磁共振成像重建与伪影去除方法研究
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摘要
磁共振成像技术利用核磁共振原理对人体或生物体的某部分进行断面成像或立体成像,以获得组织和器官的解剖结构、功能结构和病变状况。磁共振成像技术是一种无损体外探测技术,是二十一世纪生物学和医学研究的重要工具。但是磁共振成像重建技术仍然存在重建图像质量不高的问题,临床上期待给出更有效的方法。
     功能磁共振成像(fMRI)是90年代初磁共振成像技术的一项新发展。该技术基于血氧含量水平依赖对比度机制(blood oxygenation level dependent,BOLD),能够实时地对大脑皮层神经功能活动进行成像,为临床MR诊断从单一形态学的研究到形态与功能信息相结合的系统研究开辟了一条崭新的道路。fMRI以较高的空间分辨率、时间分辨率及完全无损的特性已成为进行脑功能研究的重要工具。
     较之一般成像技术,回波平面成像技术(EPI)由于采样时间短,能够在几秒之内得到整个脑部的图像,这已成为fMRI广泛采用的一种技术。通过对fMRI中的任务相关的信号改变的分析检测可以确定对应的功能活动。但是,在1.5Tesla的磁场中,任务相关的信号改变范围通常在1~2%之间。为了获得对功能反应的较高检测率,需要高度稳定的信号。在图像采集过程中,有很多因素导致伪影。所有这些干扰因素都对功能激活区域的准确检测及定位造成不同程度的影响,虽然通过改善成像设备的硬件性能、优化扫描参数等措施可以减小这些干扰效应,但去除效果不是太理想。目前主要采用的为k空间校正方法,后处理是一种值得探讨的方法。
     生理伪影是功能信号检测的主要干扰因素,主要包括呼吸伪影和心脏运动伪影。这些伪影的出现严重影响了脑功能信号的有效检出,必须研究有效的去除生理伪影的方法。
     针对以上问题,本课题的主要目的有两个方面:一是研究新的磁共振图像重建方法,能重建更高质量的图像,以及对于序列图像重建,如何使时间分辨率和空间分辨率二者之间均衡;二是研究功能磁共振图像中生理伪影的去除方法,使功能信号检测更有效。
     本文主要的研究成果包括以下几个方面:
     1)提出了一种非笛卡尔采样的磁共振图像重建方法。对于非均匀采样数据,用非均匀FFT方法对其重建,大大提高了重建图像的速度。同时该方法的加权系数能以多种满足条件的函数形式给出,而已有方法的加权系数是给定的,所以相比之下该方法具有更大的灵活性,精度更高。最终结果表明该方法具有较好的重建图像质量。
     2)提出了一种基于信息相关性的动态磁共振图像重建方法。该方法利用已获取的两幅高空间分辨率参考图像作为先验信息,通过减少编码方式获取序列中其它数据,采集数据时间减少,重建可得到较高空间分辨率的图像。同时考虑到需要求解的系统为病态的,采用改进的TSVD方法进行正则化,重建序列图像。文中还给出利用其它几种方法实现的结果。结果表明,该方法具有较好的重建效果。
     3)提出了一种基于功率谱相减去除生理伪影的方法。生理伪影是由具体的周期性生理活动引起的,所以总是对应一定的频率,在功率谱上有较明显的特征。由于脑脊液中体素不包含任何功能激发信号,只含有生理伪影和随机噪声,所以首先选择脑脊液中体素,得到时间序列,估计出噪声的功率谱。然后取感兴趣体素,其功率谱减去脑脊液的平均功率谱,可得到去除生理伪影后的功率谱。实验结果表明该方法能有效地去除生理伪影。
     4)提出了一种基于空间独立成分分析去除生理伪影的方法。利用空间独立成分分析方法对功能磁共振数据分解,对独立成分对应的时间序列求功率谱,判断是否含有生理伪影,然后将含有生理伪影的独立成分去除并重建去除生理伪影后的数据。实验结果表明该方法能有效去除生理伪影。
     5)提出了一种基于图像空间数据的欠采样生理伪影去除方法。在利用长重复时间(repetition time,TR)采集的多层数据研究中,采用典型的成像参数(秒数量级),则每层不足以对生理伪影严格采样,得到的时间序列被高频生理伪影引起的混叠谱分量所污染。我们将原来按层排列的时间序列按时间顺序重排列,并对每幅图像取均值,得到一个时间序列,求功率谱,估计生理频率。然后根据频率混叠性质,判断混叠位置,采用滤波器去除呼吸生理伪影。实验结果表明该方法能较好地解决混叠问题,从而较好地去除生理伪影。
     论文最后给出工作展望:如何重建高质量的磁共振图像,以及如何有效地去除包括生理伪影在内的多种伪影仍然是我们以后的研究工作重点。
Magnetic Resonance Imaging (MRI) techniques are used to obtain anatomical, functional, and pathological information of certain part of human bodies or animals based on the principles of nuclear magnetic resonance. MRI is a non-invasive technique, and especially an important tool for medical research. The problem, that the reconstructed images using MRI have low quality, still exists, so more efficient methods are expected.
