cao Z. Optimized projection matrix for compressive sensing [J]. Eurasip Journalon Advances in Signal Processing.2010.
[80] Wang Z, Arce G R, Paredes J L. Colored random projections for compressed sensing [C].Honolulu, HI, United states: Institute of Electrical and Electronics Engineers Inc.,2007.
[81] Babacan S D, Molina R, Katsaggelos A K. Fast Bayesian compressive sensing using Laplacepriors [C]. Taipei, Taiwan: Institute of Electrical and Electronics Engineers Inc.,2009.
[82] Babacan S D, Molina R, Katsaggelos A K. Bayesian compressive sensing using laplace priors[J]. IEEE Transactions on Image Processing.2010,19(1):53-63.
[83] Tzagkarakis G, Tsakalides P. Bayesian compressed sensing imaging using a gaussian scalemixture [C]. Dallas, TX, United states: Institute of Electrical and Electronics Engineers Inc.,2010.
[84]石光明，刘丹华，高大化，等.压缩感知理论及其研究进展[J].电子学报.2009,37(5):1070-1081.
[85] Tropp J A, Gilbert A C. Signal recovery from random measurements via orthogonal matchingpursuit [J]. IEEE Transactions on Information Theory.2007,53(12):4655-4666.
[86] Donoho D L, Tsaig Y, Drori I,etc. Sparse solution of underdetermined linear equations bystagewise rthogonal matching pursuit [J]. IEEE Transactions on Information Theory,2012,58(2):1094-1121.
[87] Needell D, Vershynin R. Signal recovery from incomplete and inaccurate measurements viaregularized orthogonal matching pursuit [J]. IEEE Journal on Selected Topics in SignalProcessing.2010,4(2):310-316.
[88] Fan N. Super-Resolution using Regularized Orthogonal Matching Pursuit based on compressedsensing theory in the wavelet domain [C]. Tianjin, China: IEEE Computer Society,2009.
[89] Needell D, Tropp J A. CoSaMP: Iterative signal recovery from incomplete and inaccuratesamples [J]. Applied and Computation Harmonic Analysis,2009,26:301-321.
[90] Dai W, Milenkovic O. Subspace pursuit for compressive sensing signal reconstruction [J].IEEE Transactions on Information Theory,2009,55(5):2230-2249.
[91] Do T T, Gan L, Nguyen N. etc. Sparsity adaptive matching pursuit algorithm for practicalcompressed sensing [C]. Asilomar Conference on Signals, Systems, and Computers, PacificGrove, California,2008,10:581-587.
[92] Candes E, Braun N, Wakin M. Sparse signal and image recovery from compressive samples
[C]. Arlington, VA, United states: Inst. of Elec. and Elec. Eng. Computer Society,2007.
[93] Saligrama V, Manqi Z. Thresholded basis pursuit: LP algorithm for oder-wise optimal supportrecovery for sparse and approximately sparse signals from noisy random measurements [J].IEEE Transactions on Information Theory.2011,57(3):1567-1586.
[94] Kim S, Koh K, Lustig M, et al. An interior-point method for large-scale1-regularized leastsquares [J]. IEEE Journal on Selected Topics in Signal Processing.2007,1(4):606-617.
[95] Koh K, Kim S, Boyd S. An efficient method, for large-scale l1-regularized convex lossminimization [C]. San Diego, CA, United states: Inst. of Elec. and Elec. Eng. ComputerSociety,2007.
[96] Figueiredo M A T, Nowak R D, Wright S J. Gradient projection for sparse reconstruction:Application to compressed sensing and other inverse problems [J]. IEEE Journal on SelectedTopics in Signal Processing.2007,1(4):586-597.
[97] Harmany Z, Thompson D, Willett R, et al. Gradient projection for linearly constrained convexoptimization in sparse signal recovery [C]. Hong Kong, Hong kong: IEEE Computer Society,2010.
[98] Jin J, Gu Y, Mei S. A stochastic gradient approach on compressive sensing signalreconstruction based on adaptive filtering framework [J]. IEEE Journal on Selected Topics inSignal Processing.2010,4(2):409-420.
[99] Broughton R L, Coope I D, Renaud P F, et al. A box constrained gradient projection algorithmfor compressed sensing [J]. Signal Processing.2011,91(8):1985-1992.
[100] Fornasier M, Pitolli F. Adaptive iterative thresholding algorithms formagnetoencephalography(MEG)[J]. Journal of Computational and Applied Mathematics.2008,221(2):386-395.
