Single-Iteration Algorithm for Compressive Sensing Reconstruction

Abstract

A single-iteration algorithm is proposed for the reconstruction of sparse signal from its incomplete set of observations. Recently, the reconstruction algorithms have been intensively developed within the Compressive Sensing framework. Most of the existing solutions are based either on l1-norm optimization methods or greedy iterative procedures with a priori known number of components or predefined number of iterations. We propose a simple non-iterative algorithm based on the analysis of noise-effect that appears in the frequency domain as a consequence of missing samples. The noise variance can be related and controlled by the number of missing samples. Accordingly, it is possible to keep the level of spectral noise below the signal components, such as to be able to accurately detect signal support and to reconstruct the entire signal. The theory is proven on various examples with multicomponent signals.

Keywords

• Compressive Sensing
• missing samples
• DFT
• reconstruction algorithms