     Functional MRI is a new development of MRI technology in the early 1990s. Cerebral cortex functional activation can be imaged real-time based on the contrast mechanisms of blood oxygenation level dependent (BOLD). And the advent of functional MRI leads to a new method for the clinical MR diagnosis, which can transform single morphological research to systematic research that combines morphology with functional information. So functional MRI has become a significant tool to study brain function with high spatial resolution, high temporal resolution, and absolutely non-invasive characteristics.
     Compared with other imaging techniques, EPI has been an extensively used method. Due to its short acquiring time of EPI, the whole brain can be imaged in several seconds, so functional imaging is of high spatial resolution. Functional activity can be determined by analyzing the task-related signal change. But in 1.5 Tesla magnetic filed, the change of functional signal is only 1~2%. To obtain high functional signal detecting rate, high steady signal is needed. During image acquisition, lots of factors can lead to artifacts and therefore interfere with the functional activated area. Though the problem can be mitigated by improving the hardware property, we can’t removal them satisfactorily. K-space based correction methods are used mostly, and post-processing strategy is a considerable method.
     Physiological artifact is an important interference of functional signal detection, including respiratory and cardiac artifact. The advent of these artifacts interfere with the detection offunctional signal, so efficient methods are expected to be presented.
     Aiming at problems mentioned above, there are two purposes in this thesis. Firstly, we want to reconstruct high quality image and make trade-off between time resolution and spatial resolution by presenting new MRI reconstruction methods. Secondly, we want to present efficient methods to remove physiological artifacts, thus functional signal can be detected more efficiently.
     The research achievements include five following methods:
     1) For non-cartesian acquisition, previous methods use regridding method and then obtain reconstruction results using FFT mostly. Based on non-uniform FFT (NUFFT) method, a new method for non-cartesian acquisition reconstruction is presented. This method gives weighted coefficients through many suitable functions, but previous methods give the weighted coefficients directly. The results show that our method can give high quality reconstruction images.
     2) For dynamic sequence images, a new high time and spatial resolution image reconstruction method is presented using information relativity. Using prior information from two reference image, high temporal and spatial resolution images can be reconstructed by reducing encoding. In the method, an ill-conditioned system is solved using modified TSVD method. At the same time, L-curve method is used to determine optimal parameter k. Some results using previous methods are given to be compared with our results. According to the comparison, our method is superior to others.
     3) Physiological artifacts are induced by concrete physiological activity and correspond to certain frequency, so they show obvious character. A method using power spectrum subtraction to removal physiological artifacts is presented. We estimate noise power spectrum from time series with selected voxel because CSF contains physiological noise and random noise without any activated signal. Using power spectrum of interested voxel, spectrum with physiological artifact removal can be obtained by subtracting estimated noise power spectrum. Experimental results show that the method can remove physiological artifacts efficiently.
     4) A spatial ICA based physiological artifacts removal method is presented. Using spatial ICA method, fMRI data can be decomposed and independent components are obtained. Power spectrum can be calculated using time series corresponding to independent components. we decide that which independent components contain physiological artifacts and reconstruct data by removal these independent components. Results show that the method can remove physiological artifacts efficiently.
     5) An image-space data based physiological artifacts removal method is given. In acquired multi-slices data research, if typical imaging parameter is used, physiological artifactscan’t be critically sampling for each slice. Resulting time series artifacts are contaminated by aliased spectral components from the high-frequency physiological artifacts, and thus previous methods are not efficient anymore. We reorder the data from original slice ordering to time ordering and obtain time series by calculating mean value of every image. Thus physiological frequency is estimated by calculating power spectrum of time series. According to the property of aliasing, we can decide the aliasing position and then remove physiological artifacts using digital filter. Experimental results illustrate that the method can remove physiological artifacts preferably.
     At the end of the paper, prospects of future research are given. The topics on how to reconstruct high quality MR image and how to remove various artifacts efficiently are our future research keystone.
引文
1. Krotz, D. Dr. Paul Lauterbur, Recalls Origins of MRI Concept[J]. Diagnostic Imaging, 1999,21(8): 24-25.
    2. Lauterbur PC. Image formation by induced local interactions: examples employing nuclear magnetic resonance[J]. Nature,1973,242: 190-191.
    3. Kumar A, Welti D, Ernst RR. NMR Fourier zeugmatogrphy[J]. Journal of Magnetic Resonance, 1975,18(1): 69-83.
    4. Mansfield P. Multi-planar image information using NMR spin echoes[J]. Journal of Physics C: Solid State Physics, 1977, 10(1): L55-58.
    5. Stehling MK, Turner R, Mansfield P. Echo-planar imaging: magnetic resonance imaging in a fraction of a seconds[J]. Science, 1991, 254(5028): 43-50.
    6. Meyer CH, Hu BS, Nishimura DG, et al. Fast Spiral coronary artery imaging[J]. Magnetic Resonance in Medicine, 1992, 28(2): 202-213.
