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Sparse signal reconstruction with ellipsoid enlargement

In this work a novel method for reconstructing sparse x in a noisy full rank linear system such as b = Ax + n is developed. The proposed method depends on enlarging the ellipsiod defined by the data constraint ∥Ax − b∥2 = ∈ and iteratively resetting the axes where the signal is zero. The proposed method has a higher reconstruction performance compared to standard iterative and ℓ1 norm minimization based sparse recovery methods. Also our method relaxes the sparsity level constraint to be reconstructed by the standard methods for an underdetermined system.