Bayesian estimation of regularization and point spread function parameters for Wiener–Hunt deconvolution

Abstract

This paper tackles the problem of image deconvolution with joint estimation of PSF parameters and hyperparameters. Within a Bayesian framework, the solution is inferred via a global a posteriori law for unknown parameters and object. The estimate is chosen as the posterior mean, numerically calculated by means of a Monte-Carlo Markov chain algorithm. The estimates are efficiently computed in the Fourier domain and the effectiveness of the method is shown on simulated examples. Results show precise estimates for PSF parameters and hyperparameters as well as precise image estimates including restoration of high-frequencies and spatial details, within a global and coherent approach.

Super-resolution in map-making based on a physical instrument model and regularized inversion

“…4) of the posterior law. Another important advantage of the Bayesian interpretation deals with the estimation of hyperparameter and instrument parameters (Orieux et al 2010). …”

“…Moreover, in as much as it relies on two sources of information, the method is based on a trade-off tuned by means of an hyperparameter. It is empirically set in the present paper and work in progress, based on Robert & Casella (2000) and Orieux et al (2010), is devoted to the question of the hyperparameter and instrument parameter auto-calibration (myopic and unsupervised inversion).…”

Semi-unsupervised Bayesian convex image restoration with location mixture of Gaussian

“…In the general case, K is dependant wrt. regularization parameters θ which is a major difficulty that blocks θ estimation [16], [21], [22]. For the well-posedness of the inverse problem we consider the energy E θ (x) = γ x c∈C φ (d t c x; θ) with the set C of cliques c and neighborhoods d c [7] and γ x > 0.…”

“…In [21], authors present a fast MCMC deconvolution method limited to quadratic prior. Work of J.-F. Giovannelli [22] presents an unsupervised convex deconvolution approach.…”

Myopic sparse image reconstruction with application to MRFM

“…We propose a myopic modification of the Bayesian MRFM reconstruction approach in Dobigeon et al, 12 whereby one performs a simple additional step in the initial Gibbs sampler, producing a Bayesian estimate of the PSF and a Bayesian reconstruction of the image. Our approach can be related to the recent paper of Orieux et al 19 who introduced a Metropolis-within-Gibbs algorithm to estimate the parameters that tune the device response. This strategy focuses on reconstruction with smoothness constraints and requires recomputation of the entire PSF at each step of the algorithm.…”