Proceedings ArticleDOI
Non-binary deterministic measurement matrix construction employing maximal curves
Ali Mohades,Mohamad Mahdi Mohades,Aliakbar Tadaion +2 more
- pp 1-5
TLDR
This paper has employed algebraic geometry codes to construct low coherence non-binary sensing matrices employing maximal curves and shows that these matrices outperform the Gaussian matrices in terms of noiseless and noisy signal recovery.Abstract:
Designing a measurement matrix is a principal problem in the theory of compressive sensing. Channel coding generator matrices are commonly employed to design a measurement matrix. Based on authors knowledge, a few studies have been made to connect algebraic geometry codes and compressive sensing. In this paper, we have employed algebraic geometry codes to construct low coherence non-binary sensing matrices. With this method, we have introduced a new group of deterministic sensing matrices employing maximal curves. Comparison of Gaussian matrix and proposed matrices shows that these matrices outperform the Gaussian matrices in terms of noiseless and noisy signal recovery.read more
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Book
Compressed sensing
TL;DR: It is possible to design n=O(Nlog(m)) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct knowledge of the N most important coefficients, and a good approximation to those N important coefficients is extracted from the n measurements by solving a linear program-Basis Pursuit in signal processing.
Journal ArticleDOI
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
TL;DR: In this paper, the authors considered the model problem of reconstructing an object from incomplete frequency samples and showed that with probability at least 1-O(N/sup -M/), f can be reconstructed exactly as the solution to the lscr/sub 1/ minimization problem.
Journal ArticleDOI
An Introduction To Compressive Sampling
TL;DR: The theory of compressive sampling, also known as compressed sensing or CS, is surveyed, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition.
Journal ArticleDOI
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
Joel A. Tropp,Anna C. Gilbert +1 more
TL;DR: It is demonstrated theoretically and empirically that a greedy algorithm called orthogonal matching pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(m ln d) random linear measurements of that signal.
Signal Recovery from Random Measurements Via Orthogonal Matching Pursuit: The Gaussian Case
Joel A. Tropp,Anna C. Gilbert +1 more
TL;DR: In this paper, a greedy algorithm called Orthogonal Matching Pursuit (OMP) was proposed to recover a signal with m nonzero entries in dimension 1 given O(m n d) random linear measurements of that signal.
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