Two-part reconstruction in compressed sensing

Two-part reconstruction is a framework for signal recovery in compressed sensing (CS), in which the advantages of two different algorithms are combined. Our framework allows to accelerate the reconstruction procedure without compromising the reconstruction quality. To illustrate the efficacy of our two-part approach, we extend the author's previous Sudocodes algorithm and make it robust to measurement noise. In a 1-bit CS setting, promising numerical results indicate that our algorithm offers both a reduction in run-time and improvement in reconstruction quality.

[1]  Prateek Jain,et al.  One-Bit Compressed Sensing: Provable Support and Vector Recovery , 2013, ICML.

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

[3]  Laurent Jacques,et al.  Robust 1-Bit Compressive Sensing via Binary Stable Embeddings of Sparse Vectors , 2011, IEEE Transactions on Information Theory.

[4]  J. Tropp,et al.  CoSaMP: Iterative signal recovery from incomplete and inaccurate samples , 2008, Commun. ACM.

[5]  M. A. Iwen,et al.  Compressed sensing with sparse binary matrices: Instance optimal error guarantees in near-optimal time , 2013, J. Complex..

[6]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[7]  Piotr Indyk.  Explicit constructions for compressed sensing of sparse signals , 2008, SODA '08.

[8]  S. Frick,et al.  Compressed Sensing , 2014, Computer Vision, A Reference Guide.

[9]  Richard G. Baraniuk,et al.  1-Bit compressive sensing , 2008, 2008 42nd Annual Conference on Information Sciences and Systems.

[10]  Mike E. Davies,et al.  Iterative Hard Thresholding for Compressed Sensing , 2008, ArXiv.

[11]  Richard G. Baraniuk,et al.  Sudocodes ߝ Fast Measurement and Reconstruction of Sparse Signals , 2006, 2006 IEEE International Symposium on Information Theory.

[12]  Nazanin Rahnavard,et al.  GBCS: A two-step compressive sensing reconstruction based on group testing and basis pursuit , 2011, 2011 - MILCOM 2011 Military Communications Conference.

[13]  Piotr Indyk,et al.  Combining geometry and combinatorics: A unified approach to sparse signal recovery , 2008, 2008 46th Annual Allerton Conference on Communication, Control, and Computing.

[14]  A. Robert Calderbank,et al.  Efficient and Robust Compressed Sensing Using Optimized Expander Graphs , 2009, IEEE Transactions on Information Theory.