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On the Compressed Measurements over Finite Fields: Sparse or Dense Sampling [article]

Jin-Taek Seong, Heung-No Lee
2012 arXiv   pre-print
Our results are obtained while the sparseness of the sensing matrices as well as the size of the finite fields are varied.  ...  One of interesting conclusions includes that unless the signal is "ultra" sparse, the sensing matrices do not have to be dense.  ...  In addition, the numbers of measurements with respect to different sparse factors are obtained.  ... 
arXiv:1211.5207v1 fatcat:7c6cipsm6bca5pf7beix3f5nl4

Sparse Binary Matrices of LDPC Codes for Compressed Sensing

Weizhi Lu, Kidiyo Kpalma, Joseph Ronsin
2012 2012 Data Compression Conference  
Compressed sensing shows that one undetermined measurement matrix can losslessly compress sparse signals if this matrix satisfies Restricted Isometry Property (RIP).  ...  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.  ...  Introduction Compressed sensing [1] - [4] shows that a sparse vector x with k nonzero entries can be losslessly compressed with an undermined measurement matrix A R m×n , where k<<n and m<<n, supposing  ... 
doi:10.1109/dcc.2012.60 dblp:conf/dcc/LuKR12 fatcat:n6qqd4z52vdptpusvutr6wlzwa

Compressed Sensing Based Apple Image Measurement Matrix Selection

Ying Xiao, Wanlin Gao, Ganghong Zhang, Han Zhang
2015 International Journal of Distributed Sensor Networks  
The purpose of this paper is to design a measurement matrix of apple image based on compressed sensing to realize low cost sampling apple image.  ...  Compressed sensing based apple image sampling method makes a breakthrough to the limitation of the Nyquist sampling theorem.  ...  Materials and Methods Theory of Compressed Sensing. Compressed sensing can sample and compress signals at the same time.  ... 
doi:10.1155/2015/901073 fatcat:zck2dflr75a4pixq7r7yrlgzxq

Compressive Sensing Algorithms for Signal Processing Applications: A Survey

Mohammed M. Abo-Zahhad, Aziza I. Hussein, Abdelfatah M. Mohamed
2015 International Journal of Communications, Network and System Sciences  
Compressed Sensing (CS), also known as compressive sampling, is a DSP technique efficiently acquiring and reconstructing a signal completely from reduced number of measurements, by exploiting its compressibility  ...  This paper gives a survey of both theoretical and numerical aspects of compressive sensing technique and its applications.  ...  By now, many papers deal with Gaussian or Bernoulli random matrices in connection with sparse recovery [13] .  ... 
doi:10.4236/ijcns.2015.86021 fatcat:vx2l5d2tunhn3cbsdtfrfjaj2a

Compressive Sensing Algorithms for Signal Processing Applications: A Survey

Mohammed M. Abo-Zahhad, Aziza I. Hussein, Abdelfatah M. Mohamed
2015 International Journal of Communications, Network and System Sciences  
Compressed Sensing (CS), also known as compressive sampling, is a DSP technique efficiently acquiring and reconstructing a signal completely from reduced number of measurements, by exploiting its compressibility  ...  This paper gives a survey of both theoretical and numerical aspects of compressive sensing technique and its applications.  ...  By now, many papers deal with Gaussian or Bernoulli random matrices in connection with sparse recovery [13] .  ... 
doi:10.4236/ijcns.2015.85021 fatcat:jklt3phauvafno3d2634pj55qi

A Survey on Compressive Sensing

Shu-Tao LI, Dan WEI
2009 ACTA AUTOMATICA SINICA  
The field of compressive sensing provides a stri ct er sampling condition when the signal is known to be sparse or compressible.  ...  Compressi ve sensing speci fically yields a sub-Nyquist sampling criterion. Compressi ve sensing contains three main problems: sparse representation, measurement matrix and reconstruction algorithm.  ...  CONCLUSION Compressive sensing has changed the way the intellectual community deals with signals especially its acquisition and compression.  ... 
doi:10.3724/sp.j.1004.2009.01369 fatcat:timna6siirgzzc4yqshwf4wlwe

