Bayesian Restoration Using a New Nonstationary Edge-Preserving Image Prior

Variational Bayesian Image Restoration Based on a Product of $t$-Distributions Image Prior

“…The main theoretical contribution is that by constraining the approximation of the posterior in the variational framework, we bypass the need for knowing the normalization constant of this prior. Thus, we avoid having to use improper priors, i.e., priors whose normalization constant is empirically selected; see, for example, [9]- [11], [17], [18], and [19]. Furthermore, the proposed methodology does not require empirical parameter selection as in the MAP methodology that uses a similar-in-spirit prior in [17] and [18].…”

“…In [17], [18], and [19], some of us proposed a new hierarchical image prior for image restoration, image super-resolution, and blind image deconvolution problems, respectively. This prior is Student-t based, is in a product form, and is able to capture the local image discontinuities and thus provide edge-preserving capabilities for those problems.…”

“…In this manner, the use of improper priors is avoided and all the parameters of the prior model are estimated from the data. Thus, the "trial and error" parameter "tweaking" required in [17]- [19] and other state-of-the-art recently proposed restoration algorithms, which makes their use difficult use for nonexperts, is avoided. Furthermore, the proposed restoration algorithm provides competitive performance compared with previous methods.…”

Blind deblurring of natural images

“…Although that is not a valid assumption in many real-life situations, the problem is still hard, because the blur operator typically is very ill-conditioned. Several approaches to this problem, using prior information on the estimated image, can be found in [4,5,6].…”

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

“…This new prior can use arbitrary linear operators, not just first order differences as in TV and can combine them, in contrast to [16], in a non-linear manner. In order to avoid the over parameterization due to the spatially varying nature of the herein proposed prior, a model with two layers of hidden variables is proposed, which extends the one used in [15] and [16]. If the hidden variables of the second layer are marginalized the resulting density function has similar form to a Student's-t pdf thus we refer to it as Modified Student's-t.…”