Impact of External Phenomena In Compressed Sensing Methods For Wireless Sensor Networks

Abstract

Compressed sensing represents an interesting approach in signal processing and reconstruction. The theory involves a surprising number of branches of mathematics: linear algebra, functional analysis, convex and non-convex optimization, nonlinear approximation theory and probability. In general, the applications of compressed sensing can be found (or searched) wherever it is possible to express the signal in sparse representation in a “standard” base or in a base that was adjusted for particular signal. Core applications of compressed sensing today include image processing, signal denoising, image deblurring and inpainting. This paper addresses analysis the influence of external phenomena on the signal reconstruction using compressed sensing in wireless sensor networks. Such external phenomena include, for instance, additive white Gaussian noise (AWGN), attenuation or time shift. Three acoustic input signals sparse in frequency domain are used in experiments. The first one with significant frequency band from 500Hz up to 700Hz. The second signal with one significant frequency band from 2400Hz up to 3100Hz with considerable frequency bands between 0Hz to 1000Hz and 5000Hz to 6000Hz. The third signal used is a synthesized artificial sound invented for the experiment purposes only. It is strictly sparse in the frequency domain and has exactly three frequency bands between 400Hz and 500Hz, 2000Hz and 2100Hz, 9000Hz and 9100Hz. The results show that additive noise as well as attenuation have significant effect on the reconstruction accuracy using the selected distribution scenario and reconstruction method. On the other side, the time shift has no significant effect on the reconstruction.