Metrics for Evaluating the Efficiency of Compressing Sensing Techniques

Fatima Salahdine, Elias Ghribi, Naima Kaabouch
2020 2020 International Conference on Information Networking (ICOIN)  
Performing compressive sensing requires analyzing and investigating the efficiency of the measurement matrix and the recovery algorithm.  ...  The second is how to recover the sparse signal from few measurements.  ...  Compressive sensing involves three main processes, namely sparse representation, linear measurement, and recovery.  ... 
doi:10.1109/icoin48656.2020.9016490 dblp:conf/icoin/SalahdineGK20 fatcat:n4d5cf4jb5awzjoyh2deot7q2y

Toward deterministic compressed sensing

Jeffrey D. Blanchard
2013 Proceedings of the National Academy of Sciences of the United States of America  
This important line of research has not yet established deterministic compressed sensing performance on par with the random measurement models.  ...  In PNAS, Monajemi et al. (4) provide a major step forward in understanding the potential for deterministic measurement matrices in compressed sensing.  ... 
doi:10.1073/pnas.1221228110 pmid:23319642 pmcid:PMC3557084 fatcat:bh7p5f4byzblblhm3cglsfzwz4

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

Multiple Target Localization in WSNs Based on Compressive Sensing Using Deterministic Sensing Matrices

Thu L. N. Nguyen, Yoan Shin
2015 International Journal of Distributed Sensor Networks  
Furthermore, compressive sensing allows that a sparse signal can be reconstructed from few measurements, and choosing a suitable sensing matrix is also important.  ...  In this paper, we use compressive sensing for multiple target localization in WSNs. We formulate multiple target locations as a sparse matrix in the discrete time domain.  ...  Our proposed method is a compressive sensing using deterministic sensing matrices for multiple target localization in WSNs based on sparse and inconsistent signal measurements.  ... 
doi:10.1155/2015/947016 fatcat:5xaxifvpnbc5dony6k4knpuzim

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

Compressive Sensing [chapter]

Aswin C. Sankaranarayanan, Richard G. Baraniuk
2020 Computer Vision  
Compressive Sensing, Fig. 1 (a) Compressive sensing measurement process with a random Gaussian measurement matrix and discrete cosine transform (DCT) matrix .  ...  The vector of coefficients s is sparse with K = 4. (b) Measurement process with y = x.  ... 
doi:10.1007/978-3-030-03243-2_647-1 fatcat:g6yiupnxpve7zgvzy2fnglaaxu

Preface to the Special Issue on Sparse Approximate Solution of Linear Systems

Gitta Kutyniok, Allan Pinkus, Holger Rauhut, Vladimir Temiyakov
2014 Linear Algebra and its Applications  
sensing and sparse approximation.  ...  Within this theory the assumed prior information is that the vector x is approximately sparse, in the sense that the error of best k-term approximation min {z : z 0 ≤k} x − z , with 0024-3795/$ -see front  ...  This is precisely the content of the article on "One-bit compressed sensing with non-Gaussian measurements" by Ai, Lapanowski, Plan, and Vershynin.  ... 
doi:10.1016/j.laa.2013.06.019 fatcat:pgdhr5wjr5hntge466ytjmko44

Deterministic Compressed Sensing Matrices from Multiplicative Character Sequences [article]

Nam Yul Yu
2010 arXiv   pre-print
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements.  ...  In this paper, a K × N measurement matrix for compressed sensing is deterministically constructed via multiplicative character sequences.  ...  Numerical results revealed that the compressed sensing matrices show stable and reliable performance in matching pursuit recovery for sparse signals with or without measurement noise.  ... 
arXiv:1011.2740v1 fatcat:tnadnqshsbbe5gtmzn5wbmlsbe

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  ...  The number of measurements and the universality of different structure matrices are compared.  ...  Fig. 1 1 (a) Compressive sensing measurement process with a random Gaussian measurement matrix Φ and DCT matrix Ψ as sparsifying matrix. (b) Measurement process with Θ = ΦΨ.  ... 
doi:10.1007/s11704-015-3326-8 fatcat:ftl6hdkjdvaqflxcjo2imcn26a
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