Image and Audio-Speech Denoising Based on Higher-Order Statistical Modeling of Wavelet Coefficients and Local Variance Estimation

Abstract

At first, this paper is concerned with wavelet-based image denoising using Bayesian technique. In conventional denoising process, the parameters of probability density function (PDF) are usually calculated from the first few moments, mean and variance. In the first part of our work, a new image denoising algorithm based on Pearson Type VII random vectors is proposed. This PDF is used because it allows higher-order moments to be incorporated into the noiseless wavelet coefficients' probabilistic model. One of the cruxes of the Bayesian image denoising algorithms is to estimate the variance of the clean image. Here, maximum a posterior (MAP) approach is employed for not only noiseless wavelet-coefficient estimation but also local observed variance acquisition. For the local observed variance estimation, the selection of noisy wavelet-coefficient model, either a Laplacian or a Gaussian distribution, is based upon the corrupted noise power where Gamma distribution is used as a prior for the variance. Evidently, our selection of prior is motivated by analytical and computational tractability. In our experiments, our proposed method gives promising denoising results with moderate complexity. Eventually, our image denoising method can be simply extended to audio/speech processing by forming matrix representation whose rows are formed by time segments of digital speech waveforms. This way, the use of our image denoising methods can be exploited to improve the performance of various audio/speech tasks, e.g., denoised enhancement of voice activity detection to capture voiced speech, significantly needed for speech coding and voice conversion applications. Moreover, one of the voice abnormality detections, called oropharyngeal dysphagia classification, is also required denoising method to improve the signal quality in elderly patients. We provide simple speech examples to demonstrate the prospects of our techniques.

MAP estimation of Pearson Type IV random vectors in AWGN

“…In [8], we assume that noisy wavelet coefficients is the Gaussian distribution with zero mean and variance θ(k),…”

Nonlinear Wavelet Density Estimation for Truncated and Dependent Observations

“…For dependent case, Liang et al 23 discussed global L 2 error of the nonlinear wavelet estimators of the density function in the Besov space under censoring and stationary α-mixing assumptions, Truoug and Patil 31 gave an asymptotic expression of the MISE in nonlinear wavelet regression for complete data with α-mixing setting. In addition, Tian 29 considered estimations and optimal designs for two-dimensional Haar-wavelet regression models, Chen et al 6 investigated efficient statistical modeling of wavelet coefficients for image denoising, Kittisuwan et al 20 discussed image and audio-speech denoising based on higher-order statistical modeling of wavelet coefficients and local variance estimation.…”

NONLINEAR WAVELET ESTIMATION OF CONDITIONAL DENSITY UNDER LEFT-TRUNCATED AND Α-Mixing ASSUMPTIONS

“…For the dependent case, Liang et al (2005) discussed the global L 2 error of the nonlinear wavelet estimators of the density function in the Besov space under censoring and stationary α-mixing assumptions, Cai and Liang (2011) investigated the nonlinear wavelet density estimation for truncated and dependent observations; for complete data, Truoug and Patil (2001) gave an asymptotic expression of the MISE in nonlinear wavelet regression with α-mixing data. In addition, Tian (2009) considered estimations and optimal designs for twodimensional Haar-wavelet regression models, Chen et al (2009) investigated efficient statistical modeling of wavelet coefficients for image denoising, Kittisuwan et al (2010) discussed image and audio-speech denoising based on higher-order statistical modeling of wavelet coefficients and local variance estimation. However, there is not much research on the asymptotic MISE formula for the nonlinear wavelet estimator of conditional density function with left-truncated data, even for independent and complete data.…”