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International Journal of Scientific and Engineering Research
ISSN Online 2229-5518
ISSN Print: 2229-5518 2    
Website: http://www.ijser.org
scirp IJSER >> Volume 3,Issue 2,February 2012
Survey of Compressive Sensing
Full Text(PDF, )  PP.395-398  
Author(s)
Usham Dias, Milind Rane, S. R. Bandewar
KEYWORDS
—compressive sensing, sensing matrix, sparse representation, multiw avelet transform;
ABSTRACT
In the conventional sampling process, for perfect reconstruction of signal according to Nyquist-Shannnon sampling theorem, a band-limited analog signal has to be sampled at atleast twice its highest frequency. The Nyquist-Shannon sampling theorem provides a sufficient condition, but not a necessary one, for perfect reconstruction. The field of compressive sensing provides a stricter sampling condition when the signal is known to be sparse or compressible. Compressive sensing specifically yields a sub-Nyquist sampling criterion. Compressive sensing contains three main problems: sparse representation, measurement matrix and reconstruction algorithm. By now, some available measurement matrices have been discovered, such as Gaussian or Bernoulli independent and identically distributed (i.i.d) random matrices, scrambled Fourier matrix and some structurally random matrices etc. For nonlinear reconstruction, besides the Basis Pursuit (BP) method, several fast greedy algorithms have been proposed, such as the orthogonal matching pursuit (OMP), Regularized OMP, Compressive Sampling OMP. When reconstructing 2D images, besides BP, another popular method is through the minimization of total variation (min-TV) [2].
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[12] Philip Breen, ―Algorithms for Sparse Approximation‖, Year 4 Project, School of Mathematics, University of Edinburgh, 2009

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