[101] Fornasier M, Rauhut H. Iterative thresholding algorithms [J]. Applied and ComputationalHarmonic Analysis.2008,25(2):187-208.
[102] Bredies K. An iterative thresholding-like algorithm for inverse problems with sparsityconstraints in Banach space [J]. Journal of Inverse and Ill-Posed Problems.2009,17(1):19-26.
[103] Khoramian S. An iterative thresholding algorithm for linear inverse problems withmulti-constraints and its applications [J]. Applied and Computational Harmonic Analysis.2012,32(1):109-130.
[104] Blumensath T, Yaghoobi M, Davies M E. Iterative hard thresholding and L0regularisation
[C]. Honolulu, HI, United states: Institute of Electrical and Electronics Engineers Inc.,2007.
[105] Gribonval R, Nielsen M. Highly sparse representations from dictionaries are unique andindependent of the sparseness measure [J]. Applied and Computational Harmonic Analysis.2007,22(3):335-355.
[106] Chartrand R. Exact reconstruction of sparse signals via nonconvex minimization [J]. IEEESignal Processing Letters.2007,14(10):707-710.
[107] Gilbert A C, Muthukrishnan S, Strauss M. Improved time bounds for near-optimal sparseFourier representations [C]. San Diego, CA, United states: SPIE,2005.
[108] Gilbert A C, Strauss M J, Tropp J A, et al. One sketch for all: Fast algorithms for compressedsensing [C]. San Diego, CA, United states: Association for Computing Machinery,2007.
[109]李树涛,魏丹.压缩传感综述[J].自动化学报,2009,35(11):1369-1377.
[110] Tropp J A. Greed is good: Algorithmic results for sparse approximation [J]. IEEETransactions on Information Theory.2004,50(10):2231-2242.
[111] Do T T, Gan L, Nguyen N, et al. Sparsity adaptive matching pursuit algorithm for practicalcompressed sensing [C]. Pacific Grove, CA, United states: IEEE Computer Society,2008.
[112] Sun G L, Zhang Y, Lv L Q, et al. Research on iterative thresholding matching pursuit basedon adaptive sparsity [J]. Journal of Computational Information Systems.2011,7(1):34-41.
[113] Candès E, Tao T. The Dantzig selector: Statistical estimation when p is much larger than n [J].Annals of Statistics,2007,35(6):2313-2351.
[114]Boyd S, Vandenberghe L. convex optimization [M]. Cambridge: Cambridge University Press,2004.
[115] Figueiredo M A T, Nowak R D, Wright S J. Gradient projection for sparse reconstruction:Application to compressed sensing and other inverse problems [J]. IEEE Journal on SelectedTopics in Signal Processing.2007,1(4):586-597.
[116] Harmany Z, Thompson D, Willett R, et al. Gradient projection for linearly constrained convexoptimization in sparse signal recovery [C]. Hong Kong, Hong kong: IEEE Computer Society,2010.
[117]郭海燕，王天荆，杨震. DCT域的语音信号自适应压缩感知[J].仪器仪表学报.2010,31(6):1262-1268.
[118]孙林慧，杨震，叶蕾.基于自适应多尺度压缩感知的语音压缩与重构[J].电子学报.2011,39(1):40-45.
[119]郭海燕，杨震.基于近似KLT域的语音信号压缩感知[J].电子与信息学报.2009,31(12):2948-2952.
[120] Xu T T, Yang Z, Shao X. Adaptive compressed sensing of speech signal based on data-drivendictionary [C].200915th Asia-Pacific Conference on Communications, APCC2009.2009,257-260.
[121] Sreenivas T V, Kleijn W B. Compressive sensing for sparsely excited speech signals [C].Acoustics, Speech and Signal Processing,2009. ICASSP2009. IEEE InternationalConference on,2009:4125–4128.
[122]季云云，杨震.基于自相关观测的语音信号压缩感知[J].信号处理.2011,127(2):207-214.
[123] Gemmeke J F, Hamme H V, Cranen B, et al. Compressive Sensing for Missing DataImputation in Noise Robust Speech Recognition [J]. Selected Topics in Signal Processing,IEEE Journal of.2010,4(2):272-287.
[124] Gemmeke J F, Cranen B. Using sparse representations for missing data imputation in noiserobust speech recognition [C]. European Signal Processing Conf.(EUSIPCO), Lausanne，Switzerland，August2008.
[125] Giacobello D, Christensen M G, Murthi M N, et al. Retrieving sparse patterns using acompressed sensing framework: applications to speech coding based on sparse linearprediction [J]. Signal Processing Letters, IEEE.2010,17(1):103-106.
