CG-M-FOCUSS and Its Application to Distributed Compressed Sensing

M-FOCUSS is one of the most successful and efficient methods for sparse representation. To reduce the computational cost of M-FOCUSS and to extend its availability for large scale problems, M-FOCUSS is extended to CG-M-FOCUSS by incorporating conjugate gradient (CG) iterations in this paper. Furthermore, the CG-M-FOCUSS is applied to distributed compressed sensing. We illustrate the performance of CG-M-FOCUSS by an MRI image reconstruction example, in which CG-M- FOCUSS can not only reconstruct the MRI image with high precision, but also considerably reduce the computational time.

[1]  Bhaskar D. Rao,et al.  An affine scaling methodology for best basis selection , 1999, IEEE Trans. Signal Process..

[2]  Michael Zibulevsky,et al.  Underdetermined blind source separation using sparse representations , 2001, Signal Process..

[3]  Bhaskar D. Rao,et al.  Signal processing with the sparseness constraint , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[4]  R.G. Baraniuk,et al.  Compressive Sensing [Lecture Notes] , 2007, IEEE Signal Processing Magazine.

[5]  Ting Sun,et al.  Single-pixel imaging via compressive sampling , 2008, IEEE Signal Process. Mag..

[6]  I F Gorodnitsky,et al.  Neuromagnetic source imaging with FOCUSS: a recursive weighted minimum norm algorithm. , 1995, Electroencephalography and clinical neurophysiology.

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

[8]  Stephen P. Boyd,et al.  An Interior-Point Method for Large-Scale $\ell_1$-Regularized Least Squares , 2007, IEEE Journal of Selected Topics in Signal Processing.

[9]  Joseph F. Murray,et al.  Dictionary Learning Algorithms for Sparse Representation , 2003, Neural Computation.

[10]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[11]  Stephen J. Wright,et al.  Numerical Optimization (Springer Series in Operations Research and Financial Engineering) , 2000 .

[12]  R.G. Baraniuk,et al.  Distributed Compressed Sensing of Jointly Sparse Signals , 2005, Conference Record of the Thirty-Ninth Asilomar Conference onSignals, Systems and Computers, 2005..

[13]  Stéphane Mallat,et al.  Matching pursuits with time-frequency dictionaries , 1993, IEEE Trans. Signal Process..

[14]  Mineichi Kudo,et al.  Performance analysis of minimum /spl lscr//sub 1/-norm solutions for underdetermined source separation , 2004, IEEE Transactions on Signal Processing.

[15]  K. Kreutz-Delgado,et al.  Deriving algorithms for computing sparse solutions to linear inverse problems , 1997, Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136).

[16]  Andrzej Cichocki,et al.  Adaptive Blind Signal and Image Processing - Learning Algorithms and Applications , 2002 .

[17]  Yuanqing Li,et al.  Analysis of Sparse Representation and Blind Source Separation , 2004, Neural Computation.

[18]  Bhaskar D. Rao,et al.  Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm , 1997, IEEE Trans. Signal Process..

[19]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[20]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[21]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[22]  Bhaskar D. Rao,et al.  Sparse solutions to linear inverse problems with multiple measurement vectors , 2005, IEEE Transactions on Signal Processing.

[23]  D. Donoho,et al.  Maximal Sparsity Representation via l 1 Minimization , 2002 .

[24]  Richard G. Baraniuk,et al.  Compressive Sensing , 2008, Computer Vision, A Reference Guide.

[25]  Joel A. Tropp,et al.  Greed is good: algorithmic results for sparse approximation , 2004, IEEE Transactions on Information Theory.

[26]  Michael Elad,et al.  Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[27]  Daniel W. C. Ho,et al.  Underdetermined blind source separation based on sparse representation , 2006, IEEE Transactions on Signal Processing.

[28]  M. Hestenes,et al.  Methods of conjugate gradients for solving linear systems , 1952 .