Analysis of gradient based algorithm for signal reconstruction in the presence of noise

Common problem in signal processing is reconstruction of the missing signal samples. Missing samples can occur by intentionally omitting signal coefficients to reduce memory requirements, or to speed up the transmission process. Also, noisy signal coefficients can be considered as missing ones, since they have wrong values due to the noise. The reconstruction of these coefficients is demanding task, considered within the Compressive sensing area. Signal with large number of missing samples can be recovered, if certain conditions are satisfied. There is a number of algorithms used for signal reconstruction. In this paper we have analyzed the performance of iterative gradient-based algorithm for sparse signal reconstruction. The parameters influence on the optimal performances of this algorithm is tested. Two cases are observed: non-noisy and noisy signal case. The theory is proved on examples.