Iterative feature refinement for accurate undersampled MR image reconstruction

Accelerating MR scan is of great significance for clinical, research and advanced applications, and one main effort to achieve this is the utilization of compressed sensing (CS) theory. Nevertheless, the existing CSMRI approaches still have limitations such as fine structure loss or high computational complexity. This paper proposes a novel iterative feature refinement (IFR) module for accurate MR image reconstruction from undersampled K-space data. Integrating IFR with CSMRI which is equipped with fixed transforms, we develop an IFR-CS method to restore meaningful structures and details that are originally discarded without introducing too much additional complexity. Specifically, the proposed IFR-CS is realized with three iterative steps, namely sparsity-promoting denoising, feature refinement and Tikhonov regularization. Experimental results on both simulated and in vivo MR datasets have shown that the proposed module has a strong capability to capture image details, and that IFR-CS is comparable and even superior to other state-of-the-art reconstruction approaches.

[1]  F Liu,et al.  Compressed sensing MRI combined with SENSE in partial k-space , 2012, Physics in medicine and biology.

[2]  Jing Yuan,et al.  PANDA‐ T1ρ : Integrating principal component analysis and dictionary learning for fast T1ρ mapping , 2015, Magnetic resonance in medicine.

[3]  Sylvain Paris,et al.  Error-Tolerant Image Compositing , 2010, ECCV.

[4]  L. Ying,et al.  Sensitivity encoding reconstruction with nonlocal total variation regularization , 2011, Magnetic resonance in medicine.

[5]  L. Ying,et al.  Accelerating SENSE using compressed sensing , 2009, Magnetic resonance in medicine.

[6]  Leon Axel,et al.  Combination of Compressed Sensing and Parallel Imaging for Highly-Accelerated 3 D First-Pass Cardiac Perfusion MRI , 2009 .

[7]  Wotao Yin,et al.  An Iterative Regularization Method for Total Variation-Based Image Restoration , 2005, Multiscale Model. Simul..

[8]  Eero P. Simoncelli,et al.  Image quality assessment: from error visibility to structural similarity , 2004, IEEE Transactions on Image Processing.

[9]  Michael Lustig,et al.  k-t SPARSE: High frame rate dynamic MRI exploiting spatio-temporal sparsity , 2006 .

[10]  M. Elad,et al.  $rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation , 2006, IEEE Transactions on Signal Processing.

[11]  Luo Jianhua,et al.  Adaptive Image Decomposition by Improved Bilateral Filter , 2011 .

[12]  Wei Lin,et al.  A rapid and robust numerical algorithm for sensitivity encoding with sparsity constraints: Self‐feeding sparse SENSE , 2010, Magnetic resonance in medicine.

[13]  D. Donoho,et al.  Sparse MRI: The application of compressed sensing for rapid MR imaging , 2007, Magnetic resonance in medicine.

[14]  Rachid Deriche,et al.  Regularizing Flows for Constrained Matrix-Valued Images , 2004 .

[15]  Michael Elad,et al.  Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries , 2006, IEEE Transactions on Image Processing.

[16]  Dong Liang,et al.  Undersampled MR Image Reconstruction with Data-Driven Tight Frame , 2015, Comput. Math. Methods Medicine.

[17]  Kieren Grant Hollingsworth,et al.  Reducing acquisition time in clinical MRI by data undersampling and compressed sensing reconstruction , 2015, Physics in medicine and biology.

[18]  Rama Chellappa,et al.  Gradient-Based Image Recovery Methods From Incomplete Fourier Measurements , 2012, IEEE Transactions on Image Processing.

[19]  Yoram Bresler,et al.  MR Image Reconstruction From Highly Undersampled k-Space Data by Dictionary Learning , 2011, IEEE Transactions on Medical Imaging.

[20]  Robert D. Nowak,et al.  An EM algorithm for wavelet-based image restoration , 2003, IEEE Trans. Image Process..

[21]  Gabriel Peyré,et al.  The Numerical Tours of Signal Processing , 2011, Computing in Science & Engineering.

[22]  L. Ying,et al.  Regularized sensitivity encoding (SENSE) reconstruction using bregman iterations , 2009, Magnetic resonance in medicine.

[23]  Zhong Chen,et al.  Undersampled MRI reconstruction with patch-based directional wavelets. , 2012, Magnetic resonance imaging.

[24]  Jean-Michel Morel,et al.  Fast Cartoon + Texture Image Filters , 2010, IEEE Transactions on Image Processing.

[25]  Shiqian Ma,et al.  An efficient algorithm for compressed MR imaging using total variation and wavelets , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[26]  Stanley Osher,et al.  Iterative Regularization and Nonlinear Inverse Scale Space Applied to Wavelet-Based Denoising , 2007, IEEE Transactions on Image Processing.

[27]  S. Osher,et al.  Nonlinear inverse scale space methods , 2006 .

[28]  M. Lustig,et al.  Compressed Sensing MRI , 2008, IEEE Signal Processing Magazine.

[29]  Dong Liang,et al.  Highly Undersampled Magnetic Resonance Image Reconstruction Using Two-Level Bregman Method With Dictionary Updating , 2013, IEEE Transactions on Medical Imaging.

[30]  ANTONIN CHAMBOLLE,et al.  An Algorithm for Total Variation Minimization and Applications , 2004, Journal of Mathematical Imaging and Vision.

[31]  Jean-Michel Morel,et al.  A non-local algorithm for image denoising , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[32]  Dong Liang,et al.  Adaptive Dictionary Learning in Sparse Gradient Domain for Image Recovery , 2013, IEEE Transactions on Image Processing.

[33]  Dong Liang,et al.  k‐t ISD: Dynamic cardiac MR imaging using compressed sensing with iterative support detection , 2012, Magnetic resonance in medicine.

[34]  D. O. Walsh,et al.  Adaptive reconstruction of phased array MR imagery , 2000, Magnetic resonance in medicine.

[35]  Gabriel Peyré,et al.  The Numerical Tours of Signal Processing , 2011, Comput. Sci. Eng..

[36]  Junfeng Yang,et al.  A Fast Alternating Direction Method for TVL1-L2 Signal Reconstruction From Partial Fourier Data , 2010, IEEE Journal of Selected Topics in Signal Processing.

[37]  Wotao Yin,et al.  Bregman Iterative Algorithms for (cid:2) 1 -Minimization with Applications to Compressed Sensing ∗ , 2008 .

[38]  L. Bregman The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming , 1967 .

[39]  Peter Boesiger,et al.  Compressed sensing in dynamic MRI , 2008, Magnetic resonance in medicine.

[40]  Di Guo,et al.  Magnetic resonance image reconstruction using trained geometric directions in 2D redundant wavelets domain and non-convex optimization. , 2013, Magnetic resonance imaging.

[41]  Tom Goldstein,et al.  The Split Bregman Method for L1-Regularized Problems , 2009, SIAM J. Imaging Sci..

[42]  L. He,et al.  MR Image Reconstruction from Sparse Radial Samples Using Bregman Iteration , 2006 .

[43]  Jeffrey A. Fessler,et al.  Parallel MR Image Reconstruction Using Augmented Lagrangian Methods , 2011, IEEE Transactions on Medical Imaging.