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Optimized Structured Sparse Sensing Matrices for Compressive Sensing [article]

Tao Hong, Xiao Li, Zhihui Zhu, Qiuwei Li
2019 arXiv   pre-print
Moreover, a regularization is added to enforce the robustness of the optimized structured sparse sensing matrix to the sparse representation error (SRE) of signals of interests.  ...  We consider designing a robust structured sparse sensing matrix consisting of a sparse matrix with a few non-zero entries per row and a dense base matrix for capturing signals efficiently We design the  ...  Acknowledgment This research is supported in part by ERC Grant agreement No. 320649, and in part by the Intel Collaborative Research Institute for Computational Intelligence (ICRI-CI).  ... 
arXiv:1709.06895v3 fatcat:o3ul5tpmbzcu7kwcmunq6sm54y

Sparse Binary Matrices of LDPC Codes for Compressed Sensing

Weizhi Lu, Kidiyo Kpalma, Joseph Ronsin
2012 2012 Data Compression Conference  
And significantly, for this type of matrices with a given size, the optimal matrix for compressed sensing can be approximated and constructed according to some rules.  ...  Compressed sensing shows that one undetermined measurement matrix can losslessly compress sparse signals if this matrix satisfies Restricted Isometry Property (RIP).  ...  Since bigger g denotes higher orthogonality in structure for a matrix with a given degree d, LDPC matrices construction algorithms are also available to construct measurement matrices for compressed sensing  ... 
doi:10.1109/dcc.2012.60 dblp:conf/dcc/LuKR12 fatcat:n6qqd4z52vdptpusvutr6wlzwa

Adapted statistical compressive sensing: Learning to sense gaussian mixture models

Julio M. Duarte-Carvajalino, Guoshen Yu, Lawrence Carin, Guillermo Sapiro
2012 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
We show that the optimized sensing matrix outperforms random sampling matrices originally exploited both in CS and SCS.  ...  This follows the paradigm of statistical compressive sensing (SCS), where a statistical model, a GMM in particular, replaces the standard sparsity model of classical compressive sensing (CS), leading to  ...  The authors would like to thank David Brady, Robert Calderbank, Wotao Yin, and Stan Osher for feedback on the work here reported.  ... 
doi:10.1109/icassp.2012.6288708 dblp:conf/icassp/Duarte-CarvajalinoYCS12 fatcat:tsoforaj7zaqja57xr4swcrwku

Overview of Compressed Sensing: Sensing Model, Reconstruction Algorithm, and Its Applications

Yuan Fang, Lixiang Li, Liwei Liu, Haipeng Peng, Jürgen Kurths, Yixian Yang
2020 Applied Sciences  
First, we introduce several common sensing methods for CS, like sparse dictionary sensing, block-compressed sensing, and chaotic compressed sensing.  ...  Lastly, we offer recommendation for broad CS applications, such as data compression, image processing, cryptography, and the reconstruction of complex networks.  ...  There are many classical sensing matrices, such as the random, deterministic, and structured random matrices. The Gaussian and Bernoulli matrices are typical random matrices.  ... 
doi:10.3390/app10175909 fatcat:pkbbog5khjdqhj73dwergi62he

Measure What Should be Measured: Progress and Challenges in Compressive Sensing

Thomas Strohmer
2012 IEEE Signal Processing Letters  
In this paper I discuss some of the recent progress in compressive sensing and point out key challenges and opportunities as the area of compressive sensing and sparse representations keeps evolving.  ...  Is compressive sensing overrated? Or can it live up to our expectations? What will come after compressive sensing and sparsity? And what has Galileo Galilei got to do with it?  ...  Structured sensing matrices Much of the theory concerning explicit performance bounds for compressive sensing revolves around Gaussian and other random matrices.  ... 
doi:10.1109/lsp.2012.2224518 fatcat:tswgkgjqkbblnmeajkq5smilea

Sparsification of Matrices and Compressed Sensing [article]

Fintan Hegarty, Padraig Ó Catháin, Yunbin Zhao
2018 arXiv   pre-print
Potential applications have motivated the search for constructions of sparse compressed sensing matrices (i.e., matrices containing few non-zero entries).  ...  Many probabilistic matrix constructions have been proposed, and it is now well known that matrices with entries drawn from a suitable probability distribution are essentially optimal for compressed sensing  ...  First we survey some previous work on sparse compressed sensing matrices.  ... 
arXiv:1506.03523v4 fatcat:6xzmccllefcbzeoaip6dasjv7m

Book Review: A mathematical introduction to compressive sensing

Joel A. Tropp
2016 Bulletin of the American Mathematical Society  
Many thanks to Richard Baraniuk, John Bruer, Mark Davenport, Anna Gilbert, Michael McCoy, and Madeleine Udell for their contributions.  ...  We have machinery for developing optimization problems that can enforce various types of structure.  ...  See [CRPW12, ALMT14, TOH15] for some others. Compressed sensing also makes a vigorous argument for the importance of convex optimization.  ... 
doi:10.1090/bull/1546 fatcat:qoslzikju5hwxc6rf2orsi42wy

