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Uniform uncertainty principle and signal recovery via Regularized orthogonal matching pursuit. (English) Zbl 1183.68739
Summary: This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements—L 1 -minimization methods and iterative methods (Matching Pursuits). We find a simple Regularized version of Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the speed and transparency of OMP and the strong uniform guarantees of L 1 -minimization. Our algorithm, ROMP, reconstructs a sparse signal in a number of iterations linear in the sparsity, and the reconstruction is exact provided the linear measurements satisfy the uniform uncertainty principle.
68W20Randomized algorithms
65T50Discrete and fast Fourier transforms (numerical methods)
41A46Approximation by arbitrary nonlinear expressions; widths and entropy
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