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Weighted one-norm minimization with inaccurate support estimates: Sharp analysis via the null-space property

Hassan Mansour, Rayan Saab
2015 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
First, we provide necessary and sufficient conditions for weighted l1 minimization to successfully recovery all sparse signals whose support estimate is sufficiently accurate.  ...  The resulting number of measurements can be significantly less than what is needed to ensure recovery via l1 minimization. Finally, we illustrate our results via numerical experiments.  ...  Consequently, w-NSP(k, s, C) guarantees recovery of all s sparse signals via 1 minimization so it requires m ≥ c 1 s log( N c2s ) (see, e.g., [5, Theorem 10.11] ).  ... 
doi:10.1109/icassp.2015.7178585 dblp:conf/icassp/MansourS15 fatcat:n5fb2ci3vffbdmt75w2veacfl4

Block Based Compressed Sensing Algorithm for Medical Image Compression

S. Spurthi, Parnasree Chakraborty
2016 International Journal Of Engineering And Computer Science  
Compressed sensing exploits the sparse nature of images to reduce the volume of the data required for storage purpose.  ...  Block Compressive sensing technique has been proposed to exploit the sparse nature of medical images in a transform domain to reduce the storage space.  ...  The sparse representation means data with a small number of nonzero coefficients for a given basis (and no noise) can (with high probability) be reconstructed exactly via l1-minimization.  ... 
doi:10.18535/ijecs/v5i5.62 fatcat:bm4i5yssn5atzhgke2yswyzcli

Efficient ℓ_q Minimization Algorithms for Compressive Sensing Based on Proximity Operator [article]

Fei Wen, Yuan Yang, Peilin Liu, Rendong Ying, Yipeng Liu
2016 arXiv   pre-print
We show that the proposed algorithms are the fastest methods in solving the nonconvex ℓ_q-minimization problem, while offering competent performance in recovering sparse signals and compressible images  ...  This paper considers solving the unconstrained ℓ_q-norm (0≤ q<1) regularized least squares (ℓ_q-LS) problem for recovering sparse signals in compressive sensing.  ...  Recovery of Simulated Sparse Signals We first evaluate the performance of the algorithms using simulated signals.  ... 
arXiv:1506.05374v3 fatcat:3uhac52nlfdk5b5vbkhxaogncy

Multi-Sparse Signal Recovery for Compressive Sensing [article]

Yipeng Liu, Ivan Gligorijevic, Vladimir Matic, Maarten De Vos, Sabine Van Huffel
2012 arXiv   pre-print
Signal recovery is one of the key techniques of Compressive sensing (CS). It reconstructs the original signal from the linear sub-Nyquist measurements.  ...  Classical methods exploit the sparsity in one domain to formulate the L0 norm optimization. Recent investigation shows that some signals are sparse in multiple domains.  ...  But some signals are sparse in more than one domain.  ... 
arXiv:1206.0663v1 fatcat:n6rgghgfsrbevgi37a4on3mogu

Multi-structural Signal Recovery for Biomedical Compressive Sensing

Yipeng Liu, Maarten De Vos, Ivan Gligorijevic, Vladimir Matic, Yuqian Li, Sabine Van Huffel
2013 IEEE Transactions on Biomedical Engineering  
Results show that the newly proposed method achieves better reconstruction accuracy performance in term of both L1 and L2 errors.  ...  It reconstructs a signal from sub-Nyquist random linear measurements. Classical methods only exploit the sparsity in one domain.  ...  ACKNOWLEDGMENT The scientific responsibility of this paper is assumed by the authors.  ... 
doi:10.1109/tbme.2013.2264772 pmid:23715599 fatcat:opzkrm2465gudicedtrwt6a62i

Multi-Structural Signal Recovery for Biomedical Compressive Sensing [article]

Yipeng Liu, Maarten De Vos, Ivan Gligorijevic, Vladimir Matic, Yuqian Li, Sabine Van Huffel
2013 arXiv   pre-print
Results show that the newly proposed method achieves better reconstruction accuracy performance in term of both L1 and L2 errors.  ...  It reconstructs a signal from sub-Nyquist random linear measurements. Classical methods only exploit the sparsity in one domain.  ...  Minimization/maximization of one of them can encourage sparse structure in the recovered signal.  ... 
arXiv:1306.6510v1 fatcat:cspulaemzfgbjiyg2zjrlh5yse

Split Bregman algorithms for sparse / joint-sparse and low-rank signal recovery: Application in compressive hyperspectral imaging

A. Gogna, A. Shukla, H. K. Agarwal, A. Majumdar
2014 2014 IEEE International Conference on Image Processing (ICIP)  
We show that our proposed techniques significantly outperform previous methods in terms of recovery accuracy.  ...  In this work we derive algorithms for solving two problemsthe first one is the combined l 1 -norm (sparsity) and nuclear norm (low rank) regularized least squares problem and the second one is the l 2,1  ...  Tables 1 and 2, show that recovery via sparse / jointsparse penalties yields considerably poor results and do not compare with the others.  ... 
doi:10.1109/icip.2014.7025260 dblp:conf/icip/GognaSAM14 fatcat:4y6lp35qtrdcpcxw5ycvcffcxq

Compressed-Sensed-Domain L1-PCA Video Surveillance

Ying Liu, Dimitris A. Pados
2016 IEEE transactions on multimedia  
The background scene is then obtained by projecting the CS measurement vector onto the L 1 principal components followed by total-variation (TV) minimization image recovery.  ...  / on 06/17/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Proc. of SPIE Vol. 9484 94840B-8 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/17/2016 Terms of Use: http  ...  CS recovery on the columns of Y L1 L , i.e. y L1 L,t , t = 1, 2, ..., N .  ... 
doi:10.1109/tmm.2016.2514848 fatcat:cpg6ialozvashpwgguumvaglfq

