A Theoretically Guaranteed Deep Optimization Framework for Robust Compressive Sensing MRI

Magnetic Resonance Imaging (MRI) is one of the most dynamic and safe imaging techniques available for clinical applications. However, the rather slow speed of MRI acquisitions limits the patient throughput and potential indi cations. Compressive Sensing (CS) has proven to be an efficient technique for accelerating MRI acquisition. The most widely used CS-MRI model, founded on the premise of reconstructing an image from an incompletely filled k-space, leads to an ill-posed inverse problem. In the past years, lots of efforts have been made to efficiently optimize the CS-MRI model. Inspired by deep learning techniques, some preliminary works have tried to incorporate deep architectures into CS-MRI process. Unfortunately, the convergence issues (due to the experience-based networks) and the robustness (i.e., lack real-world noise modeling) of these deeply trained optimization methods are still missing. In this work, we develop a new paradigm to integrate designed numerical solvers and the data-driven architectures for CS-MRI. By introducing an optimal condition checking mechanism, we can successfully prove the convergence of our established deep CS-MRI optimization scheme. Furthermore, we explicitly formulate the Rician noise distributions within our framework and obtain an extended CS-MRI network to handle the real-world nosies in the MRI process. Extensive experimental results verify that the proposed paradigm outperforms the existing state-of-the-art techniques both in reconstruction accuracy and efficiency as well as robustness to noises in real scene

Combining local regularity estimation and total variation optimization for scale-free texture segmentation

Texture segmentation constitutes a standard image processing task, crucial to many applications. The present contribution focuses on the particular subset of scale-free textures and its originality resides in the combination of three key ingredients: First, texture characterization relies on the concept of local regularity ; Second, estimation of local regularity is based on new multiscale quantities referred to as wavelet leaders ; Third, segmentation from local regularity faces a fundamental bias variance trade-off: In nature, local regularity estimation shows high variability that impairs the detection of changes, while a posteriori smoothing of regularity estimates precludes from locating correctly changes. Instead, the present contribution proposes several variational problem formulations based on total variation and proximal resolutions that effectively circumvent this trade-off. Estimation and segmentation performance for the proposed procedures are quantified and compared on synthetic as well as on real-world textures

Flexible Multi-layer Sparse Approximations of Matrices and Applications

The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the complexity of applying linear operators in high dimension by approximately factorizing the corresponding matrix into few sparse factors. The approach relies on recent advances in non-convex optimization. It is first explained and analyzed in details and then demonstrated experimentally on various problems including dictionary learning for image denoising, and the approximation of large matrices arising in inverse problems

CMB map restoration

Estimating the cosmological microwave background is of utmost importance for cosmology. However, its estimation from full-sky surveys such as WMAP or more recently Planck is challenging: CMB maps are generally estimated via the application of some source separation techniques which never prevent the final map from being contaminated with noise and foreground residuals. These spurious contaminations whether noise or foreground residuals are well-known to be a plague for most cosmologically relevant tests or evaluations; this includes CMB lensing reconstruction or non-Gaussian signatures search. Noise reduction is generally performed by applying a simple Wiener filter in spherical harmonics; however this does not account for the non-stationarity of the noise. Foreground contamination is usually tackled by masking the most intense residuals detected in the map, which makes CMB evaluation harder to perform. In this paper, we introduce a novel noise reduction framework coined LIW-Filtering for Linear Iterative Wavelet Filtering which is able to account for the noise spatial variability thanks to a wavelet-based modeling while keeping the highly desired linearity of the Wiener filter. We further show that the same filtering technique can effectively perform foreground contamination reduction thus providing a globally cleaner CMB map. Numerical results on simulated but realistic Planck data are provided

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

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