Variational Bayesian Sparse Kernel-Based Blind Image Deconvolution With Student's-t Priors

Abstract

In this paper, we present a new Bayesian model for the blind image deconvolution (BID) problem. The main novelty of this model is the use of a sparse kernel-based model for the point spread function (PSF) that allows estimation of both PSF shape and support. In the herein proposed approach, a robust model of the BID errors and an image prior that preserves edges of the reconstructed image are also used. Sparseness, robustness, and preservation of edges are achieved by using priors that are based on the Student's-t probability density function (PDF). This pdf, in addition to having heavy tails, is closely related to the Gaussian and, thus, yields tractable inference algorithms. The approximate variational inference methodology is used to solve the corresponding Bayesian model. Numerical experiments are presented that compare this BID methodology to previous ones using both simulated and real data.

An efficient variational Bayesian inference approach via Studient's-t priors for acoustic imaging in colored noises

“…Taking the vehicle in the wind tunnel test as shown in Fig.1 for example, most of sources mainly locate on the small parts of the rearview mirrors and wheels, whereas for the rest parts, there are few sources existing. And such a sparse distribution can be represented by a centralized PDF function that has a very high value around the original zero (sparsity) and a long heavy tail (dynamic range of source powers), such as Laplacian priors [4] and Student's-t priors [9]. Recently, the authors have proposed to apply Double Exponential DE (x) priors based on JMAP for robust super resolution acoustic imaging [5].…”

“…For acoustic imaging in the colored noises, we have applied the VB inference in Eq. (7)(8)(9)(10)(11)(12)(13)(14) to obtain optimal distributions q(x 0 ),q(γ) and q(ν) in Eq. (11) for best approximating the posterior p(x 0 , γ, ν|y 0 ).…”

Recursive Variational Bayesian Inference to Simultaneous Registration and Fusion

“…VB has low computational costs in comparison with the sampling methods, such as Markov Chain Monte Carlo (MCMC). It has widespread use in machine learning, signal processing and many other fields, such as the state space model [10,11], time series [12,13], Mixture Models [14], filter [15][16][17], image [18][19][20], communication [21,22], speech recognition [23] and graphical models [24,25].…”

Variational Bayesian Image Restoration With a Product of Spatially Weighted Total Variation Image Priors

“…In [17] a TV prior was used for the image while Gaussian priors were used for the point spread function (PSF). In [18] a Student's-t prior in product form was used for the image. However, the normalization constant for this prior was approximated.…”

“…However, the normalization constant for this prior was approximated. In [18] also a kernel based sparse Student's-t prior was used for the PSF. This prior provides a mechanism, for the first time, to estimate the spatial support of the PSF also.…”