Nonparametric Bayesian Models for Signal Processing
- Publication Type:
- Thesis
- Issue Date:
- 2019
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An essential component in signal processing is to remove various kinds of noise from the signal. It is possible to introduce noise during the process of signal storage, transmission and acquisition. Signal quality after denoising affects subsequent signal analysis profoundly. Low-rank representation is a popular method in signal processing. It is aimed to capture underlying low-dimensional structures of high dimensional signal and attracted much attention in the area of the pattern recognition and signal processing. Such successful applications were mainly due to its effectiveness in exploring low dimensional manifolds embedded in data, which can be naturally characterized by low rankness of the data matrix.
This thesis conducts research on processing various signals as well as getting the low-rank representation of the signal via the variational Bayesian inference techniques. This study proposed four different nonparametric Bayesian models for image denoising, inpainting, video foreground/background separation and bio-medical signal processing as follows.
(1) A hybrid denoising model based on variational Bayesian inference and Stein's unbiased risk estimator (SURE) is presented, which consists of two complementary steps. In the first step, the variational Bayesian singular value thresholding (SVT) performs a low-rank approximation of the nonlocal image patch matrix to simultaneously remove the noise and estimate the noise variance. In the second step, the conventional SURE full rank SVT and its divergence formulas for rank-reduced eigen-triplets is modified to remove the residual artefacts.
(2) A hierarchical kernelized sparse Bayesian matrix factorization (KSBMF) model is developed to integrate side information. The KSBMF automatically infers the parameters and latent variables including the reduced rank using the variational Bayesian inference. Also, the model simultaneously achieves low-rankness through sparse Bayesian learning and sparsity through an enforced constraint on latent factor matrices. The KSBMF is further connected with the nonlocal image processing framework to develop two algorithms for image denoising and inpainting.
(3) A robust kernelized Bayesian matrix factorization (RKBMF) model is proposed to decompose a data set into low rank and sparse components. Moreover, the model integrates the side information of similarity between frames to improve information extraction from the video. RKBMF is employed to extract background and foreground information from a traffic video.
(4) A hierarchical Dirichlet process nonnegative matrix factorization (DPNMF) model is presented in which the Gaussian mixture model is used to approximate the complex noise distribution. Moreover, the model is cast in the nonparametric Bayesian framework by using Dirichlet process mixture to infer the necessary number of Gaussian components. A mean-field variational inference algorithm is derived for the proposed nonparametric Bayesian model. The model is tested on synthetic data sets contaminated by Gaussian, sparse and mixed noise. The proposed model is then applied to extract muscle synergies from the electromyographic (EMG) signal and to select discriminative features for motor imagery single-trial electroencephalogram (EEG) classification.
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