[126]叶蕾，杨震，郭海燕.基于小波变换和压缩感知的低速率语音编码方案[J].仪器仪表学报.2010,31(7):1569-1575.
[127] Goyal V K, Fletcher A K, Rangan S. Compressive Sampling and Lossy Compression [J].Signal Processing Magazine, IEEE.2008,25(2):48-56.
[128] Griffin A, Hirvonen T, Tzagkarakis C, et al. Single-channel and Multi-channel SinusoidalAudio Coding Using Compressed Sensing [J]. Audio, Speech, and Language Processing,IEEE Transactions on.2011,19(5):1382-1395.
[129] Griffin A, Hirvonen T, Mouchtaris A, et al. Encoding the sinusoidal model of an audio signalusing compressed sensing [C].2009IEEE International Conference on Multimedia and Expo(ICME).2009:153-156.
[130] Xu T, Yang Z, Shao X. Novel speech secure communication system based on informationhiding and compressed sensing [C]. Porto, Portugal: IEEE Computer Society,2009.
[131] Ma H, Xiong J, Xu Y, et al. Packet loss concealment for speech transmission based oncompressed sensing [C]. IET International Communication Conference on Wireless Mobileand Computing,2009:327-330.
[132] Xu T, Wang W. A block-based compressed sensing method for underdetermined blind speechseparation incorporating binary mask [C]. Dallas, TX, United states: Institute of Electricaland Electronics Engineers Inc.,2010.
[133] Griffin A, Tsakalides P. Compressed sensing of audio signals using multiple sensors [C]. inProc.16th European Signal Processing Conference (EUSIPCO '08)，Lausanne，Switzerland，2008.
[134] Blumensath T, Davies M E.Gradient pursuits [J]. IEEE Trans. on Signal Processing，2008，56(6):2370–2382.
[135] Vaidyanathan P P. Theory Of Linear Prediction [M]. San Rafael, United States: Morgan&Claypool Publishers,2007.
[136] Benesty J, Makino S, Chen J. Speech enhancement [M]. Berlin, Germany: Springer,2005.
[137] Tashev I, Lovitt A, Acero A. Unified Framework for Single Channel Speech Enhancement [C].IEEE Pacific Rim Conference on Communications, Computers and Signal Processing,2009:883-888.
[138] Hao J, Attias H, Nagarajan S, et al. Speech enhancement, gain, and noise spectrum adaptationusing approximate bayesian estimation [J]. IEEE Transactions on Audio, Speech andLanguage Processing.2009,17(1):24-37.
[139] Yoshioka T, Nakatani T, Okuno H G. Noisy speech enhancement based on prior knowledgeabout spectral envelope and harmonic structure [C].2010IEEE International Conference onAcoustics Speech and Signal Processing (ICASSP),2010:4270-4273.
[140] Tantibundhit C, Pernkopf F, Kubin G. Joint time–frequency segmentation algorithm fortransient speech decomposition and speech enhancement [J]. IEEE Transactions on Audio,Speech, and Language Processing,2010,18(6):1417-1428.
[141] Mallat S. A Wavelet Tour of Signal Processing [M].2nd ed. New York: Academic Press,1998.
[142] Hansen P C, O’Leary D P, The use of the L-curve in the regularization of discrete ill-posedproblems [J]. SIAM Journal on Scientific Computing,1993,14(6):1487–1503.
[143]叶蕾, et al.基于压缩感知观测序列倒谱距离的语音端点检测算法[J].信号处理,2011,27(1):67-72.
[144] Coifman R R and Donoho D L. Translation-Invariant De-noising [J]. New York: Springer-Verlag,1995:125-150.
[145] Donoho D, Johnstone I M. Ideal spatial adaptation by wavelet shrinkage [J]. Biomet rika,1994,81(3):425-455.
[146] Zhang L H, Rong G F. A kind of modified speech enhancement algorithm based on waveletpackage transformation [C]. Proceedings of the2008International Conference on WaveletAnalysis and Pattern Recognition, Hong Kong,30-31Aug.2008:421-425.
[147]李映,等.基于信号稀疏表示的形态成分分析:进展和展望[J].电子学报,2009,37(1):146-152.
[148]王大凯,等.小波分析及其在信号处理中的应用[M].北京:电子工业出版社,2006.
[149]鲍长春.高质量的4kb/s散布脉冲CELP语音编码算法[J].电子学报,2003,31(2):1-5.