KEYWORDS: Matrices, Reconstruction algorithms, Iterative methods, Computer programming, Interference (communication), Signal generators, Bridges, Transparency, Compressed sensing, Signal to noise ratio
This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set
of linear measurements - L1-minimization methods and iterative methods (Matching Pursuits). We find a simple
regularized version of the Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the
speed and transparency of OMP and the strong uniform guarantees of the L1-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. In the case of inaccurate
measurements and approximately sparse signals, the noise level of the recovery is proportional to &sqrt;log n parallel e parallel 2
where e is the error vector.
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