On signal reconstruction algorithms and speedup opportunities

Compressive Sensing (CS) reduces sampling data at the cost of increased signal reconstruction time. This problem has been addressed by a different set of algorithmic approaches under various realistic assumptions. Graphical Processing Units (GPU), Multicore architectures, distributed cloud computing are among technologies used to speed up data intensive and compute intensive algorithms. In this study, state of the art sample reconstruction algorithms (SRA) have been presented and surveyed. Opportunities to speed up their performances using parallel & distributed computing platforms have been also investigated and summarized. Finally, the study concludes with a detailed list of project ideas for further developments of these algorithms.

[1]  Aggelos K. Katsaggelos,et al.  Deep fully-connected networks for video compressive sensing , 2016, Digit. Signal Process..

[2]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[3]  Emmanuel J. Candès,et al.  Quantitative Robust Uncertainty Principles and Optimally Sparse Decompositions , 2004, Found. Comput. Math..

[4]  R. Tibshirani,et al.  Least angle regression , 2004, math/0406456.

[5]  K. Bredies,et al.  Iterative soft-thresholding converges linearly , 2007 .

[6]  Akram Aldroubi,et al.  Perturbations of measurement matrices and dictionaries in compressed sensing , 2012 .

[7]  Tinoosh Mohsenin,et al.  Accelerating compressive sensing reconstruction OMP algorithm with CPU, GPU, FPGA and domain specific many-core , 2015, 2015 IEEE International Symposium on Circuits and Systems (ISCAS).

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

[9]  Justin Ziniel,et al.  Fast bayesian matching pursuit , 2008, 2008 Information Theory and Applications Workshop.

[10]  Wei Lu,et al.  Modified Basis Pursuit Denoising(modified-BPDN) for noisy compressive sensing with partially known support , 2009, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing.

[11]  Fred Godtliebsen,et al.  On the use of Gibbs priors for Bayesian image restoration , 1997, Signal Process..

[12]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[13]  Jérôme Darbon,et al.  A Simple Compressive Sensing Algorithm for Parallel Many-Core Architectures , 2013, J. Signal Process. Syst..

[14]  Rabab Kreidieh Ward,et al.  Distributed Compressive Sensing: A Deep Learning Approach , 2015, IEEE Transactions on Signal Processing.

[15]  P. Campadelli,et al.  Intrinsic Dimension Estimation: Relevant Techniques and a Benchmark Framework , 2015 .

[16]  Ali Bilgin,et al.  Randomized Iterative Hard Thresholding for Sparse Approximations , 2014, 2014 Data Compression Conference.

[17]  Peter Bühlmann.  Regression shrinkage and selection via the Lasso: a retrospective (Robert Tibshirani): Comments on the presentation , 2011 .

[18]  Zhiqiang Xu,et al.  Compressed Sensing Matrices From Fourier Matrices , 2013, IEEE Transactions on Information Theory.

[19]  Karin Schnass,et al.  Dictionary Identification—Sparse Matrix-Factorization via $\ell_1$ -Minimization , 2009, IEEE Transactions on Information Theory.

[20]  G. Giannakis,et al.  Distributed spectrum sensing for cognitive radios by exploiting sparsity , 2008, 2008 42nd Asilomar Conference on Signals, Systems and Computers.

[21]  F. Santosa,et al.  Linear inversion of ban limit reflection seismograms , 1986 .

[22]  E. Candès,et al.  Sparsity and incoherence in compressive sampling , 2006, math/0611957.

[23]  Enrico Magli,et al.  PISTA: Parallel Iterative Soft Thresholding algorithm for sparse image recovery , 2013, 2013 Picture Coding Symposium (PCS).

[24]  Justin P. Haldar,et al.  Accelerating advanced MRI reconstructions on GPUs , 2008, J. Parallel Distributed Comput..

[25]  Yi Shen,et al.  GA-BFO based signal reconstruction for compressive sensing , 2013, 2013 IEEE International Conference on Information and Automation (ICIA).

[26]  Stephen J. Wright,et al.  Toeplitz-Structured Compressed Sensing Matrices , 2007, 2007 IEEE/SP 14th Workshop on Statistical Signal Processing.

[27]  Eero P. Simoncelli,et al.  Sparse decomposition of transformation-invariant signals with continuous basis pursuit , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[28]  João M. F. Xavier,et al.  Distributed Basis Pursuit , 2010, IEEE Transactions on Signal Processing.

[29]  Chinmay Hegde,et al.  Random Projections for Manifold Learning , 2007, NIPS.

[30]  Graeme Pope,et al.  Compressive sensing: a summary of reconstruction algorithms , 2009 .

[31]  Gennian Ge,et al.  Deterministic Construction of Compressed Sensing Matrices via Algebraic Curves , 2012, IEEE Transactions on Information Theory.

[32]  Dennis Sundman,et al.  Greedy Algorithms for Distributed Compressed Sensing , 2014 .

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

[34]  J. Claerbout,et al.  Robust Modeling With Erratic Data , 1973 .

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

[36]  João Manuel R. S. Tavares,et al.  Reconstruction Algorithms in Compressive Sensing : An Overview , 2016 .

[37]  Emmanuel J. Candès,et al.  Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? , 2004, IEEE Transactions on Information Theory.

[38]  R. Tibshirani,et al.  Regression shrinkage and selection via the lasso: a retrospective , 2011 .

[39]  Meenakshi,et al.  A Survey of Compressive Sensing Based Greedy Pursuit Reconstruction Algorithms , 2015 .

[40]  Mona Singh,et al.  Computational solutions for omics data , 2013, Nature Reviews Genetics.

[41]  Deanna Needell,et al.  CoSaMP: Iterative signal recovery from incomplete and inaccurate samples , 2008, ArXiv.