Comparison of iterative sparse recovery algorithms

Most signals can be represented sparsely in a basis. Recently, Compressive Sensing Theorem which offers convex optimization algorithms based on ℓ₁-minimization for sparse signal recovery is often being used. In this paper, some of the iterative signal recovery algorithms alternative to ℓ₁-minimization solution which are Orthogonal Matching Pursuit (OMP), Compressive Sampling Matching Pursuit (CoSaMP), Iterative Hard Thresholding (IHT) and Lipschitz Iterative Hard Theresholding (LIHT) are compared in noisy and noiseless conditions with various tests. Iterative algorithms alternative to the ℓ₁ optimization method with similar performance are verified. OMP algorithm that works at higher true reconstruction rates in noisy and noiseless conditions can be preferred instead of convex optimization methods.