    7. J. I. Jackson, C. H. Meyer, D. G. Nishimura, and A. Macovski. Selection of a convolution function for Fourier inversion using gridding[J]. IEEE Trans. Med. Imag., vol. 10, pp. 472–478, 1991.
    8. Lauzon ML, Rutt BK. Polar sampling in k-space: reconstruction effects[J]. Magnetic Resonance in Medicine, 1998, 46(4): 76-782.
    9. Noll DC. Multishot rosette trajectories for specially selective MR imaging[J]. IEEE Transactions on Medical Imaging, 1997, 16(4): 372-377.
    10. Gai N, Axel L. Elimination of Nyquist Ghosts in MRI by using fast linogram imaging[J]. Journal of Magnetic Resonance Imaging, 1997, 7(6):1166-1169.
    11. Ogura Y, Sekihara K. A new method for static imaging of a rotating object[J]. Journal of Magnetic Resonance, 1989, 83(1): 177-182.
    12. Scheffle K, Hennig J. Frequency resolved single-shot MR imaging using stochasitic k-space trajectoryes[J].Magnetic Resonance in Medicine, 1996, 35(4): 569-576.
    13. D. C. Noll. Conjugate phase reconstruction with spatially variant sample density correction[J]. In ISMRM Eleventh Scientific Meeting, 2003, page 476.
    14. Moriguchi H, Duerk JL. Modified Block Uniform Resampling (BURS) Algorithm Using Truncated Singular Value Decomposition: Fast Accurate Gridding With Noise and Artifact Reduction[J]. Magnetic Resonance in Medicine, 2001, 46: 1189-1201.
    15. D. Rosenfeld. New approach to gridding using regularization and estimation theory[J]. Magn. Reson. Med., 2002, 48: 193–202.
    16. Ogawa, S., Lee, T., Kay, A., and Tank, D. (1990). Brain magnetic resonance imaging with contrast dependent on blood oxygenation[C]. Proceeding of the National Academy of Science, USA, 87(24): 9868-9872.
    17. Dagli MS, Ingeholm JE, Haxby JV. Localization of cardiac-induced signal change in fMRI[J]. Neuroimage 1999, 9:407–15.
    18. Buonocore MH and Gao L. Ghost artifact reduction for echo planner imaging using image phase correction [J]. Magn. Reson. Med. 1997, 38:89-100.
    19. Foxall DL, Harvey PR, Huang J. Rapid iterative reconstruction for echo planner imaging [J]. Magn. Reson. Med. 1999, 42:541-547.
    20. Kim S-G, Ugurbil K. Functional magnetic resonance imaging of the human brain [J]. J Neurosci Methods, 1997, 74:229-243.
    21. Bullmore ET, Brammer MJ, Rable-Hesketh S, et al. Methods for diagnosis and treatment of stimulus-correlated motion in generic brain activation studies using fMRI [J]. Human Brain Mapping, 1999, 7:38-48.
    22. Kennedy A, Baker JR, Weisskoff RM, et al. Motion detection and correction in functional MR imaging [J]. Human Brain Mapping, 1995, 3:224-235.
    23. Woods RP, Cherry SR, Mazziotta JC. Rapid automated algorithm for aligning and reslicing PET images [J]. J. Comput. Assist. Tomogr. 1992, 16:620-633.
    24. Friston KJ, Williams S, Howard R, et al. Movement-related effects in fMRI time-series [J]. Magn. Reson. Med. 1996, 35:346-355.
    25. Eddy WF, Fitzgerald M and Nol DC. Improved image registration by using Fourier interpolation [J]. Magn. Reson. Med. 1996, 36:923-93.
    26. Kim B, Boes JL, Bland PH, et al. Motion correction in fMRI via registration of individual slices into an anatomical volume [J]. Magn. Reson. Med. 1999, 31:964-972.
    27. Cox RW and Jesmanowicz A. Real-time 3D image registration for functional MRI [J]. Magn. Reson. Med. 1999, 42:1014-1018.
    28. Jenkinson M and Smith S. The role of registration in functional magnetic resonance imaging [M]. In Hajnal, J., Hill, D. L. G. and Hawkes, D. J., editors, Medical Image Registration, 183-198. CRC Press, 2001.
    29. Alexander ME and Somorjia RL. The registration of MR images using multi-scale robust methods [J]. Magn.Reson. Imag. 1996, 14:453-468.
    30. Biswal BB and Hyde JS. Contour-based regisrration technique to differentiate between task-activated and head motion-induced signal varitations in fMRI [J]. Magn. Reson. Med. 1996, 38:470-476.
    31. Noll DC and Schneider W. Respiration artifacts in functional brain imaging: sources of signal variation and compensation strategies [C]. Proc. 2nd Soc. Magn. Reson. 1994,p.647.
    32. Kupusamy K, Lin W, Haccke EM. Importance of EKG gating in functional magnetic resonance imaging of human motor cortex [C]. Abs. Soc. Neurosci. 1995, p.1420.
    33. Hu X and Kim SG. Reduction of physiological noise in functional image using navigator echo [J]. Magn. Reson. Med. 1994, 31:495-503.
