Methods to reduce perturbation effects in compressive sampling

Abstract

With compressive sampling (CS), few measurements or samples will be enough for signal reconstruction as long as the signal can be represented in a basis domain and the coefficients are sparse. Fortunately, many signals in nature can be expressed with sparse bases. However, there arise the CS problems of perturbations which can be broadly classified into additive and multiplicative. The additive perturbation such as additive white Gaussian noise (AWGN) inevitably incurs recovery noise in general, but can be more serious if CS is used. Signal power should be sufficiently large compared to the amount of the additive perturbation to apply CS. Simply increasing the signal power, however, may incur additional interference noise if there are multiple signal sources. Furthermore, another serious problems may arise when there exist multiplicative perturbations. Multiplicative perturbation may cause a mismatch between the assumed signal basis and that in the measurements, and as a result, signal-dependent noise is generated. Therefore, boosting of signal power will also increase the noise from the multiplicative perturbation. To use CS, the adverse effects from additive and multiplicative perturbations should be reduced. In this thesis, methods to alleviate the adverse effects from these perturbations are suggested. Firstly, diversified-CS (dCS) method is introduced as a remedy against the additive perturbation of CS. This method will cut down the noise of the recovered signal by extracting diversity gain from given measurements with virtual multiple branches of recovery. Diversity technique is commonly used in a wireless receiver to reduce noise by combining signals from multi-sensors. However, dCS method uses only a single sensor to extract the diversity gain by building virtual branches. This technique is also applied to the applications of spectrum sensing and spherical harmonics reconstruction to demonstrate the noise reduction. Furthermore, simulation results verify dCS method is effective in reducing the recovery noise. Secondly, an iterative basis refinement method is suggested for the reduction of the adverse effects from multiplicative perturbation. This method determines active bases (initially blindly), estimates the mismatch in the identified active bases, and adjusts the bases according to the perturbation. It is applied to the application of CS wireless receiver for the sparse signal acquisition and reconstruction, where the source of the multiplicative perturbation is the Doppler frequency offset introduced by a wireless fading channel. Simulation results corroborate the effectiveness of this algorithm in suppressing the adverse effects of multiplicative perturbations on signal recovery. Although the proposed methods in this thesis are mainly introduced to wireless signal applications, it has a potential to be used in other CS applications that suffer from additive and multiplicative perturbations. Show more