Blind Source Separation In The Time-Frequency Domain

Blind source separation aims to recover the original source signals given only observations of their mixtures. The common approaches to the source separation problem include second or higher order statistics based methods, principal component analysis, independent component analysis, and sparse component analysis. Most of these methods are developed in the time domain, and thus inherently assume the stationarity of the underlying signals. Since most real life signals of interest are non-stationary, which means that the statistical properties of these signals change over time, the majority of the time-domain and frequency-domain methods in literature are not suitable to be applied to these signals. Therefore, we are exploring a new approach to achieve source separation using the knowledge of time-frequency analysis and information theory.

Adaptive Signal Decomposition On The Time-Frequency Plane

In many applications, such as array processing and sensor networks, it is desirable to extract components that generate the observed output signals. In this project, we introduce one approach to extract components that are well-concentrated on the time-frequency plane. In order to quantify the compactness or the concentration of the extracted components, we use the entropy measure as adapted to the time-frequency distributions. It has been shown that signals which achieve minimum entropy on the time-frequency plane are Gabor logons. Based on this idea, an adaptive Gabor logon extraction approach is proposed to extract the most significant Gabor logons as the components from a given set of observed signals using an adaptive filtering method.

Image Denoising Based On Wavelet Transform and Information Theory

Image denoising is a well-known problem in signal processing. Wavelet decomposition based approaches have been applied successfully to the image denoising problem. Most wavelet thresholding methods do not take the spatial correlation between the wavelet coefficients into account. We present a new image denoising approach that incorporates the intra-scale dependencies between the wavelet coefficients into the thresholding algorithm. The co-occurrence matrix of the wavelet coefficients and their neighbors is constructed to represent the spatial dependencies. An information-theoretic criterion, the 2-D joint entropy of the wavelet co-occurrence matrix, is used as the cost function to determine the optimal threshold.