    34. Biswal B, DeYoe EA, Hyde JS. Reduction of physiological fluctuations in fMRI using digital filters [J]. Magn. Reson. Med. 1996, 35:117-123.
    35. Hu X, Le TH, Parrish T et al. Retrospective estimation and compensation of physiological fluctuation in functional MRI [J]. Magn. Reson. Med. 1995, 34:210-221.
    36. Bandettini PA, Jesmanowicz A, Wong EG, et al. Processing strategies for time-course data sets in functional MRI of the human brain [J]. Magn. Reson. Med. 1993, 30:161-173.
    37. Buonocore MH and Maddock RJ. Noise suppression digital filter for functional magnetic resonance imaging based on image reference data [J]. Magn. Reson. Med. 1997, 38:456-469.
    38. U. Ziyan, J. Ulmer, T. Talavage. Image space based estimation and removal of respiration noise from fMRI data[C]. Proceeding of the 10 th Scientific Meeting of the International Society for Magnetic Resonance in Medicine, 2002, p.1407.
    1. F. Bloch, W. W. Hansen, and M. E. Packard, Nuclear induction[J]. Phys Rev, 1946, 69: 127.
    2. E. M. Purcell, H. C. Torrey, and R. V. Pound. Resonance absorption by nuclear magnetic moments in a solid[J]. Phys Rev, 1946, 69: 37.
    3. P. C. Lauterbur. Image formation by induced local interactions: Examples exploring nuclear magnetic resonance[J]. Nature, 1973, 242: 190.
    4. 赵喜平编著. 磁共振成像系统的原理及应用[M]. 北京:科学出版社,2000. 20-147, 296-389, 622-631.
    5. P. Mansfield, P.G. Morris著,宗贤钧等译. 生物医学中的核磁共振成像[M]. 浙江大学出版社,1987: 29-34.
    6. Brian Andrew Hargreaves. Spin-manipulation methods for efficient Magnetic Resonance Imaging[D]. [Phd thesis]. USA: Stanford University, 2001.
    7. Reduced aliasing artifacts using variable-density k-space sampling trajectories[J]. Magnetic Resonance in Medicine, 2000, 43:452-458.
    8. D. C. Noll. Conjugate phase reconstruction with spatially variant sample density correction[C]. In ISMRM Eleventh Scientific Meeting, 2003, page 476.
    9. J. I. Jackson, C. H. Meyer, D. G. Nishimura, and A. Macovski. Selection of a convolution function for Fourier inversion using gridding[J]. IEEE Trans. Med. Imag., 1991, vol. 10, pp. 472–478.
    10.Roy, C.S. and C.S. Sherrington, On the regulation of the blood-supply of the brain[J]. J Physiol (London), 1890, 11: p. 85-108.
    11.Ogawa, S., T. Lee, A. Nayak, and P. Glynn. Oxygenation-sensitive contrast in magnetic resonance image of rodent brain at high magnetic fields[J]. Magn Reson Med, 1990, 14: p. 68-78.
    12.Ogawa, S., D.W. Tank, R. Menon, et al. Intrinsic signal changes accompanying sensory stimulation: Functional brain mapping with magnetic resonance imaging[C]. Proc. Natl. Acad. Sci., USA, 1992. 89: p.5951- 5955.
    13.Bandettini, P.A., E.C. Wong, R.S. Hinks, R.S. Tikofsky, and J.S. Hyde. Time course EPI of human brain function during task activation[J]. Magn. Reson. Med., 1992, 25: p. 390-397.
    14.Kwong, K.K., J.W. Belliveau, D.A. Chesler, et al.. Dynamic magnetic resonance imaging of human brain activity during primary sensory stimulation[C]. Proc. Natl. Acad. Sci., USA, 1992, 89: p. 5675-5679.
    15.Villringer A and Dirnagl U. Coupling of brain activity and cerebral blood flow: Basis of functional neuroimaging [J]. Cerebrovasc. Brain. Metab. Rev. 1995, 7:1040-1047.
    16.Pauling L, Coryell CD. The magnetic properties and structure of hemoglobin, oxyhemoglobin and carbon monoxyhemoglobin [C]. Proc. Natl. Acad. Sci. USA, 1936, 22:210-216.
    17.Schenck JF. The role of magnetic susceptibility in magnetic resonance imaging: MRImagnetic compatibility of the first and second kinds [J]. Medical Physics, 1996, 23(6): 815-850.
    18.Thulborn KR, Waterton JC, Matthews PM, et al. Oxygen Dependence of the Transverse Relaxation Time of Water Protons in Whole Blood at High Field [J]. Biochim. Biophys.Acta. 1982, 714:265-270.
    19.Ogawa S, Lee TM, Kay A R, et al. Brain Magnetic Resonance Imaging with Contrast dependent on Blood Oxygenation [J]. Proc. Natl. Acad. Sci. USA ,1990, 87:9868-9872.
    20.Turner, R., Le Bihan, D., Moonen, C. T. W., Despres, D. and Frank, J. (1991) Echo-Planar Time Course MRI of Cat Brain Oxygenation Changes[J]. Magn. Reson. Med. 22:159-166.
