Epigraphical Projection and Proximal Tools for Solving Constrained Convex Optimization Problems: Part I

We propose a proximal approach to deal with convex optimization problems involving nonlinear constraints. A large family of such constraints, proven to be effective in the solution of inverse problems, can be expressed as the lower level set of a sum of convex functions evaluated over different, but possibly overlapping, blocks of the signal. For this class of constraints, the associated projection operator generally does not have a closed form. We circumvent this difficulty by splitting the lower level set into as many epigraphs as functions involved in the sum. A closed half-space constraint is also enforced, in order to limit the sum of the introduced epigraphical variables to the upper bound of the original lower level set. In this paper, we focus on a family of constraints involving linear transforms of l_1,p balls. Our main theoretical contribution is to provide closed form expressions of the epigraphical projections associated with the Euclidean norm and the sup norm. The proposed approach is validated in the context of image restoration with missing samples, by making use of TV-like constraints. Experiments show that our method leads to significant improvements in term of convergence speed over existing algorithms for solving similar constrained problems

A proximal approach for constrained cosparse modelling

International audienceThe concept of cosparsity has been recently introduced in the arena of compressed sensing. In cosparse modelling, the ℓ0 (or ℓ1) cost of an analysis-based representation of the target signal is minimized under a data fidelity constraint. By taking benefit from recent advances in proximal algorithms, we show that it is possible to efficiently address a more general framework where a convex block sparsity measure is minimized under various convex constraints. The main contribution of this work is the introduction of a new epigraphical projection technique, which allows us to consider more flexible data fidelity constraints than the standard linear or quadratic ones. The validity of our approach is illustrated through an application to an image reconstruction problem in the presence of Poisson noise

Vector Lifting Schemes for Stereo Image Coding

International audienceMany research efforts have been devoted to the improvement of stereo image coding techniques for storage or transmission. In this paper, we are mainly interested in lossyto- lossless coding schemes for stereo images allowing progressive reconstruction. The most commonly used approaches for stereo compression are based on disparity compensation techniques. The basic principle involved in this technique first consists of estimating the disparity map. Then, one image is considered as a reference and the other is predicted in order to generate a residual image. In this work, we propose a novel approach, based on Vector Lifting Schemes (VLS), which offers the advantage of generating two compact multiresolution representations of the left and the right views. We present two versions of this new scheme. A theoretical analysis of the performance of the considered VLS is also conducted. Experimental results indicate a significant improvement using the proposed structures compared with conventional methods

Epigraphical splitting for solving constrained convex optimization problems with proximal tools

International audienceWe propose a proximal approach to deal with a class of convex variational problems involving nonlinear constraints. A large family of constraints, proven to be effective in the solution of inverse problems, can be expressed as the lower level set of a sum of convex functions evaluated over different blocks of the linearly-transformed signal. For such constraints, the associated projection operator generally does not have a simple form. We circumvent this difficulty by splitting the lower level set into as many epigraphs as functions involved in the sum. In particular, we focus on constraints involving q-norms with q ≥ 1, distance functions to a convex set, and L1,p-norms with p ∈ {2, +∞}. The proposed approach is validated in the context of image restoration by making use of constraints based on Non-Local Total Variation. Experiments show that our method leads to significant improvements in term of convergence speed over existing algorithms for solving similar constrained problems. A second application to a pulse shape design problem is provided in order to illustrate the flexibility of the proposed approach

Region-of-interest based rate control scheme for high efficiency video coding

International audienceIn this paper, we propose a new rate control scheme designed for the newest high efficiency video coding (HEVC) standard, and aimed at enhancing the quality of regions of interest (ROI). Our approach allocates a higher bit rate to the region of interest while keeping the global bit rate close to the assigned target value. This algorithm is developed for a videoconferencing system, where the ROIs (typically, faces) are automatically detected and each coding unit is classified in a region of the interest map. This map is given as input to the rate control algorithm and the bit allocation is made accordingly. Experimental results show that the proposed scheme achieves accurate target bit rates and provides an improvement in the region of interest quality, both in objective metrics and based on subjective quality evaluation

ROI-BASED RATE CONTROL USING TILES FOR AN HEVC ENCODED VIDEO STREAM OVER A LOSSY NETWORK

International audienceThe growth in the use of high definition (HD) and above video resolutions streams has outstripped the rate at which network infrastructure has been deployed. Video streaming applications require appropriate rate control techniques that make use of the specific characteristics of the video content, such as the regions of interest (ROI). With the introduction of high efficiency video coding (HEVC) streams, we consider new coding features to make a novel ROI-based rate control (RC) algorithm. The proposed approach introduces tiling in a ROI-based rate control scheme. It aims at enhancing the quality of important regions (i.e. faces for a videoconferencing system) considering independently coded regions lying within an ROI and helps evaluating the ROI quality under poor channel conditions. Our work consists of two major steps. First, we designed a RC algorithm based on an independent processing of tiles of different regions. Second, we investigate the effect of ROI-and tile-based rate control algorithm on the decoded quality of the stream transmitted over a lossy channel

Lifting schemes for joint coding of stereoscopic pairs of satellite images

electronic version (5 pp.)International audienceStereo data compression is an important issue for the new generation of vision systems. In this paper, we are interested in lossless coding methods for stereo images allowing progressive reconstruction. Most of the existing approaches account for the mutual similarities between the left and the right images. More precisely, the disparity compensation process consists in predicting the right image from the left one based on the disparity map. Then, the disparity map, the reference image, and the residual image are encoded. In this work, we propose a novel approach based on the concept of vector lifting scheme. Its main feature is that it does not generate one residual image but two compact multiresolution representations of the left and the right views, driven by the underlying disparity map. Experimental results show a significant improvement using this technique compared with conventional methods

Side information estimation and new symmetric schemes for multi-view distributed video coding

This paper deals with distributed video coding (DVC) for multi-view sequences. DVC of multi-view sequences is a recent field of research, with huge potential impact in applications such as videosurveil- lance, real-time event streaming from multiple cameras, and, in general, immersive communications. It raises however several problems, and in this paper we tackle two of them. Based on the principles of Wyner–Ziv (WZ) coding, in multi-view DVC many estimations can be generated in order to create the side information (SI) at the decoder. It has been shown that the quality of the SI strongly influences the global coding performances. Therefore, this paper proposes to study the contribution of multiple SI estimations (in the temporal and view directions) to the global performances. Moreover, we propose new symmetric schemes for longer group of pictures (GOP) in multi-view DVC and show that we can further exploit the long-term correlations using a new kind of estimation, called diagonal. For such schemes, several decoding strategies may be envisaged. We perform a theoretical study of the temporal and inter- view dependencies, and confirm by experiments the conclusion about the best decoding strategy

Disparity map estimation under convex constraints using proximal algorithms

International audienceIn this paper, we propose a new approach for estimating depth maps of stereo images which are prone to various types of noise. This method, based on a parallel proximal algorithm, gives a great flexibility in the choice of the constrained criterion to be minimized, thus allowing us to take into account different types of noise distributions. Our main objective is to present an iterative estimation method based on recent convex optimization algorithms and proximal tools. Results for several error measures demonstrate the effectiveness and robustness of the proposed method for disparity map estimation even in the presence of perturbations