Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the proposed framework with structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared to traditional sparse inverse problem techniques. This interpretation also suggests an effective dictionary motivated initialization for the MAP-EM algorithm. We demonstrate that in a number of image inverse problems, including inpainting, zooming, and deblurring, the same algorithm produces either equal, often significantly better, or very small margin worse results than the best published ones, at a lower computational cost.Comment: 30 page

A multi-view approach to cDNA micro-array analysis

The official published version can be obtained from the link below.Microarray has emerged as a powerful technology that enables biologists to study thousands of genes simultaneously, therefore, to obtain a better understanding of the gene interaction and regulation mechanisms. This paper is concerned with improving the processes involved in the analysis of microarray image data. The main focus is to clarify an image's feature space in an unsupervised manner. In this paper, the Image Transformation Engine (ITE), combined with different filters, is investigated. The proposed methods are applied to a set of real-world cDNA images. The MatCNN toolbox is used during the segmentation process. Quantitative comparisons between different filters are carried out. It is shown that the CLD filter is the best one to be applied with the ITE.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the National Science Foundation of China under Innovative Grant 70621001, Chinese Academy of Sciences under Innovative Group Overseas Partnership Grant, the BHP Billiton Cooperation of Australia Grant, the International Science and Technology Cooperation Project of China under Grant 2009DFA32050 and the Alexander von Humboldt Foundation of Germany

Combining Contrast Invariant L1 Data Fidelities with Nonlinear Spectral Image Decomposition

This paper focuses on multi-scale approaches for variational methods and corresponding gradient flows. Recently, for convex regularization functionals such as total variation, new theory and algorithms for nonlinear eigenvalue problems via nonlinear spectral decompositions have been developed. Those methods open new directions for advanced image filtering. However, for an effective use in image segmentation and shape decomposition, a clear interpretation of the spectral response regarding size and intensity scales is needed but lacking in current approaches. In this context, $L^1$ data fidelities are particularly helpful due to their interesting multi-scale properties such as contrast invariance. Hence, the novelty of this work is the combination of $L^1$-based multi-scale methods with nonlinear spectral decompositions. We compare $L^1$ with $L^2$ scale-space methods in view of spectral image representation and decomposition. We show that the contrast invariant multi-scale behavior of $L^1-TV$ promotes sparsity in the spectral response providing more informative decompositions. We provide a numerical method and analyze synthetic and biomedical images at which decomposition leads to improved segmentation.Comment: 13 pages, 7 figures, conference SSVM 201

Automatic Structural Scene Digitalization

In this paper, we present an automatic system for the analysis and labeling of structural scenes, floor plan drawings in Computer-aided Design (CAD) format. The proposed system applies a fusion strategy to detect and recognize various components of CAD floor plans, such as walls, doors, windows and other ambiguous assets. Technically, a general rule-based filter parsing method is fist adopted to extract effective information from the original floor plan. Then, an image-processing based recovery method is employed to correct information extracted in the first step. Our proposed method is fully automatic and real-time. Such analysis system provides high accuracy and is also evaluated on a public website that, on average, archives more than ten thousands effective uses per day and reaches a relatively high satisfaction rate.Comment: paper submitted to PloS On

Spectral Representations of One-Homogeneous Functionals

This paper discusses a generalization of spectral representations related to convex one-homogeneous regularization functionals, e.g. total variation or $\ell^1$-norms. Those functionals serve as a substitute for a Hilbert space structure (and the related norm) in classical linear spectral transforms, e.g. Fourier and wavelet analysis. We discuss three meaningful definitions of spectral representations by scale space and variational methods and prove that (nonlinear) eigenfunctions of the regularization functionals are indeed atoms in the spectral representation. Moreover, we verify further useful properties related to orthogonality of the decomposition and the Parseval identity. The spectral transform is motivated by total variation and further developed to higher order variants. Moreover, we show that the approach can recover Fourier analysis as a special case using an appropriate $\ell^1$-type functional and discuss a coupled sparsity example

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

Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE