Accelerating dynamic magnetic resonance imaging by nonlinear sparse coding

Although being high-dimensional, dynamic magnetic resonance images usually lie on low-dimensional manifolds. Nonlinear models have been shown to capture well that latent low-dimensional nature of data, and can thus lead to improvements in the quality of constrained recovery algorithms. This paper advocates a novel reconstruction algorithm for dynamic magnetic resonance imaging (dMRI) based on nonlinear dictionary learned from low-spatial but high-temporal resolution images. The nonlinear dictionary is initially learned using kernel dictionary learning, and the proposed algorithm subsequently alternates between sparsity enforcement in the feature space and the data-consistency constraint in the original input space. Extensive numerical tests demonstrate that the proposed scheme is superior to popular methods that use linear dictionaries learned from the same set of training data.

[1]  Michael Elad,et al.  Linearized Kernel Dictionary Learning , 2015, IEEE Journal of Selected Topics in Signal Processing.

[2]  Mariya Doneva,et al.  Compressed sensing reconstruction for magnetic resonance parameter mapping , 2010, Magnetic resonance in medicine.

[3]  Leslie Ying,et al.  Dynamic magnetic resonance imaging using compressed sensing with self-learned nonlinear dictionary (NL-D) , 2015, 2015 IEEE 12th International Symposium on Biomedical Imaging (ISBI).

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

[5]  Y. C. Pati,et al.  Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

[6]  Justin P. Haldar,et al.  Further development of image reconstruction from highly undersampled (k, t)-space data with joint partial separability and sparsity constraints , 2011, 2011 IEEE International Symposium on Biomedical Imaging: From Nano to Macro.

[7]  Mathews Jacob,et al.  A blind compressive sensing frame work for accelerated dynamic MRI , 2012, 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI).

[8]  Alexander J. Smola,et al.  Learning with Kernels: support vector machines, regularization, optimization, and beyond , 2001, Adaptive computation and machine learning series.

[9]  A. Atiya,et al.  Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond , 2005, IEEE Transactions on Neural Networks.

[10]  Sebastian Kozerke,et al.  MRI temporal acceleration techniques , 2012, Journal of magnetic resonance imaging : JMRI.

[11]  Gunnar Rätsch,et al.  Kernel PCA and De-Noising in Feature Spaces , 1998, NIPS.

[12]  Kjersti Engan,et al.  Method of optimal directions for frame design , 1999, 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258).

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

[14]  Daniel Rueckert,et al.  Dictionary Learning and Time Sparsity for Dynamic MR Data Reconstruction , 2014, IEEE Transactions on Medical Imaging.

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

[16]  Mathews Jacob,et al.  Accelerated Dynamic MRI Exploiting Sparsity and Low-Rank Structure: k-t SLR , 2011, IEEE Transactions on Medical Imaging.

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

[18]  A. Bruckstein,et al.  K-SVD : An Algorithm for Designing of Overcomplete Dictionaries for Sparse Representation , 2005 .

[19]  Hanchao Qi,et al.  Using the kernel trick in compressive sensing: Accurate signal recovery from fewer measurements , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

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

[21]  Leslie Ying,et al.  Compressed Sensing Dynamic Cardiac Cine MRI Using Learned Spatiotemporal Dictionary , 2014, IEEE Transactions on Biomedical Engineering.

[22]  Leslie Ying,et al.  A kernel-based compressed sensing approach to dynamic MRI from highly undersampled data , 2013, 2013 IEEE 10th International Symposium on Biomedical Imaging.

[23]  Rama Chellappa,et al.  Kernel dictionary learning , 2012, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[24]  Bernhard Schölkopf,et al.  Kernel Principal Component Analysis , 1997, ICANN.

[25]  P. Lauterbur,et al.  An efficient method for dynamic magnetic resonance imaging , 2002, 5th IEEE EMBS International Summer School on Biomedical Imaging, 2002..

[26]  Leslie Ying,et al.  Undersampled dynamic magnetic resonance imaging using kernel principal component analysis , 2014, 2014 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

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

[28]  Sebastian Kozerke,et al.  4497 MR Image Reconstruction Exploiting Nonlinear Transforms , 2013 .