    21.Jezzard P, Heinemann F, Taylor J, et al. Comparison of EPI Gradient-Echo Contrast Changes in Cat Brain Caused by Respiratory Challenges with Direct Simultaneous Evaluation of Cerebral Oxygenation via a Cranial Window [J]. NMR in Biomed, 1994, 7:35-44.
    22.Turner R and Ordidge RJ. Technical challenges of functional magnetic resonance imaging: The Biophysics and technology behind a reliable neuroscientific tool for mapping the human brain [J]. IEEE Eng. Med. Biol.Mag., 2000, 19:42-54.
    23.Friston KJ, Frith C D, Frackowiak RSJ, et al. Characterizing dynamic brain responses with fMRI [J]. NeuroImage, 1995, 2:166-172.
    24.Kastrup A, Kruger G, Glover G, et al. Regional variability of cerebral blood oxygenation response to hypercapnia [J]. Neuroimage, 1999, 10:675-68.
    25.Aguirre G, Zarahn E and d'Esposito M. The variability of human: BOLD hemodynamic responses [J]. Neuroimage, 1998, 8:360-369.
    26.Ola Friman. Adaptive analysis of Functional MRI data[D]: Phd Dissertation. Link?ping: Link?ping Studies in Science and Technology, 2003.
    27.王世杰. 功能磁共振数据处理与分析方法研究[D]:[博士论文]. 南京:东南大学生物医学工程系影像科学与技术实验室,2004.
    1. Cooley JW, Tukey JW. An algorithm for the machine calculation of complex Fourier series[J]. Math Comput 1965;19:297–301.
    2. J. O’Sullivan. A fast sinc function gridding algorithm for Fourier inversion in computer tomography[J]. IEEE Trans. Med. Imag., vol. MI-4, pp.200–207, 1985.
    3. J. I. Jackson, C. H. Meyer, D. G. Nishimura, and A. Macovski. Selection of a convolution function for Fourier inversion using gridding[J]. IEEE Trans. Med. Imag., vol. 10, pp. 472–478, 1991.
    4. D. Rosenfeld. An optimal and efficient new gridding algorithm using singular value decomposition[J]. Magn. Reson. Med., vol. 40, pp. 14–23, 1998.
    5. Moriguchi H, Wendt M, Duerk JL. Applying the uniform resampling (URS) algorithm to a Lissajous trajectory: fast image reconstruction with optimal gridding[J]. Magn Reson Med 2000;44:766–781.
    6. Sedarat H, Nisimura DG. Gridding reconstruction using optimal, shift variant interpolating kernels[C]. In: Proceedings of the 7th Annual Meeting of ISMRM, Philadelphia, 1999. p 93.
    7. Sedarat H, Nisimura DG. On the optimality of the gridding reconstruction algorithm[J]. IEEE Trans Med Imaging 2000;19:306–317.
    8. D. Rosenfeld. New approach to gridding using regularization and estimation theory[J]. Magn. Reson. Med., 2002, 48: 193–202.
    9. Tikhonov AN, Arsenin VY. Solutions of ill-posed problems[M]. New York: John Wiley and Sons; 1977.
    10. Van de Walle R, Barrett HH, Myers KJ, et al. Reconstruction of MR images from data acquired on a general non-regular grid by pseudoinverse calculation. IEEE Transactions on Medical Imaging, 2000, 19(12): 1160-1167.
    11. 张明淳 工程矩阵理论 [M] 东南大学出版社.
    12. A. Dutt and V. Rokhlin. Fast Fourier transforms for nonequispaced data. SIAM J. Sci. Comp., vol. 14, pp. 1368–1393, 1993.
    13. G. Beylkin. On the fast Fourier transform of functions with singularities[J]. Appl. Computat. Harmonic Anal., vol. 2, pp. 363–382, 1995.
    14. Q H Liu and N Nguyen. An accurate algorithm for non-uniform fast Fourier transforms (NUFFT’s)[J]. IEEE Microwave and Guided Wave Letters, 1998, vol. 8, no. 1, pp. 18-20.
    15. Q. H. Liu, N. Nguyen, and X. Y. Tang. Accurate algorithm for nonuniform fast forwardd and inverse Fourier transform and their applications[J]. IEEE International Conference IGARSS '98, 1998, 288-290.
    16. K. Fourmont. Non-equispaced fast Fourier transforms with application to tomography[J]. Journal of Fourier analysis and Applications, 2003, 9: 431-450.
    17. G. Sarty, R. Bennett, R. Cox. Direct reconstruction of non-Cartesian k-space data using a non-uniform fast Fourier transform[J]. Magn. Reson. Med. 45 (2001) 908–915.
    18. Sarty GE. The natural k-plane coordinate reconstruction method for magnetic resonance imaging: mathematical foundations[J]. Int J Imaging Syst Technol 1997;8:519–528.
    19. 陈桂明 主编 应用MATLAB语言处理信号与数字图像[Z]. 第二版. 北京:科学出版社,2001.
