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.