Javier Mateos

Blind Deconvolution Using a Variational Approach to Parameter, Image, and Blur Estimation

Following the hierarchical Bayesian framework for blind deconvolution problems, in this paper, we propose the use of simultaneous autoregressions as prior distributions for both the image and blur, and gamma distributions for the unknown parameters (hyperparameters) of the priors and the image formation noise. We show how the gamma distributions on the unknown hyperparameters can be used to prevent the proposed blind deconvolution method from converging to undesirable image and blur estimates and also how these distributions can be inferred in realistic situations. We apply variational methods to approximate the posterior probability of the unknown image, blur, and hyperparameters and propose two different approximations of the posterior distribution. One of these approximations coincides with a classical blind deconvolution method. The proposed algorithms are tested experimentally and compared with existing blind deconvolution methods

Bayesian and regularization methods for hyperparameter estimation in image restoration

In this paper, we propose the application of the hierarchical Bayesian paradigm to the image restoration problem. We derive expressions for the iterative evaluation of the two hyperparameters applying the evidence and maximum a posteriori (MAP) analysis within the hierarchical Bayesian paradigm. We show analytically that the analysis provided by the evidence approach is more realistic and appropriate than the MAP approach for the image restoration problem. We furthermore study the relationship between the evidence and an iterative approach resulting from the set theoretic regularization approach for estimating the two hyperparameters, or their ratio, defined as the regularization parameter. Finally the proposed algorithms are tested experimentally.

A survey of classical methods and new trends in pansharpening of multispectral images

There exist a number of satellites on different earth observation platforms, which provide multispectral images together with a panchromatic image, that is, an image containing reflectance data representative of a wide range of bands and wavelengths. Pansharpening is a pixel-level fusion technique used to increase the spatial resolution of the multispectral image while simultaneously preserving its spectral information. In this paper, we provide a review of the pan-sharpening methods proposed in the literature giving a clear classification of them and a description of their main characteristics. Finally, we analyze how the quality of the pansharpened images can be assessed both visually and quantitatively and examine the different quality measures proposed for that purpose.

Super Resolution of Images and Video

Abstract This book focuses on the super resolution of images and video. The authors’ use of the term super resolution (SR) is used to describe the process of obtaining a high resolution (HR) image, or a sequence of HR images, from a set of low resolution (LR) observations. This process has also been referred to in the literature as resolution enhancement (RE). SR has been applied primarily to spatial and temporal RE, but also to hyperspectral image enhancement. This book concentrates on motion based spatial RE, although the authors also describe motion free and hyperspectral image SR problems. Also examined is the very recent research area of SR for compression, which consists of the intentional downsampling, during pre-processing, of a video sequence to be compressed and the application of SR techniques, during post-processing, on the compressed sequence.It is clear that there is a strong interplay between the tools and techniques developed for SR and a number of other inverse problems encountered in sig...

Bayesian resolution enhancement of compressed video

Super-resolution algorithms recover high-frequency information from a sequence of low-resolution observations. In this paper, we consider the impact of video compression on the super-resolution task. Hybrid motion-compensation and transform coding schemes are the focus, as these methods provide observations of the underlying displacement values as well as a variable noise process. We utilize the Bayesian framework to incorporate this information and fuse the super-resolution and post-processing problems. A tractable solution is defined, and relationships between algorithm parameters and information in the compressed bitstream are established. The association between resolution recovery and compression ratio is also explored. Simulations illustrate the performance of the procedure with both synthetic and nonsynthetic sequences.

Image restoration in astronomy: a Bayesian perspective

When preparing an article on image restoration in astronomy, it is obvious that some topics have to be dropped to keep the work at reasonable length. We have decided to concentrate on image and noise models and on the algorithms to find the restoration. Topics like parameter estimation and stopping rules are also commented on. We start by describing the Bayesian paradigm and then proceed to study the noise and blur models used by the astronomical community. Then the prior models used to restore astronomical images are examined. We describe the algorithms used to find the restoration for the most common combinations of degradation and image models. Then we comment on important issues such as acceleration of algorithms, stopping rules, and parameter estimation. We also comment on the huge amount of information available to, and made available by, the astronomical community.

Bayesian multichannel image restoration using compound Gauss-Markov random fields

In this paper, we develop a multichannel image restoration algorithm using compound Gauss-Markov random fields (CGMRF) models. The line process in the CGMRF allows the channels to share important information regarding the objects present in the scene. In order to estimate the underlying multichannel image, two new iterative algorithms are presented and their convergence is established. They can be considered as extensions of the classical simulated annealing and iterative conditional methods. Experimental results with color images demonstrate the effectiveness of the proposed approaches.

A Bayesian approach for the estimation and transmission of regularization parameters for reducing blocking artifacts

With block-based compression approaches for both still images and sequences of images annoying blocking artifacts are exhibited, primarily at high compression ratios. They are due to the independent processing (quantization) of the block transformed values of the intensity or the displaced frame difference. We propose the application of the hierarchical Bayesian paradigm to the reconstruction of block discrete cosine transform (BDCT) compressed images and the estimation of the required parameters. We derive expressions for the iterative evaluation of these parameters applying the evidence analysis within the hierarchical Bayesian paradigm. The proposed method allows for the combination of parameters estimated at the coder and decoder. The performance of the proposed algorithms is demonstrated experimentally.

Hyperparameter estimation in image restoration problems with partially known blurs

This work is motivated by the observation that it is not pos- sible to reliably estimate simultaneously all the necessary hyperparam- eters in an image restoration problem when the point-spread function is assumed to be the sum of a known deterministic and an unknown ran- dom component. To solve this problem we propose to use gamma hy- perpriors for the unknown hyperparameters. Two iterative algorithms that simultaneously restore the image and estimate the hyperparameters are derived, based on the application of evidence analysis within the hierar- chical Bayesian framework. Numerical experiments are presented that show the benefits of introducing hyperpriors for this problem.

Restoration of severely blurred high range images using stochastic and deterministic relaxation algorithms in compound Gauss–Markov random fields

Abstract Over the last few years, a growing number of researchers from varied disciplines have been utilizing Markov random fields (MRF) models for developing optimal, robust algorithms for various problems, such as texture analysis, image synthesis, classification and segmentation, surface reconstruction, integration of several low level vision modules, sensor fusion and image restoration. However, no much work has been reported on the use of Simulated Annealing (SA) and Iterative Conditional Mode (ICM) algorithms for maximum a posteriori estimation in image restoration problems when severe blurring is present. In this paper 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 SA and ICM algorithms has not been established. We propose two new iterative restoration algorithms which can be considered as extensions of the classical SA and ICM approaches and whose convergence is established. Finally, they are tested on real and synthetic images and the results compared with the restorations obtained by other iterative schemes.