An automated signal reconstruction method based on analysis of compressive sensed signals in noisy environment

An analysis of signal reconstruction possibility using a small set of samples corrupted by noise is considered. False detection and/or misdetection of sparse signal components may occur as a twofold influence of noise: one is a consequence of missing samples, while the other appears from an external source. This analysis allows us to determine a minimal number of available samples required for a non-iterative reconstruction. Namely, using a predefined probability of error, it is possible to define a general threshold that separates signal components from spectral noise. In the cases when some components are masked by noise, this threshold can be iteratively updated. It will render that all components are detected, providing an iterative version of blind and simple compressive sensing reconstruction algorithm.