On recovery of sparse signals via l1 minimization
IEEE Transactions on Information Theory
Toeplitz random encoding MR imaging using compressed sensing
ISBI'09 Proceedings of the Sixth IEEE international conference on Symposium on Biomedical Imaging: From Nano to Macro
Relaxed conditions for sparse signal recovery with general concave priors
IEEE Transactions on Signal Processing
Shifting inequality and recovery of sparse signals
IEEE Transactions on Signal Processing
Performance bounds for expander-based compressed sensing in the presence of poisson noise
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
Sampling rate reduction for 60 GHz UWB communication using compressive sensing
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
Reed muller sensing matrices and the LASSO
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
Toeplitz compressed sensing matrices with applications to sparse channel estimation
IEEE Transactions on Information Theory
Exact optimization for the l1-Compressive Sensing problem using a modified Dantzig-Wolfe method
Theoretical Computer Science
Two-dimensional random projection
Signal Processing
The method for constructing block sparse measurement matrix based on orthogonal vectors
PCM'12 Proceedings of the 13th Pacific-Rim conference on Advances in Multimedia Information Processing
A Simple Compressive Sensing Algorithm for Parallel Many-Core Architectures
Journal of Signal Processing Systems
Performance analysis of partial segmented compressed sampling
Signal Processing
Image representation using block compressive sensing for compression applications
Journal of Visual Communication and Image Representation
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The problem of recovering a sparse signal x Rn from a relatively small number of its observations of the form y = Ax Rk, where A is a known matrix and k «n, has recently received a lot of attention under the rubric of compressed sensing (CS) and has applications in many areas of signal processing such as data cmpression, image processing, dimensionality reduction, etc. Recent work has established that if A is a random matrix with entries drawn independently from certain probability distributions then exact recovery of x from these observations can be guaranteed with high probability. In this paper, we show that Toeplitz-structured matrices with entries drawn independently from the same distributions are also sufficient to recover x from y with high probability, and we compare the performance of such matrices with that of fully independent and identically distributed ones. The use of Toeplitz matrices in CS applications has several potential advantages: (i) they require the generation of only O(n) independent random variables; (ii) multiplication with Toeplitz matrices can be efficiently implemented using fast Fourier transform, resulting in faster acquisition and reconstruction algorithms; and (iii) Toeplitz-structured matrices arise naturally in certain application areas such as system identification.