Block-based Collaborative 3-D Transform Domain Modeling in Inverse Imaging

The recent developments in image and video denoising have brought a new generation of filtering algorithms achieving unprecedented restoration quality. This quality mainly follows from exploiting various features of natural images. The nonlocal self-similarity and sparsity of representations are key elements of the novel filtering algorithms, with the best performance achieved by adaptively aggregating multiple redundant and sparse estimates. In a very broad sense, the filters are now able, given a perturbed image, to identify its plausible representative in the space or manifold of possible solutions. Thus, they are powerful tools not only for noise removal, but also for providing accurate adaptive regularization to many ill-conditioned inverse imaging problems. In this thesis we show how the image modeling of the well-known Block-matching 3-D transform domain (BM3D) filter can be exploited for designing efficient algorithms for image reconstruction. First, we formalize the BM3D-modeling in terms of the overcomplete sparse frame representation. We construct analysis and synthesis BM3D-frames and study their properties, making BM3D-modeling available for use in variational formulations of image reconstruction problems. Second, we demonstrate that standard variational formulations based on single objective optimization, such as Basis Pursuit Denoising and its various extensions, cannot be used with the imaging models generating non-tight frames, such as BM3D. We propose an alternative sparsity promoting problem formulation based on the generalized Nash equilibrium (GNE). Finally, using BM3D-frames we develop practical algorithms for image deblurring and super-resolution problems. To the best of our knowledge, these algorithms provide results which are the state of the art in the field

A Unified Conditional Framework for Diffusion-based Image Restoration

Diffusion Probabilistic Models (DPMs) have recently shown remarkable performance in image generation tasks, which are capable of generating highly realistic images. When adopting DPMs for image restoration tasks, the crucial aspect lies in how to integrate the conditional information to guide the DPMs to generate accurate and natural output, which has been largely overlooked in existing works. In this paper, we present a unified conditional framework based on diffusion models for image restoration. We leverage a lightweight UNet to predict initial guidance and the diffusion model to learn the residual of the guidance. By carefully designing the basic module and integration module for the diffusion model block, we integrate the guidance and other auxiliary conditional information into every block of the diffusion model to achieve spatially-adaptive generation conditioning. To handle high-resolution images, we propose a simple yet effective inter-step patch-splitting strategy to produce arbitrary-resolution images without grid artifacts. We evaluate our conditional framework on three challenging tasks: extreme low-light denoising, deblurring, and JPEG restoration, demonstrating its significant improvements in perceptual quality and the generalization to restoration tasks

Quantifying Uncertainty in High Dimensional Inverse Problems by Convex Optimisation

Inverse problems play a key role in modern image/signal processing methods. However, since they are generally ill-conditioned or ill-posed due to lack of observations, their solutions may have significant intrinsic uncertainty. Analysing and quantifying this uncertainty is very challenging, particularly in high-dimensional problems and problems with non-smooth objective functionals (e.g. sparsity-promoting priors). In this article, a series of strategies to visualise this uncertainty are presented, e.g. highest posterior density credible regions, and local credible intervals (cf. error bars) for individual pixels and superpixels. Our methods support non-smooth priors for inverse problems and can be scaled to high-dimensional settings. Moreover, we present strategies to automatically set regularisation parameters so that the proposed uncertainty quantification (UQ) strategies become much easier to use. Also, different kinds of dictionaries (complete and over-complete) are used to represent the image/signal and their performance in the proposed UQ methodology is investigated.Comment: 5 pages, 5 figure

Restoration of Poissonian Images Using Alternating Direction Optimization

Much research has been devoted to the problem of restoring Poissonian images, namely for medical and astronomical applications. However, the restoration of these images using state-of-the-art regularizers (such as those based on multiscale representations or total variation) is still an active research area, since the associated optimization problems are quite challenging. In this paper, we propose an approach to deconvolving Poissonian images, which is based on an alternating direction optimization method. The standard regularization (or maximum a posteriori) restoration criterion, which combines the Poisson log-likelihood with a (non-smooth) convex regularizer (log-prior), leads to hard optimization problems: the log-likelihood is non-quadratic and non-separable, the regularizer is non-smooth, and there is a non-negativity constraint. Using standard convex analysis tools, we present sufficient conditions for existence and uniqueness of solutions of these optimization problems, for several types of regularizers: total-variation, frame-based analysis, and frame-based synthesis. We attack these problems with an instance of the alternating direction method of multipliers (ADMM), which belongs to the family of augmented Lagrangian algorithms. We study sufficient conditions for convergence and show that these are satisfied, either under total-variation or frame-based (analysis and synthesis) regularization. The resulting algorithms are shown to outperform alternative state-of-the-art methods, both in terms of speed and restoration accuracy.Comment: 12 pages, 12 figures, 2 tables. Submitted to the IEEE Transactions on Image Processin

Fast Two-step Blind Optical Aberration Correction

The optics of any camera degrades the sharpness of photographs, which is a key visual quality criterion. This degradation is characterized by the point-spread function (PSF), which depends on the wavelengths of light and is variable across the imaging field. In this paper, we propose a two-step scheme to correct optical aberrations in a single raw or JPEG image, i.e., without any prior information on the camera or lens. First, we estimate local Gaussian blur kernels for overlapping patches and sharpen them with a non-blind deblurring technique. Based on the measurements of the PSFs of dozens of lenses, these blur kernels are modeled as RGB Gaussians defined by seven parameters. Second, we remove the remaining lateral chromatic aberrations (not contemplated in the first step) with a convolutional neural network, trained to minimize the red/green and blue/green residual images. Experiments on both synthetic and real images show that the combination of these two stages yields a fast state-of-the-art blind optical aberration compensation technique that competes with commercial non-blind algorithms.Comment: 28 pages, 20 figures, accepted at ECCV'22 as a poste

Distributed Deblurring of Large Images of Wide Field-Of-View

Image deblurring is an economic way to reduce certain degradations (blur and noise) in acquired images. Thus, it has become essential tool in high resolution imaging in many applications, e.g., astronomy, microscopy or computational photography. In applications such as astronomy and satellite imaging, the size of acquired images can be extremely large (up to gigapixels) covering wide field-of-view suffering from shift-variant blur. Most of the existing image deblurring techniques are designed and implemented to work efficiently on centralized computing system having multiple processors and a shared memory. Thus, the largest image that can be handle is limited by the size of the physical memory available on the system. In this paper, we propose a distributed nonblind image deblurring algorithm in which several connected processing nodes (with reasonable computational resources) process simultaneously different portions of a large image while maintaining certain coherency among them to finally obtain a single crisp image. Unlike the existing centralized techniques, image deblurring in distributed fashion raises several issues. To tackle these issues, we consider certain approximations that trade-offs between the quality of deblurred image and the computational resources required to achieve it. The experimental results show that our algorithm produces the similar quality of images as the existing centralized techniques while allowing distribution, and thus being cost effective for extremely large images.Comment: 16 pages, 10 figures, submitted to IEEE Trans. on Image Processin