Analysis of Gradient based Algorithm for Signal reconstruction in the Presence of Noise

TL;DR

This paper evaluates an iterative gradient-based algorithm for reconstructing sparse signals with missing or noisy samples, analyzing how different parameters affect its performance in both noisy and noise-free scenarios.

Contribution

It provides a detailed analysis of the parameter effects on the gradient-based reconstruction algorithm's performance in noisy and noise-free conditions.

Findings

Algorithm performs effectively in reconstructing sparse signals.

Parameter tuning significantly impacts reconstruction accuracy.

Performance varies between noisy and non-noisy signal cases.

Abstract

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.