Effective Image Restorations Using a Novel Spatial Adaptive Prior

Bayesian or Maximum a posteriori (MAP) approaches can effectively overcome the ill-posed problems of image restoration or deconvolution through incorporating a priori image information. Many restoration methods, such as nonquadratic prior Bayesian restoration and total variation regularization, have been proposed with edge-preserving and noise-removing properties. However, these methods are often inefficient in restoring continuous variation region and suppressing block artifacts. To handle this, this paper proposes a Bayesian restoration approach with a novel spatial adaptive (SA) prior. Through selectively and adaptively incorporating the nonlocal image information into the SA prior model, the proposed method effectively suppress the negative disturbance from irrelevant neighbor pixels, and utilizes the positive regularization from the relevant ones. A two-step restoration algorithm for the proposed approach is also given. Comparative experimentation and analysis demonstrate that, bearing high-quality edge-preserving and noise-removing properties, the proposed restoration also has good deblocking property

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

Graph Spectral Image Processing

Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation

Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian-Wishart processes

Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected with measurement errors on discretized grids. In order to accurately smooth noisy functional observations and deal with the issue of high-dimensional observation grids, we propose a novel Bayesian method based on the Bayesian hierarchical model with a Gaussian-Wishart process prior and basis function representations. We first derive an induced model for the basis-function coefficients of the functional data, and then use this model to conduct posterior inference through Markov chain Monte Carlo. Compared to the standard Bayesian inference that suffers serious computational burden and unstableness for analyzing high-dimensional functional data, our method greatly improves the computational scalability and stability, while inheriting the advantage of simultaneously smoothing raw observations and estimating the mean-covariance functions in a nonparametric way. In addition, our method can naturally handle functional data observed on random or uncommon grids. Simulation and real studies demonstrate that our method produces similar results as the standard Bayesian inference with low-dimensional common grids, while efficiently smoothing and estimating functional data with random and high-dimensional observation grids where the standard Bayesian inference fails. In conclusion, our method can efficiently smooth and estimate high-dimensional functional data, providing one way to resolve the curse of dimensionality for Bayesian functional data analysis with Gaussian-Wishart processes.Comment: Under revie

Nonparametric neighborhood statistics for MRI denoising

technical reportThis paper presents a novel method for denoising MR images that relies on an optimal estimation, combining a likelihood model with an adaptive image prior. The method models images as random fields and exploits the properties of independent Rician noise to learn the higher-order statistics of image neighborhoods from corrupted input data. It uses these statistics as priors within a Bayesian denoising framework. This paper presents an information-theoretic method for characterizing neighborhood structure using nonparametric density estimation. The formulation generalizes easily to simultaneous denoising of multimodal MRI, exploiting the relationships between modalities to further enhance performance. The method, relying on the information content of input data for noise estimation and setting important parameters, does not require significant parameter tuning. Qualitative and quantitative results on real, simulated, and multimodal data, including comparisons with other approaches, demonstrate the effectiveness of the method

Bayesian Spatial Binary Regression for Label Fusion in Structural Neuroimaging

Many analyses of neuroimaging data involve studying one or more regions of interest (ROIs) in a brain image. In order to do so, each ROI must first be identified. Since every brain is unique, the location, size, and shape of each ROI varies across subjects. Thus, each ROI in a brain image must either be manually identified or (semi-) automatically delineated, a task referred to as segmentation. Automatic segmentation often involves mapping a previously manually segmented image to a new brain image and propagating the labels to obtain an estimate of where each ROI is located in the new image. A more recent approach to this problem is to propagate labels from multiple manually segmented atlases and combine the results using a process known as label fusion. To date, most label fusion algorithms either employ voting procedures or impose prior structure and subsequently find the maximum a posteriori estimator (i.e., the posterior mode) through optimization. We propose using a fully Bayesian spatial regression model for label fusion that facilitates direct incorporation of covariate information while making accessible the entire posterior distribution. We discuss the implementation of our model via Markov chain Monte Carlo and illustrate the procedure through both simulation and application to segmentation of the hippocampus, an anatomical structure known to be associated with Alzheimer's disease.Comment: 24 pages, 10 figure

Deconvolution and Restoration of Optical Endomicroscopy Images

Optical endomicroscopy (OEM) is an emerging technology platform with preclinical and clinical imaging applications. Pulmonary OEM via fibre bundles has the potential to provide in vivo, in situ molecular signatures of disease such as infection and inflammation. However, enhancing the quality of data acquired by this technique for better visualization and subsequent analysis remains a challenging problem. Cross coupling between fiber cores and sparse sampling by imaging fiber bundles are the main reasons for image degradation, and poor detection performance (i.e., inflammation, bacteria, etc.). In this work, we address the problem of deconvolution and restoration of OEM data. We propose a hierarchical Bayesian model to solve this problem and compare three estimation algorithms to exploit the resulting joint posterior distribution. The first method is based on Markov chain Monte Carlo (MCMC) methods, however, it exhibits a relatively long computational time. The second and third algorithms deal with this issue and are based on a variational Bayes (VB) approach and an alternating direction method of multipliers (ADMM) algorithm respectively. Results on both synthetic and real datasets illustrate the effectiveness of the proposed methods for restoration of OEM images

Poisson-Gaussian noise parameter estimation in fluorescence microscopy imaging

International audienceIn this paper, we present a new fully automatic approach for noise parameter estimation in the context of fluorescence imaging systems. In particular, we address the problem of Poisson-Gaussian noise modeling in the nonstationary case. In microscopy practice, the nonstationarity is due to the photobleaching effect. The proposed method consists of an adequate moment based initialization followed by Expectation-Maximization iterations. This approach is shown to provide reliable estimates of the mean and the variance of the Gaussian noise and of the scale parameter of Poisson noise, as well as of the photobleaching rates. The algorithm performance is demonstrated on both synthetic and real fluorescence microscopy image sequences