    1. Twieg DB, Katz J, Peshock RM. A general treatment of NMR imaging with chemical shifts and motion[J]. Magn Reson Med., 1987, 5:32-46.
    2. Z. P. Liang and P. C. Lauterbur. An efficient method for dynamic magnetic resonance imaging[J]. IEEE Trans Med. Imaging, 1994, 13: 677-686.
    3. M. R. Smith et al. Application of autoregressive moving average parametric modeling in magnetic resonance imaging reconstruction[J]. IEEE Trans. Med. Imag., 1986,132-139.
    4. C. P. Hess, Z. P. Liang, A. G. Webb and P. C. Lauterbur. Maximum cross-entropy generalized series reconstruction[C]. International Conference on ICIP98, 1998, 1: 4-7.
    5. X. Hu. On the “keyhole” technique[J]. Journal Magn. Resonance Imag., 1994, 4: 231.
    6. J. E. Bioshop, I. Soutar, W. Kucharczyk, and D. B. Plewes. Rapid sequential imaging with shared-echo fast spin-echo MR imaging[C]. In Works-in-Progress Proc. 10th Annu. Meet. Soc. Magn. Reson. Imag., 1992, New York, Apr. 26-29, p. S22.
    7. J. van Vaals, H. H. Tuithof, and W. T. Dixon. Increased time resolution in dynamic imaging[C]. In Proc. 10th Annu. Meet. Soc. Magn. Reson. Imag., 1992, New York, Apr. 26-29, p. 44.
    8. E. Loli Piccolomini, A. Baronio and F. Zama. A method for solving the indirect approximation problem[J]. Appl. Math. And Comp., 1996, 77: 97-107.
    9. E. Loli Piccolomini, G. Landi and F. Zama. A B-spline parametric model for high resolution dynamic Magnetic Resonance Imaging[J]. Applied Mathematics and Computation, 2003.
    10. L. L. Schumaker. Spline functions: basic theory[M]. John Wiley and Sons, Inc., New York, 1981.
    11. Z.-P. Liang. Generalized series imaging with multiple references[C]. Proceeding of Annual International Conference, 2001, 2244-2247.
    12. P. C. Hansen. Analysis of discrete ill-posed problems by means of the L-curve[J]. SIAM Rev., 1992, 34: 561-580.
    13. Tikhonov AN, Arsenin VY. Solutions of ill-posed problems[M]. New York: John Wiley and Sons, 1977.
    14. D. P. O,Leary P. C. Hansen. The use of L-curve in the regularization of discrete ill-posed problems[J]. SIAM J. Sci. Comp., 1993, 14: 1487-1503.
    15. Per Christian Hansen, Takashi Sekii, and Hiromoto Shibahashi. The modified truncated SVD method for regularization in general form[J]. SIAM J. SCI. STAT. COMPUT., 1992, 13: 1142-1150.
    1. Bandettini PA, Birn RM, Donahue KM. Functional MRI: background, methodology, limits, and implementation [M]. In J. T. Cacippo, L. G. Tassinary, & G. G. Berntson (Eds.), Handbook of psychophysiology (2nd ed., pp. 978-1014). Cambridge, UK: Cambridge University Press, 2000.
    2. Dagli MS, Ingeholm JE, Haxby JV. Localization of cardiac-induced signal change in fMRI[J]. Neuroimage 1999, 9:407–15.
    3. Ostuni JL, Santha AKS, Mattay VS, et al. Analysis of interpolation effects in the reslicing functional MR images [J]. J Comput Assist Tomogr, 1997, 21:803-810.
    4. Kim B, Bose JL, Bland PH, et al. Motion correction in fMRI via registration of individual slices into an anatomical volume [J]. Magn. Reson. Med. 1999, 41:964-972.
    5. Jezzard P and Clare S. Sources of distortion in functional MRI data [J]. Human Brain Mapping 1999, 8:80-85.
    6. Friston K, Williams S, Howard R. et al. Movement related effects in fMRI time series [J]. Magn. Reson. Med. 1996, 35:346-355.
    7. Grootoonk S, Hutton C, Ashburner J, et al. Characterisation and correction of interpolation effects in the realignment of fMRI time series [J]. NeuroImage, 2000, 11:49-57.
    8. Weisskoff R M, Baker J, Belliveau J, Davis T L,KwongKK, CohenMS and Rosen B R Power spectrum analysis of functionally-weighted MR data: what’s in the noise? Proc. Soc. Magnetic Resonance, 1st Ann. Meeting (New York) (Society of Magnetic Resonance in Medicine). 1993,p7
    9. Jezzard P 1999 Physiological noise: strategies for correction Functional MRI (Berlin: Springer) pp173–82
    10. Hu X, Le T H, Parrish T. Retrospective estimation and correction of physiological fluctuation in functional MRI[J]. Magn. Reson. Med. 1995, 34:210-221.
    11. Noll DC, Schneider W. Theory, simulation, and compensation of physiological motion artifacts in functionalMRI. IEEE Intl Conf Imaging Processing, Austin, TX, 1994, p. 40-4.
