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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:

68W20 Randomized algorithms
65T50 Numerical methods for discrete and fast Fourier transforms
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
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