Journal
SIGNAL PROCESSING
Volume 86, Issue 3, Pages 533-548Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.sigpro.2005.05.028
Keywords
basis pursuit; underdetermined systems of linear equations; random matrix theory; linear programming; overcomplete systems; sparse representations; random signs matrix ensemble; partial Fourier matrix ensemble; partial Hadamard matrix ensemble
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Finding the sparsest solution to a set of underdetermined linear equations is NP-hard in general. However, recent research has shown that for certain systems of linear equations, the sparsest solution (i.e. the solution with the smallest number of nonzeros), is also the solution with minimal l(1) norm, and so can be found by a computationally tractable method. For a given n by m matrix Phi defining a system y = Phi alpha, with n
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