Digital image processing of the Ghent altarpiece : supporting the painting's study and conservation treatment

In this article, we show progress in certain image processing techniques that can support the physical restoration of the painting, its art-historical analysis, or both. We show how analysis of the crack patterns could indicate possible areas of overpaint, which may be of great value for the physical restoration campaign, after further validation. Next, we explore how digital image inpainting can serve as a simulation for the restoration of paint losses. Finally, we explore how the statistical analysis of the relatively simple and frequently recurring objects (such as pearls in this masterpiece) may characterize the consistency of the painter’s style and thereby aid both art-historical interpretation and physical restoration campaign

Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the proposed framework with structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared to traditional sparse inverse problem techniques. This interpretation also suggests an effective dictionary motivated initialization for the MAP-EM algorithm. We demonstrate that in a number of image inverse problems, including inpainting, zooming, and deblurring, the same algorithm produces either equal, often significantly better, or very small margin worse results than the best published ones, at a lower computational cost.Comment: 30 page

Bayesian inference for inverse problems

Traditionally, the MaxEnt workshops start by a tutorial day. This paper summarizes my talk during 2001'th workshop at John Hopkins University. The main idea in this talk is to show how the Bayesian inference can naturally give us all the necessary tools we need to solve real inverse problems: starting by simple inversion where we assume to know exactly the forward model and all the input model parameters up to more realistic advanced problems of myopic or blind inversion where we may be uncertain about the forward model and we may have noisy data. Starting by an introduction to inverse problems through a few examples and explaining their ill posedness nature, I briefly presented the main classical deterministic methods such as data matching and classical regularization methods to show their limitations. I then presented the main classical probabilistic methods based on likelihood, information theory and maximum entropy and the Bayesian inference framework for such problems. I show that the Bayesian framework, not only generalizes all these methods, but also gives us natural tools, for example, for inferring the uncertainty of the computed solutions, for the estimation of the hyperparameters or for handling myopic or blind inversion problems. Finally, through a deconvolution problem example, I presented a few state of the art methods based on Bayesian inference particularly designed for some of the mass spectrometry data processing problems.Comment: Presented at MaxEnt01. To appear in Bayesian Inference and Maximum Entropy Methods, B. Fry (Ed.), AIP Proceedings. 20pages, 13 Postscript figure