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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.
MSC:
68W20Randomized algorithms
65T50Discrete and fast Fourier transforms (numerical methods)
41A46Approximation by arbitrary nonlinear expressions; widths and entropy
References:
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