基于分离Bregman迭代协同稀疏性的图像压缩感知恢复算法
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摘要
目前存在的CS恢复算法中大都采用固定的基函数,也就是在确定的域中对信号进行分解,比如:DCT域、小波域和梯度域,但这些域都忽略了自然信号的非平稳特性,缺乏自适应能力,从而不能够将图像分解得足够稀疏,也就使得CS恢复的效果很差,限制了CS在图像方面的应用。提出了一种基于分离Bregman迭代方法求解协同稀疏模型正则化的图像压缩感知恢复算法,能够在有效地刻画图像的局部平滑性和非局部自相似性的同时,获得更高质量的图像恢复效果。实验证明了本文提出算法的有效性,并且在峰值信噪比PSNR方面,比目前主流最好的算法高1 dB。
Most of conventional CS recovery methods utilized a set of fixed bases( e. g. DCT,wavelet and gradient domain) for the entirety of a signal,which are irrespective of the non- stationarity of natural signals and cannot achieve high enough degree of sparsity,thus resulting in poor recovery performance. This paper proposes a new collaborative sparsity regularized framework for image compressive sensing recovery based on split Bregman iteration,which enforces image intrinsic local smoothness and nonlocal self- similarity,greatly improving image recovery performance. Experimental results demonstrate that the novel CS recovery strategy achieves significant performance improvements over the current state- of-the- art schemes by 1 dB in the peak signal- to- noise ratio( PSNR).
Most of conventional CS recovery methods utilized a set of fixed bases( e. g. DCT,wavelet and gradient domain) for the entirety of a signal,which are irrespective of the non- stationarity of natural signals and cannot achieve high enough degree of sparsity,thus resulting in poor recovery performance. This paper proposes a new collaborative sparsity regularized framework for image compressive sensing recovery based on split Bregman iteration,which enforces image intrinsic local smoothness and nonlocal self- similarity,greatly improving image recovery performance. Experimental results demonstrate that the novel CS recovery strategy achieves significant performance improvements over the current state- of-the- art schemes by 1 dB in the peak signal- to- noise ratio( PSNR).
引文
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[2]CANDES E,TAO T.Near-optimal signal recovery from random projections and universal encoding strategies?[J].IEEE Transactions on Information Theory,2006,52(12):5245–5406.
[3]李树涛,魏丹.压缩传感综述[J].自动化学报,2009,35(11):1369–11377.
[4]刘丹华,石光明,周佳社,等.基于Compressed Sensing框架的图像多描述编码方法[J],红外与毫米波学报,2009,28(4):298-302.
[5]ZHANG J,ZHAO D,JIANG F.Spatially directional predictive coding for block-based compressive sensing of natural images[C]//Proc.of International on Image Processin.,Melbourne,Australia:IEEE,2013:1021–1025.
[6]ZHANG J,ZHAO D,ZHAO C,et al.Compressed sensing recovery via collaborative sparsity[C]//Proc.of IEEE Data Compression Conference,Snowbird,Utah,USA:IEEE,2012:287–296.
[7]HE L,CARIN L.Exploiting structure in wavelet-based Bayesian compressive sensing[J].IEEE Transactions on Signal Processing,2009,57(9):3488–3497.
[8]MUN S,FOWLER J E.Block compressed sensing of images using directional transforms[C]//Proc.of International Conference on Image Processing.Cairo,Egypt:IEEE,2009:3021–3024.
[9]LI C,YIN W,ZHANG Y.TVAL3:TV Minimization by Augmented Lagrangian and Alternating Direction Algorithm[D].2009.http://www.caam.rice.edu/~optimization/L1/TVAL3/.
[10]WU X,ZHANG X,WANG J.Model-guided adaptive recovery of compressive sensing[C]//Proc.of Data Compression Conference,Snowbird,USA:IEEE,2009:123–132.
[11]ZHANG J,LIU S,XIONG R,et al.Improved total variation based image compressive sensing recovery by nonlocal regularization[C]//Proc.of IEEE Int.Sym.of Circuits and Systems,Beijing,China:IEEE,2013:2836–2839.
[12]KIM Y,NADAR M S,BILGIN A.Compressive sensing using a Gaussian scale mixtures model in wavelet domain[C]//Proc.of International Conference on Image Processing.Hongkong:IEEE,2010:3365–3368.
[13]HE L,CARIN L.Exploiting structure in wavelet-based Bayesian compressive sensing[J].IEEE Transactions on Signal Processing,2009,57(9):3488–3497.
[14]CHEN C,TRAMEL E W,FOWLER J E.Compressed sensing recovery of images and Video using multihy-pothesis predictions[C]//Proc.of the 45thAsilomar Conference on Signals,Systems,and Computers,Pacific Grove,CA:IEEE,2011:1193–1198.
[15]ZHANG J,ZHAO D,ZHAO C,et al.Image compressive sensing recovery via collaborative sparsity[J].IEEE Journal on Emerging and Selected Topics in Circuits and Systems,2012,2(3):380–391.
[16]GOLDSTEIN T,OSHER S.The split Bregman algorithm for L1 regularized problems[J].SIAM J.Imaging Sci.,2009,2(2):323–343.
[17]CAI J,OSHER S,SHEN Z.Split Bregman methods and frame based image restoration[J].Multiscale Model.Simul.,2010,8(2):337–369.
[18]HUANG J,ZHANG S,LI H,et al.Composite splitting algorithms for convex optimization[J].Computer Vision and Image Understanding,2011,115(12):1610–1622.