    12. Kupusamy K, Lin W, Haccke EM. Importance of EKG gating in functional magnetic resonance imaging of human motor cortex [C]. Abs. Soc. Neurosci. 1995, p.1420.
    13. Hu X and Kim SG. Reduction of physiological noise in functional image using navigator echo [J]. Magn. Reson. Med. 1994, 31:495-503.
    14. Biswal B, DeYoe EA, Hyde JS. Reduction of physiological fluctuations in fMRI using digital filters [J]. Magn. Reson. Med. 1996, 35:117-123.
    15. G. H. Glover, T.-Q. Li, D. Ress, “Image-based method for retrospective correction of physiological motion effects in fMRI: RETROICOR,” Magn Reson Med, vol. 44, pp. 162–167, July 2000.
    16. T. H. Le, X. Hu, “Retrospective estimation and correction of physiological artifacts in fMRI by direct extraction of physiological activity from MR data,” Magn Reson Med, 1996, 35: 290–298.
    17. Buonocore MH and Maddock RJ. Noise suppression digital filter for functional magnetic resonance imaging based on image reference data [J]. Magn. Reson. Med. 1997, 38:456-469.
    18. Ogawa S, Menon RS, Tank D, et al. Functional brain mapping by blood oxygenation level-dependent contrast magnetic resonance imaging: a comparison of signal characteristics with a biophysical model [J]. Biophys. J. 1993, 64:803-812.
    19. Frahm J, Merblodt K-D, Hanicke W. Functional MRI of human brain activation at high spatial resolution [J]. Magn. Reson. Med. 1993, 29:139-144.
    20. Frahm J, Merblodt K-D, Hanicke W, et al. Brain or vein-oxygenation or flow? On signal physiology in functional MRI of human brain activation [J]. NMR Biomed. 1994, 7:45-53.
    21. Kim S-G, Hendrich K, Hu X, et al. Potential pitfalls of functional MRI using conventional gradient-recalled echo techniques [J]. NMR Biomed. 1994, 7:69-74.
    22. Weisskoff RM, Zuo CS, Boxerman JL, et al. Microscopic susceptibility variation and transverse relaxation: theory and experiment [J]. Magn. Reson. Med. 1994, 31:601-610.
    23. Kwong KK. Functional magnetic resonance imaging with echo planar imaging [J]. Magn Reson Q, 1995, 11:1-20.
    24. Noll DC, Nishimura DG, and Macovski A. Homodyne detection in magnetic resonance imaging [J]. IEEE Transaction on Medical Imaging, 1991, 10(2): 154-163.
    25. Bruder H, Fischer H, Reinfelder HE, et al. Image reconstraction for echo planner imaging with non-equidistance k-space sampling [J]. Magnetic Resonance in Medicine, 1992, 23:311-323.
    26. Ahn CB and Cho ZH. Analysis of eddy currents in nuclear magnetic resonance imaging [J]. MagneticResonance in Medicine, 1991,17(1): 149-163,
    27. Oshio K and Feinberg DA. GRASE (gradient- and spin-echo) imaging: a novel fast MRI technique [J]. Magnetic Resonance in Medicine 1991, 20(2): 344-349.
    28. Feinberg DA and Oshio K. Gradient echo shifting in fast MRI techniques (GRASE imaging) for correction of field inhomogeneity errors and chemical shift [J]. Journal of Magnetic Resonance. 1992,97:177-183.
    29. Foxall DL, Harvey PR, Huang J. Rapid iterative reconstruction for echo planner imaging [J]. Magn. Reson. Med. 1999, 42:541-547.
    30. Bruder H, Fischer H, Reinfelder HE, Schmitt F. Image reconstruction for echo planar imaging with nonequidistant k-space sampling[J]. Magn Reson Med 1992, 23:311–323.
    31. Wong EC. Shim insensitive phase correction for EPI using a two echo reference scan[C]. In: Proceedings of the SMRM, 11th Annual Meeting, Berlin, Germany, 1992. p 4514.
    32. Jesmanowicz A, Wong EC, Hyde JS. Phase correction for EPI using internal reference lines[C]. In: Proceedings of the SMRM, 12th Annual Meeting, New York, 1993. p 1239.
    33. Maier JK, Vevrek M, Glover GH. Correction of NMR data acquired by an echo planar technique [J]. US Patent #5,151,656 (1992).
    34. Jesmanowicz A, Wong EC, Hyde JS. Self-correcting EPI reconstruction algorithm[C]. In Proceedings of the SMR, 3rd Annual Meeting, Nice, France, 1995. p 619.
    35. Mandeville JB, Weisskoff RM, Garrido L. Reduction of eddy-current induced Nyquist Ghosts and sampling artifact[J]. In: Proceedings of the SMR, 3rd Annual Meeting, Nice, France, 1995. p 613.
    36. Hu X, Le TH. Artifact reduction in EPI with phase encoded reference scan[J]. Magn Reson Med 1996, 36:166–176.
    37. Buonocore MH and Gao L. Ghost artifact reduction for echo planner imaging using image phase correction [J]. Magn. Reson. Med. 1996, 38:89-100.