Stable Recovery of Weighted Sparse Signals from Phaseless Measurements via Weighted l1 Minimization [article]

Haiye Huo
2021 arXiv   pre-print
Specifically, we investigate two conditions that guarantee stable recovery of a weighted k-sparse signal via weighted l1 minimization without any phase information.  ...  We first prove that the weighted null space property (WNSP) is a sufficient and necessary condition for the success of weighted l1 minimization for weighted k-sparse phase retrievable.  ...  To the best of our knowledge, there is no study on recovery of a weighted k-sparse signal from the phaseless measurements via the weighted l 1 minimization.  ... 
arXiv:2107.04788v1 fatcat:xsovzvp4wbhvrhdklapqtcz4fa

Compressed-sensed-domainL1-PCA video surveillance

Ying Liu, Dimitris A. Pados, Fauzia Ahmad
2015 Compressive Sensing IV  
The background scene is then obtained by projecting the CS measurement vector onto the L 1 principal components followed by total-variation (TV) minimization image recovery.  ...  / on 06/17/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Proc. of SPIE Vol. 9484 94840B-8 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/17/2016 Terms of Use: http  ...  CS recovery on the columns of Y L1 L , i.e. y L1 L,t , t = 1, 2, ..., N .  ... 
doi:10.1117/12.2179722 fatcat:2roxdrxck5hjflnq2rxb5ei7vu

Wavelet-domain compressive signal reconstruction using a Hidden Markov Tree model

Marco F. Duarte, Michael B. Wakin, Richard G. Baraniuk
2008 Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing  
Our algorithm fuses recent results on iterative reweighted ℓ1-norm minimization with the wavelet Hidden Markov Tree model.  ...  In this paper, we propose a new algorithm that enables fast recovery of piecewise smooth signals, a large and useful class of signals whose sparse wavelet expansions feature a distinct "connected tree"  ...  The ℓ1-norm approach seeks a set of sparse coefficients b θ by solving the linear program b θ = arg min θ θ 1 subject to ΦΨθ = y; (1) the reconstruction of sparse signals via ℓ1-norm minimization is typically  ... 
doi:10.1109/icassp.2008.4518815 dblp:conf/icassp/DuarteWB08 fatcat:4czspurewfb6hhjgwdgb6r2j5i

A Fast and Robust Non-Sparse Signal Recovery Algorithm for Wearable ECG Telemonitoring Using ADMM-Based Block Sparse Bayesian Learning

Yunfei Cheng, Yalan Ye, Mengshu Hou, Wenwen He, Yunxia Li, Xuesong Deng
2018 Sensors  
However, ECG signals in WBAN are usually non-sparse, and most traditional compressed sensing recovery algorithms have difficulty recovering non-sparse signals.  ...  In this paper, we proposed a fast and robust non-sparse signal recovery algorithm for wearable ECG telemonitoring.  ...  Therefore, accurate recovery of non-sparse signals is very important for wearable ECG telemonitoring. In order to solve the problem of compressed sensing recovery on non-sparse signals, Zhang et al.  ... 
doi:10.3390/s18072021 pmid:29937512 pmcid:PMC6069014 fatcat:z53qhiyn7fgalc5epzxbsyfocm

Computational Aspects of Constrained L 1-L 2 Minimization for Compressive Sensing [chapter]

Yifei Lou, Stanley Osher, Jack Xin
2015 Advances in Intelligent Systems and Computing  
We study the computational properties of solving a constrained L1-L2 minimization via a difference of convex algorithm (DCA), which was proposed in our previous work [13, 19] to recover sparse signals  ...  Through experiments, we discover that both L1 and L1-L2 obtain better recovery results from more coherent matrices, which appears unknown in theoretical analysis of exact sparse recovery.  ...  We would like to thank the anonymous referee for pointing out a general convergence property of DCA and a suggestion to reorganize our previous proof of convergence.  ... 
doi:10.1007/978-3-319-18161-5_15 fatcat:v2d3qwwwujg2bdszkrwqwq6pb4

Compressed Sensing Algorithm for Real-Time Doppler Ultrasound Image Reconstruction

Sulieman Mohammed Salih Zobly
2017 Mathematical Modelling and Applications  
With compressed sensing it's possible to reconstruct signals and images using a few numbers of measurements so as to overcome the limitation of sampling in a real-time Doppler ultrasound sonogram.  ...  The result shows that regularized orthogonal matching pursuit reconstruction algorithm reconstructs the Doppler signal and gives Doppler spectrum in a real-time with high quality also ℓ1-norm reconstructs  ...  sparse signal recovery [15] .  ... 
doi:10.11648/j.mma.20170206.14 fatcat:v4o66rs5kje7zoje5vknnsguje

Motion compensation as sparsity-aware decoding in compressive video streaming

Ying Liu, Ming Li, Kanke Gao, Dimitris A. Pados
2011 2011 17th International Conference on Digital Signal Processing (DSP)  
We show that effective implicit motion compensation can be carried out at the receiver/decoder via iterative sparsity-aware recovery on adaptively forward-backward estimated Karhunen-Loève bases.  ...  falls solely on the receiver side.  ...  In the CS video decoder of [10] , each frame is individually decoded via sparse signal recovery algorithms with fixed bases such as block-based 2D-DCT (or frame-based 2D-DWT).  ... 
doi:10.1109/icdsp.2011.6005006 fatcat:qcvnqrhynrfnlbu2zc53my2ney
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