Compressed sensing recovery using polynomial approximated l0 minimization of signal and error

The development of a computationally optimal Compressed Sensing recovery algorithm based on polynomial approximated L₀ minimization of the objective signal x and the error projection, is discussed in this paper. The proposed algorithm X-L0 E-L0 minimization (XEL0) using continuous function approximation for sparse signal recovery, minimizes the L₀ norm of signal x and L₀ norm of projected recovery error A^†(y - Ax) using a set of polynomial functions, which approximate Gaussian curve, to improve the signal recovery performance and signal recovery time over the existing L₀ norm minimization based algorithms with L₂ recovery error constraints. The new algorithm for Compressed Sensing recovery reduces the computational complexity by computing L₀ norm with simple polynomial functions. This paper presents the theoretical frame work of the new algorithm, the experimental evaluation of convergence and robustness analysis along with the simulation results.