531 research outputs found
Compressed Sensing Based on Random Symmetric Bernoulli Matrix
The task of compressed sensing is to recover a sparse vector from a small
number of linear and non-adaptive measurements, and the problem of finding a
suitable measurement matrix is very important in this field. While most recent
works focused on random matrices with entries drawn independently from certain
probability distributions, in this paper we show that a partial random
symmetric Bernoulli matrix whose entries are not independent, can be used to
recover signal from observations successfully with high probability. The
experimental results also show that the proposed matrix is a suitable
measurement matrix.Comment: arXiv admin note: text overlap with arXiv:0902.4394 by other author
Convolutional compressed sensing using deterministic sequences
This is the author's accepted manuscript (with working title "Semi-universal convolutional compressed sensing using (nearly) perfect sequences"). The final published article is available from the link below. Copyright @ 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.In this paper, a new class of orthogonal circulant matrices built from deterministic sequences is proposed for convolution-based compressed sensing (CS). In contrast to random convolution, the coefficients of the underlying filter are given by the discrete Fourier transform of a deterministic sequence with good autocorrelation. Both uniform recovery and non-uniform recovery of sparse signals are investigated, based on the coherence parameter of the proposed sensing matrices. Many examples of the sequences are investigated, particularly the Frank-Zadoff-Chu (FZC) sequence, the m-sequence and the Golay sequence. A salient feature of the proposed sensing matrices is that they can not only handle sparse signals in the time domain, but also those in the frequency and/or or discrete-cosine transform (DCT) domain
Restricted Isometries for Partial Random Circulant Matrices
In the theory of compressed sensing, restricted isometry analysis has become
a standard tool for studying how efficiently a measurement matrix acquires
information about sparse and compressible signals. Many recovery algorithms are
known to succeed when the restricted isometry constants of the sampling matrix
are small. Many potential applications of compressed sensing involve a
data-acquisition process that proceeds by convolution with a random pulse
followed by (nonrandom) subsampling. At present, the theoretical analysis of
this measurement technique is lacking. This paper demonstrates that the th
order restricted isometry constant is small when the number of samples
satisfies , where is the length of the pulse.
This bound improves on previous estimates, which exhibit quadratic scaling
Structure-Based Bayesian Sparse Reconstruction
Sparse signal reconstruction algorithms have attracted research attention due
to their wide applications in various fields. In this paper, we present a
simple Bayesian approach that utilizes the sparsity constraint and a priori
statistical information (Gaussian or otherwise) to obtain near optimal
estimates. In addition, we make use of the rich structure of the sensing matrix
encountered in many signal processing applications to develop a fast sparse
recovery algorithm. The computational complexity of the proposed algorithm is
relatively low compared with the widely used convex relaxation methods as well
as greedy matching pursuit techniques, especially at a low sparsity rate.Comment: 29 pages, 15 figures, accepted in IEEE Transactions on Signal
Processing (July 2012
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