Sparsification of Matrices and Compressed Sensing

F. Hegarty, P. Ó Catháin, Y. Zhao
2018 Irish Mathematical Society Bulletin  
Potential applications have motivated the search for constructions of sparse compressed sensing matrices (i.e., matrices containing few non-zero entries).  ...  Many probabilistic matrix constructions have been proposed, and it is now well known that matrices with entries drawn from a suitable probability distribution are essentially optimal for compressed sensing  ...  First we survey some previous work on sparse compressed sensing matrices.  ... 
doi:10.33232/bims.0081.5.22 fatcat:o6qy6jjghjcqjkmzb6xd4ing7m

Overcomplete compressed sensing of ray space for generating free viewpoint images

Qiang Yao, Keita Takahashi, Toshiaki Fujii
2013 2013 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference  
In this paper, we focus on compressed sensing to sparsely capture a ray space at encoder and reconstruct it at decoder.  ...  sensed data.  ...  COMPRESSED SENSING AND SPARSE REPRESENTATION In this section, we briefly review the background of compressed sensing and sparse representation.  ... 
doi:10.1109/apsipa.2013.6694266 dblp:conf/apsipa/YaoTF13 fatcat:nr56stm2gnbb5glwqcl4iskamm

Compressed sensing with sparse, structured matrices

Maria Chiara Angelini, Federico Ricci-Tersenghi, Yoshiyuki Kabashima
2012 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
In the context of the compressed sensing problem, we propose a new ensemble of sparse random matrices which allow one (i) to acquire and compress a ρ0-sparse signal of length N in a time linear in N and  ...  More generally, we show that several ensembles of dense random matrices can be converted into ensembles of sparse random matrices, having the same thresholds, but much lower computational complexity.  ...  RBFR086NN1 on "Inference and Optimization in Complex Systems: From the Thermodynamics of Spin Glasses to Message Passing Algorithms".  ... 
doi:10.1109/allerton.2012.6483301 dblp:conf/allerton/AngeliniRK12 fatcat:7l4ccrywh5dvzngq3cx4bqciae

A Survey on Compressive Sensing

Shu-Tao LI, Dan WEI
The field of compressive sensing provides a stri ct er sampling condition when the signal is known to be sparse or compressible.  ...  By now, some available measurement matrices have been discovered, such as Gaussian or Bernoulli independent and identically distributed (i.i.d) random matrices, scrambled Fourier matrix and some structurally  ...  Of Electronics & Telecommunication, Vishwakarma Institute of Technology, for his help in the field of optimization.  ... 
doi:10.3724/sp.j.1004.2009.01369 fatcat:timna6siirgzzc4yqshwf4wlwe

State of the art and prospects of structured sensing matrices in compressed sensing

Kezhi Li, Shuang Cong
2015 Frontiers of Computer Science  
Compressed sensing (CS) enables people to acquire the compressed measurements directly and recover sparse or compressible signals faithfully even when the sampling rate is much lower than the Nyquist rate  ...  However, the pure random sensing matrices usually require huge memory for storage and high computational cost for signal reconstruction.  ...  State of the Art and Prospects of Structured Sensing Matrices in Compressed Sensing Fig. 2 Block diagram for the random demodulator.  ... 
doi:10.1007/s11704-015-3326-8 fatcat:ftl6hdkjdvaqflxcjo2imcn26a

Reconstruction of Compressively Sensed Images using Convex Tikhonov Sparse Dictionary Learning and Adaptive Spectral Filtering [article]

Nishant Deepak Keni, Amol Mangirish Singbal, Rizwan Ahmed
2019 arXiv   pre-print
Consequently, high PSNR and low MSE is obtained using the proposed algorithm for our compressive sensing framework.  ...  In this article, we use a closed form stabilized convex optimization technique for both sparse coding and dictionary learning.  ...  compressively sensed images without assuming any structure in the sensed images.  ... 
arXiv:1801.09135v2 fatcat:cufxwsrievcztif26kwoyksv4e

Optimizing Matrices For Compressed Sensing Using Existing Goodness Measures: Negative Results, And An Alternative [article]

Alankar Kotwal, Ajit Rajwade
2017 arXiv   pre-print
We then introduce a paradigm for optimizing sensing matrices that overcomes the looseness of compressed sensing upper bounds using an average case error approach.  ...  The bound that arises out of sparse recovery analysis in compressed sensing involves input signal sparsity and some property of the sensing matrix.  ...  Do there exist principled and mathematically founded ways to find matrices that are 'optimal', in some sense, for recovery using compressed sensing methods?  ... 
arXiv:1707.03355v1 fatcat:hogj7l7eendkdd4zredxeqevie

Deep Unfolding Basis Pursuit: Improving Sparse Channel Reconstruction via Data-Driven Measurement Matrices [article]

Pengxia Wu, Julian Cheng
2022 arXiv   pre-print
The obtained data-driven measurement matrices are applied to existing sparse reconstruction algorithms, leading to flexible hybrid data-driven implementations for sparse channel estimation.  ...  Existing sparse channel estimation schemes widely adopt random measurement matrices, which have been criticized for their suboptimal reconstruction performance.  ...  Therefore, the random matrices are default choices for compressed sensing with a sufficiently large value of M .  ... 
arXiv:2007.05177v3 fatcat:zchgghdcwzglpa44ytbgepww5a
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