Posterior Mean Super-Resolution with a Compound Gaussian Markov Random Field Prior

This manuscript proposes a posterior mean (PM) super-resolution (SR) method with a compound Gaussian Markov random field (MRF) prior. SR is a technique to estimate a spatially high-resolution image from observed multiple low-resolution images. A compound Gaussian MRF model provides a preferable prior for natural images that preserves edges. PM is the optimal estimator for the objective function of peak signal-to-noise ratio (PSNR). This estimator is numerically determined by using variational Bayes (VB). We then solve the conjugate prior problem on VB and the exponential-order calculation cost problem of a compound Gaussian MRF prior with simple Taylor approximations. In experiments, the proposed method roughly overcomes existing methods.Comment: 5 pages, 20 figures, 1 tables, accepted to ICASSP2012 (corrected 2012/3/23

Unsupervised amplitude and texture classification of SAR images with multinomial latent model

International audienceWe combine both amplitude and texture statistics of the Synthetic Aperture Radar (SAR) images for modelbased classification purpose. In a finite mixture model, we bring together the Nakagami densities to model the class amplitudes and a 2D Auto-Regressive texture model with t-distributed regression error to model the textures of the classes. A nonstationary Multinomial Logistic (MnL) latent class label model is used as a mixture density to obtain spatially smooth class segments. The Classification Expectation-Maximization (CEM) algorithm is performed to estimate the class parameters and to classify the pixels. We resort to Integrated Classification Likelihood (ICL) criterion to determine the number of classes in the model. We present our results on the classification of the land covers obtained in both supervised and unsupervised cases processing TerraSAR-X, as well as COSMO-SkyMed data

Blind image deconvolution: nonstationary Bayesian approaches to restoring blurred photos

High quality digital images have become pervasive in modern scientific and everyday life — in areas from photography to astronomy, CCTV, microscopy, and medical imaging. However there are always limits to the quality of these images due to uncertainty and imprecision in the measurement systems. Modern signal processing methods offer the promise of overcoming some of these problems by postprocessing these blurred and noisy images. In this thesis, novel methods using nonstationary statistical models are developed for the removal of blurs from out of focus and other types of degraded photographic images. The work tackles the fundamental problem blind image deconvolution (BID); its goal is to restore a sharp image from a blurred observation when the blur itself is completely unknown. This is a “doubly illposed” problem — extreme lack of information must be countered by strong prior constraints about sensible types of solution. In this work, the hierarchical Bayesian methodology is used as a robust and versatile framework to impart the required prior knowledge. The thesis is arranged in two parts. In the first part, the BID problem is reviewed, along with techniques and models for its solution. Observation models are developed, with an emphasis on photographic restoration, concluding with a discussion of how these are reduced to the common linear spatially-invariant (LSI) convolutional model. Classical methods for the solution of illposed problems are summarised to provide a foundation for the main theoretical ideas that will be used under the Bayesian framework. This is followed by an indepth review and discussion of the various prior image and blur models appearing in the literature, and then their applications to solving the problem with both Bayesian and nonBayesian techniques. The second part covers novel restoration methods, making use of the theory presented in Part I. Firstly, two new nonstationary image models are presented. The first models local variance in the image, and the second extends this with locally adaptive noncausal autoregressive (AR) texture estimation and local mean components. These models allow for recovery of image details including edges and texture, whilst preserving smooth regions. Most existing methods do not model the boundary conditions correctly for deblurring of natural photographs, and a Chapter is devoted to exploring Bayesian solutions to this topic. Due to the complexity of the models used and the problem itself, there are many challenges which must be overcome for tractable inference. Using the new models, three different inference strategies are investigated: firstly using the Bayesian maximum marginalised a posteriori (MMAP) method with deterministic optimisation; proceeding with the stochastic methods of variational Bayesian (VB) distribution approximation, and simulation of the posterior distribution using the Gibbs sampler. Of these, we find the Gibbs sampler to be the most effective way to deal with a variety of different types of unknown blurs. Along the way, details are given of the numerical strategies developed to give accurate results and to accelerate performance. Finally, the thesis demonstrates state of the art results in blind restoration of synthetic and real degraded images, such as recovering details in out of focus photographs

Unsupervised amplitude and texture based classification of SAR images with multinomial latent model

We combine both amplitude and texture statistics of the Synthetic Aperture Radar (SAR) images for classification purpose. We use Nakagami density to model the class amplitudes and a non-Gaussian Markov Random Field (MRF) texture model with t-distributed regression error to model the textures of the classes. A non-stationary Multinomial Logistic (MnL) latent class label model is used as a mixture density to obtain spatially smooth class segments. The Classification Expectation-Maximization (CEM) algorithm is performed to estimate the class parameters and to classify the pixels. We resort to Integrated Classification Likelihood (ICL) criterion to determine the number of classes in the model. We obtained some classification results of water, land and urban areas in both supervised and unsupervised cases on TerraSAR-X, as well as COSMO-SkyMed data

Image Restoration

This book represents a sample of recent contributions of researchers all around the world in the field of image restoration. The book consists of 15 chapters organized in three main sections (Theory, Applications, Interdisciplinarity). Topics cover some different aspects of the theory of image restoration, but this book is also an occasion to highlight some new topics of research related to the emergence of some original imaging devices. From this arise some real challenging problems related to image reconstruction/restoration that open the way to some new fundamental scientific questions closely related with the world we interact with