基于全變分?jǐn)U展方法的壓縮感知磁共振成像算法研究
doi: 10.11999/JEIT150179 cstr: 32379.14.JEIT150179
-
1.
(浙江理工大學(xué)信息學(xué)院 杭州 310018) ②(中國(guó)計(jì)量學(xué)院生物醫(yī)學(xué)工程系 杭州 310018)
基金項(xiàng)目:
國(guó)家自然科學(xué)基金(61272311)，浙江省自然科學(xué)基金(LY14F010022, LZ15F020004)，浙江省科技廳公益項(xiàng)目(2013C31021, 2015C31075)，浙江省科技廳國(guó)際科技合作研究項(xiàng)目(2013C24019)，浙江省儀器科學(xué)與技術(shù)重中之重學(xué)科開(kāi)放基金和浙江理工大學(xué)521人才培養(yǎng)計(jì)劃
The Study of Compressed Sensing MR Image Reconstruction Algorithm Based on the Extension of Total Variation Method
-
1.
(School of Information Science and Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China)
-
2.
(School of Information Science and Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China)
Funds:
The National Natural Science Foundation of China (61272311)
-
摘要: 針對(duì)全變分算法在壓縮感知磁共振成像(CS-MRI)重構(gòu)過(guò)程中存在階梯效應(yīng)的問(wèn)題，該文研究3種基于全變分?jǐn)U展方法的CS-MRI成像算法，即高階全變分、總廣義變分和組合稀疏全變分，并將其與平移不變離散小波稀疏基相結(jié)合，建立稀疏模型，采用快速?gòu)?fù)合分裂算法求解CS-MRI重構(gòu)的凸優(yōu)化問(wèn)題。同時(shí)，討論了全變分及其擴(kuò)展方法對(duì)兩種不同磁共振圖像數(shù)據(jù)和徑向欠采樣模式重構(gòu)CS-MRI的精度。實(shí)驗(yàn)結(jié)果表明，基于全變分?jǐn)U展的重構(gòu)算法能有效解決全變分重建中存在階梯效應(yīng)的缺點(diǎn)；另外，相比高階全變分和總廣義變分重構(gòu)算法，組合稀疏全變分方法具有更好的重建效果，獲得更高重構(gòu)信噪比。
-
關(guān)鍵詞:
- 磁共振圖像 /
- 壓縮感知 /
- 全變分?jǐn)U展算法 /
- 組合稀疏
Abstract: The Total Variation (TV) method is often used to reconstruct the Compressed Sensing Magnetic Resonance Imaging (CS-MRI), however, it can generate the stair effect in the reconstructed MR image. In this paper, there types of TV extension based methods, i.e. High Degree Total Variation (HDTV), Total Generalize Variation (TGV) and Group-Sparsity Total Variation (GSTV), are proposed to implement the sparse reconstruction of MR image. In addition, the shift-invariant discrete wavelet transform are integrated into these TV extension based methods as the sparsifying transform. The Fast Composite Splitting Algorithm (FCSA) is adopted to solve the convex optimization problem of CS-MRI reconstruction. And the Two different types of MR images with radial sampling trajectory are used to validate the reconstruction performance of CS-MRI by using the TV extension methods. The experiment results show that the TV extension based models can overcome the shortcomings of TV based model. Moreover, compared with HDTV and TGV methods, the GSTV method can obviously improve the reconstruction quality with higher Signal-to-Noise Ratio (SNR). -
Cands E J, Romberg J, and Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory, 2006, 52(2): 489-509. Donoho D L. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306. 婁靜濤, 李永樂(lè), 譚樹(shù)人, 等. 基于全變分的全向圖像稀疏重構(gòu)算法[J]. 電子學(xué)報(bào), 2014, 44(2): 243-249. Lou Jing-tao, Li Yong-le, Tan Shu-ren, et al.. Sparse reconstruction for omnidirectional image based on total variation[J]. Acta Electronica Sinica, 2014, 44(2): 243-249. 李然, 干宗良, 崔子冠, 等. 聯(lián)合時(shí)空特征的視頻分塊壓縮感知重構(gòu)[J]. 電子與信息學(xué)報(bào), 2014, 36(2): 285-292. Li Ran, Gan Zong-liang, Cui Zi-guan, et al.. Block compressed sensing reconstruction of video combined with temporal-spatial characteristics[J]. Journal of Electronics Information Technology, 2014, 36(2): 285-292. Lustig M, Donoho D L, and Pauly J M. Sparse MRI: the application of compressed sensing for rapid MR Imaging[J]. Magnetic Resonance in Medicine, 2007, 58(6): 1182-1195. Hu Y and Jacob M. Higher Degree Total Variation (HDTV) regularization for image recovery[J]. IEEE Transactions on Image Processing, 2012, 21(5): 2559-2571. Guo W, Qin J, and Yin W. A new detail-preserving regularity scheme[J]. SIAM Journal on Imaging Sciences, 2014, 7(2): 1309-1334. Selesnick I W and Chen P. Total variation denoising with overlapping group sparsity[C]. IEEE International Conference Acoust, Speech, Signal Processing (ICASSP), Vancouver, Canada, 2013: 1-5. Zhang S, Block K T, and Frahm J. Magnetic resonance imaging in real time: advances using radial FLASH[J]. Journal of Magnetic Resonance Imaging, 2010, 31(1): 101-109. Huang J, Zhang S, and Metaxas D. Efficient MR image reconstruction for compressed MR imaging[J]. Medical Image Analysis, 2011, 15(5): 670-679. Ning B, Qu X, Guo D, et al.. Magnetic resonance image reconstruction using trained geometric directions in 2D redundant wavelets domain and non-convex optimization[J]. Magnetic Resonance Imaging, 2013, 31(9): 1611-1622. Qu X, Hou Y, Lam F, et al.. Magnetic resonance image reconstruction from undersampled measurements using a patch-based nonlocal operator[J]. Medical Image Analysis, 2014, 18(6): 843-856. Jiang M , Jin J, Liu F, et al.. Sparsity-constrained SENSE reconstruction: an efficient implementation using a fast composite splitting algorithm[J]. Magnetic Resonance Imaging, 2013, 31(7): 1218-1227. Figueiredo M, Bioucas-Dias J, and Nowak R. Majorization minimization algorithms for wavelet-based image restoration[J]. IEEE Transactions on Image Processing, 2007, 16(12): 2980-2991. He B, Liao L Z, Han D, et al.. A new inexact alternating directions method for monotone variational inequalities[J]. Mathematical Programming, 2002, 92(1): 103-118. Jung H, Ye J C, and Kim E Y. Improved k-t BLAST and k-t SENSE using FOCUSS[J]. Physics in Medicine and Biology, 2007, 52(11): 3201-3226. -
計(jì)量
- 文章訪問(wèn)數(shù): 1710
- HTML全文瀏覽量: 177
- PDF下載量: 739
- 被引次數(shù): 0
下載:
