Modeling of Teager Energy Operated Perceptual Wavelet Packet Coefficients with an Erlang-2 PDF for Real Time Enhancement of Noisy Speech

In this paper, for real time enhancement of noisy speech, a method of threshold determination based on modeling of Teager energy (TE) operated perceptual wavelet packet (PWP) coefficients of the noisy speech and noise by an Erlang-2 PDF is presented. The proposed method is computationally much faster than the existing wavelet packet based thresholding methods. A custom thresholding function based on a combination of mu-law and semisoft thresholding functions is designed and exploited to apply the statistically derived threshold upon the PWP coefficients. The proposed custom thresholding function works as a mu-law or a semisoft thresholding function or their combination based on the probability of speech presence and absence in a subband of the PWP transformed noisy speech. By using the speech files available in NOIZEUS database, a number of simulations are performed to evaluate the performance of the proposed method for speech signals in the presence of Gaussian white and street noises. The proposed method outperforms some of the state-of-the-art speech enhancement methods both at high and low levels of SNRs in terms of standard objective measures and subjective evaluations including formal listening tests.Comment: To appear in Digital Signal Processing, 27 pages, 19 figures, 10 table

On reconstruction algorithms for signals sparse in Hermite and Fourier domains

This thesis consists of original contributions in the area of digital signal processing. The reconstruction of signals sparse (highly concentrated) in various transform domains is the primary problem analyzed in the thesis. The considered domains include Fourier, discrete Hermite, one-dimensional and two-dimensional discrete cosine transform, as well as various time-frequency representations. Sparse signals are reconstructed using sparsity measures, being, in fact, the measures of signal concentration in the considered domains. The thesis analyzes the compressive sensing reconstruction algorithms and introduces new approaches to the problem at hand. The missing samples influence on analyzed transform domains is studied in detail, establishing the relations with the general compressive sensing theory. This study provides new insights on phenomena arising due to the reduced number of signal samples. The theoretical contributions involve new exact mathematical expressions which describe performance and outcomes of reconstruction algorithms, also including the study of the influence of additive noise, sparsity level and the number of available measurements on the reconstruction performance, exact expressions for reconstruction errors and error probabilities. Parameter optimization of the discrete Hermite transform is also studied, as well as the additive noise influence on Hermite coefficients, resulting in new parameter optimization and denoising algorithms. Additionally, an algorithm for the decomposition of multivariate multicomponent signals is introduced, as well as an instantaneous frequency estimation algorithm based on the Wigner distribution. Extensive numerical examples and experiments with real and synthetic data validate the presented theory and shed a new light on practical applications of the results.Comment: Ph.D. thesis, 241 pages, in Montenegrin/Serbia