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

Anisotropic Diffusion Partial Differential Equations in Multi-Channel Image Processing : Framework and Applications

We review recent methods based on diffusion PDE's (Partial Differential Equations) for the purpose of multi-channel image regularization. Such methods have the ability to smooth multi-channel images anisotropically and can preserve then image contours while removing noise or other undesired local artifacts. We point out the pros and cons of the existing equations, providing at each time a local geometric interpretation of the corresponding processes. We focus then on an alternate and generic tensor-driven formulation, able to regularize images while specifically taking the curvatures of local image structures into account. This particular diffusion PDE variant is actually well suited for the preservation of thin structures and gives regularization results where important image features can be particularly well preserved compared to its competitors. A direct link between this curvature-preserving equation and a continuous formulation of the Line Integral Convolution technique (Cabral and Leedom, 1993) is demonstrated. It allows the design of a very fast and stable numerical scheme which implements the multi-valued regularization method by successive integrations of the pixel values along curved integral lines. Besides, the proposed implementation, based on a fourth-order Runge Kutta numerical integration, can be applied with a subpixel accuracy and preserves then thin image structures much better than classical finite-differences discretizations, usually chosen to implement PDE-based diffusions. We finally illustrate the efficiency of this diffusion PDE's for multi-channel image regularization - in terms of speed and visual quality - with various applications and results on color images, including image denoising, inpainting and edge-preserving interpolation

Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio

An augmented Lagrangian method for total variation video restoration,”

Abstract-This paper presents a fast algorithm for restoring video sequences. The proposed algorithm, as opposed to existing methods, does not consider video restoration as a sequence of image restoration problems. Rather, it treats a video sequence as a space-time volume and poses a space-time total variation regularization to enhance the smoothness of the solution. The optimization problem is solved by transforming the original unconstrained minimization problem to an equivalent constrained minimization problem. An augmented Lagrangian method is used to handle the constraints, and an alternating direction method (ADM) is used to iteratively find solutions of the subproblems. The proposed algorithm has a wide range of applications, including video deblurring and denoising, video disparity refinement, and hot-air turbulence effect reduction

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

Task-specific and interpretable feature learning

Deep learning models have had tremendous impacts in recent years, while a question has been raised by many: Is deep learning just a triumph of empiricism? There has been emerging interest in reducing the gap between the theoretical soundness and interpretability, and the empirical success of deep models. This dissertation provides a comprehensive discussion on bridging traditional model-based learning approaches that emphasize problem-specific reasoning, and deep models that allow for larger learning capacity. The overall goal is to devise the next-generation feature learning architectures that are: 1) task-specific, namely, optimizing the entire pipeline from end to end while taking advantage of available prior knowledge and domain expertise; and 2) interpretable, namely, being able to learn a representation consisting of semantically sensible variables, and to display predictable behaviors. This dissertation starts by showing how the classical sparse coding models could be improved in a task-specific way, by formulating the entire pipeline as bi-level optimization. Then, it mainly illustrates how to incorporate the structure of classical learning models, e.g., sparse coding, into the design of deep architectures. A few concrete model examples are presented, ranging from the $\ell_0$ and $\ell_1$ sparse approximation models, to the $\ell_\infty$ constrained model and the dual-sparsity model. The analytic tools in the optimization problems can be translated to guide the architecture design and performance analysis of deep models. As a result, those customized deep models demonstrate improved performance, intuitive interpretation, and efficient parameter initialization. On the other hand, deep networks are shown to be analogous to brain mechanisms. They exhibit the ability to describe semantic content from the primitive level to the abstract level. This dissertation thus also presents a preliminary investigation of the synergy between feature learning with cognitive science and neuroscience. Two novel application domains, image aesthetics assessment and brain encoding, are explored, with promising preliminary results achieved