    38. Buonocore MH and Zhu DC. High spatial resolution EPI using an odd number of interleaves [J]. Magn. Reson. Med. 1999, 41:1199-1205.
    39. Buonocore MH and Zhu DC. Image-based Ghost correction for interleaved EPI [J]. Magn. Reson. Med. 2001, 45:96-108.
    40. Jezzard P and Clars S. Sources of distortion in functional MRI data [J]. Human brain mapping, 1999, 8:80-85.
    41. Studholme C, Constable T, Duncan JS. Accurate alignment of functional EPI data to anatomical MRI using a physics-based distortion model [J]. IEEE Trans. Med. Imag. 2000,19(11): 1115-1127.
    42. Reber PJ, Wong EC, Buxton RB, et al. Correction of off resonance-related distortion in echo planar imaging using EPI-Based field maps [J]. Magn. Rseon. Med. 1998, 39:328-330.
    43. Studholme C, Constable T, Duncan JS. Accurate alignment of functional EPI data to anatomical MRI using a physics-based distortion model [J]. IEEE Trans. Med. Imag. 2000, 19(11): 1115-1127.
    44. Chen, N., & Wyrwicz, A. M. Removal of intravoxel dephasing in gradient -echo images using a field-mapbased RF refocusing technique[J]. Magnetic Resonance in Medicine, 1999,42, 807-812.
    45. Crelier, G. R., Hoge, R. D., Munger, P., & Pike, G. B. Perfusion-based functional magnetic resonance imaging with single-shot RARE and GRASE acquisitions[J]. Magnetic Resonance in Medicine, 1999,41(1), 132-136.
    46. Yang, Q. X., Williams, G. D., Demeure, R. J., Mosher, T. J., & Smith, M. B. Removal of local field gradient artifacts in T-2*-weighted images at high fields by gradient-echo slice excitationprofile imaging[J]. Magnetic Resonance in Medicine, 1998,39(3), 402-409.
    47. S. Boll. Suppression of acoustic noise in speech using spectral subtraction[J]. IEEE Trans. Acoust., Speech, Signal Process., 1979, 27: 113-120..
    48. C. Windischberger, H. Langenberger, T. Sycha et al. On the origin of respiratory artifacts in BOLD-EPI of the human brain[J]. Magnetic Resonance Imaging, 2002, 20:575-582.
    49. Sunil D, Philipos C. Loizou. A multi-band spectral substraction method for enhancing speech corrupt by color noise[C]. Proceedings of ICASSP-2002, Orlando, FL, May 2002.
    50. M. Berouti, R. Schwartz, and J. Makhoul. Enhancement of speech corrupted by acoustic noise[C]. Proc.IEEE Int. Conf. Acoust., Speech, Signal Process., Apr. 1979, 208-211.
    51. T. Youssef, A. M. Youssef, S.M. aconte. Nonparametric suppression of random and physiological noise components in functional magnetic resonance imaging using cross-correlation spectrum suntraction[J]. SPIE USE, 2003, 2: 5031-5036.
    52. 包尚联 现代医学影像物理学[Z]. 北京:北京大学医学出版社,2004.
    53. Friston KJ, Holmes AP, Poline JB, et al. Analysis of fMRI time-series revisited[J]. NeuroImage, 1995, 2:45-53.
    54. Baune A, Sommer FT, Erb M, et al. Dynamical cluster analysis of cortical fMRI activation[J]. NeuroImage, 1999, 9:477-489.
    55. Friston KJ, Phillips J, Chawla D, et al. Revealing interactions among brain systems with nonlinear PCA[J]. Human Brain Mapping, 1999, 8:92-97.
    56. Mckeown MJ, Makeig S, Brown GG, et al. Analysis of fMRI data by blind separation into independent spatial compenents[J]. Human Brain Mapping, 1998, 6:160-188.
    57. Comon P. Independent component analysis-A new concept[J]?Signal Processing, 1994, 36:287-314.
    58. Bell A, Sejnowski T. An information-maximization approach to blind separation and blind deconvolution[J]. Neural Computation, 1995, 7:1129-1159.
    59. Hyvarinen A, Oja E. Independent component analysis: algorithm and applications[J]. Neural Networks, 2000, 13:411-430.
    60. C.G. Thomas, R. A. Harshman, R. S. Menon. Noise reduction in BOLD-based fMRI using component analysis[J]. NeuroImage, 2002, 17: 1521-1537.
    61. L. Frank, R. Buxton et al. Estimation of respiration-induced noise fluctuations from undersampled multislice fMRI data[J]. Magn Reson Med, vol. 45, pp. 635-644, April 2001.
    62. Wowk B, McIntyre MC et al. K-space detection and correction of physiological artifacts in fMRI[J]. Magn Reson Med, 1998, 38:1029-1034.
    63. Alistair M. Howseman, Oliver Josephs, et al. Special issues in Functional Magnetic Resonance imaging. http://www.fil.ion.ucl.ac.uk/spm/doc/books/hbf1/Ch9.pdf, 1997.