Javier Abad

Parameter estimation in Bayesian high-resolution image reconstruction with multisensors

In this paper, we consider the estimation of the unknown parameters for the problem of reconstructing a high-resolution image from multiple undersampled, shifted, degraded frames with subpixel displacement errors. We derive mathematical expressions for the iterative calculation of the maximum likelihood estimate of the unknown parameters given the low resolution observed images. These iterative procedures require the manipulation of block-semi circulant (BSC) matrices, that is, block matrices with circulant blocks. We show how these BSC matrices can be easily manipulated in order to calculate the unknown parameters. Finally the proposed method is tested on real and synthetic images.

A Bayesian approach to blind deconvolution based on Dirichlet distributions

This paper deals with the simultaneous identification of the blur and the restoration of a noisy and blurred image. We propose the use of Dirichlet distributions to model our prior knowledge about the blurring function together with smoothness constraints on the restored image to solve the blind deconvolution problem. We show that the use of Dirichlet distributions offers a lot of flexibility in incorporating vague or very precise knowledge about the blurring process into the blind deconvolution process. The proposed MAP estimator offers additional flexibility in modeling the original image. Experimental results demonstrate the performance of the proposed algorithm.

Parameter estimation in super-resolution image reconstruction problems

We consider the estimation of the unknown hyperparameters for the problem of reconstructing a high-resolution image from multiple undersampled, shifted, degraded frames with subpixel displacement errors. We derive mathematical expressions for the iterative calculation of the maximum likelihood estimate (MLE) of the unknown hyperparameters given the low resolution observed images. Experimental results are presented for evaluating the accuracy of the proposed method.

Bayesian image restoration using a wavelet-based subband decomposition

The subband decomposition of a single channel image restoration problem is examined. The decomposition is carried out in the image model (prior model) in order to take into account the frequency activity of each band of the original image. The hyperparameters associated with each band together with the original image are rigorously estimated within the Bayesian framework. Finally, the proposed method is tested and compared with other methods on real images.

Estimation of High Resolution Images and Registration Parameters from Low Resolution Observations

In this paper we consider the problem of reconstructing a high resolution image from a set of undersampled and degraded frames, all of them obtained from high resolution images with unknown shifting displacements between them. We derive an iterative method to estimate the unknown shifts and the high resolution image given the low resolution observations. Finally, the proposed method is tested on real images.

Restoration of severely blurred high range images using compound models

We examine the use of compound Gauss Markov random fields (CGMRF) to restore severely blurred high range images. For this deblurring problem, the convergence of the simulated annealing (SA) and iterative conditional mode (ICM) algorithms has not been established. We propose two new iterative restoration algorithms which extend the classical SA and ICM approaches. Their convergence is established and they are tested on real and synthetic images.

Bayesian image restoration in astronomy: Application to images of the recent collision of comet shoemaker‐levy 9 with jupiter

In this work, we examine simple to complex methods proposed within the Bayesian paradigm to perform image restoration in astronomy. We start by describing the classical conditional and simultaneous autoregressions, then we move on to study how to incorporate smoothness constraints to the classical Richardson‐Lucy restoration method and also how to modify the image scale and define prior models on other scales than the linear one. Finally, we compare those models on images of Jupiter after the impacts of the fragments of the comet Shoemaker‐Levy 9 at two wavelengths.