Sparse approximation

About: Sparse approximation is a research topic. Over the lifetime, 18037 publications have been published within this topic receiving 497739 citations. The topic is also known as: Sparse approximation.

Signal Space CoSaMP for Sparse Recovery With Redundant Dictionaries

Abstract: Compressive sensing (CS) has recently emerged as a powerful framework for acquiring sparse signals. The bulk of the CS literature has focused on the case where the acquired signal has a sparse or compressible representation in an orthonormal basis. In practice, however, there are many signals that cannot be sparsely represented or approximated using an orthonormal basis, but that do have sparse representations in a redundant dictionary. Standard results in CS can sometimes be extended to handle this case provided that the dictionary is sufficiently incoherent or well conditioned, but these approaches fail to address the case of a truly redundant or overcomplete dictionary. In this paper, we describe a variant of the iterative recovery algorithm CoSaMP for this more challenging setting. We utilize the \mbi D-RIP, a condition on the sensing matrix analogous to the well-known restricted isometry property. In contrast to prior work, the method and analysis are “signal-focused”; that is, they are oriented around recovering the signal rather than its dictionary coefficients. Under the assumption that we have a near-optimal scheme for projecting vectors in signal space onto the model family of candidate sparse signals, we provide provable recovery guarantees. Developing a practical algorithm that can provably compute the required near-optimal projections remains a significant open problem, but we include simulation results using various heuristics that empirically exhibit superior performance to traditional recovery algorithms.

Towards 3D Face Recognition in the Real: A Registration-Free Approach Using Fine-Grained Matching of 3D Keypoint Descriptors

Abstract: Registration algorithms performed on point clouds or range images of face scans have been successfully used for automatic 3D face recognition under expression variations, but have rarely been investigated to solve pose changes and occlusions mainly since that the basic landmarks to initialize coarse alignment are not always available. Recently, local feature-based SIFT-like matching proves competent to handle all such variations without registration. In this paper, towards 3D face recognition for real-life biometric applications, we significantly extend the SIFT-like matching framework to mesh data and propose a novel approach using fine-grained matching of 3D keypoint descriptors. First, two principal curvature-based 3D keypoint detectors are provided, which can repeatedly identify complementary locations on a face scan where local curvatures are high. Then, a robust 3D local coordinate system is built at each keypoint, which allows extraction of pose-invariant features. Three keypoint descriptors, corresponding to three surface differential quantities, are designed, and their feature-level fusion is employed to comprehensively describe local shapes of detected keypoints. Finally, we propose a multi-task sparse representation based fine-grained matching algorithm, which accounts for the average reconstruction error of probe face descriptors sparsely represented by a large dictionary of gallery descriptors in identification. Our approach is evaluated on the Bosphorus database and achieves rank-one recognition rates of 96.56, 98.82, 91.14, and 99.21 % on the entire database, and the expression, pose, and occlusion subsets, respectively. To the best of our knowledge, these are the best results reported so far on this database. Additionally, good generalization ability is also exhibited by the experiments on the FRGC v2.0 database.

Sparse cooperative Q-learning

Abstract: Learning in multiagent systems suffers from the fact that both the state and the action space scale exponentially with the number of agents. In this paper we are interested in using Q-learning to learn the coordinated actions of a group of cooperative agents, using a sparse representation of the joint state-action space of the agents. We first examine a compact representation in which the agents need to explicitly coordinate their actions only in a predefined set of states. Next, we use a coordination-graph approach in which we represent the Q-values by value rules that specify the coordination dependencies of the agents at particular states. We show how Q-learning can be efficiently applied to learn a coordinated policy for the agents in the above framework. We demonstrate the proposed method on the predator-prey domain, and we compare it with other related multiagent Q-learning methods.

Noise Robust Face Image Super-Resolution Through Smooth Sparse Representation

Abstract: Face image super-resolution has attracted much attention in recent years. Many algorithms have been proposed. Among them, sparse representation (SR)-based face image super-resolution approaches are able to achieve competitive performance. However, these SR-based approaches only perform well under the condition that the input is noiseless or has small noise. When the input is corrupted by large noise, the reconstruction weights (or coefficients) of the input low-resolution (LR) patches using SR-based approaches will be seriously unstable, thus leading to poor reconstruction results. To this end, in this paper, we propose a novel SR-based face image super-resolution approach that incorporates smooth priors to enforce similar training patches having similar sparse coding coefficients. Specifically, we introduce the fused least absolute shrinkage and selection operator-based smooth constraint and locality-based smooth constraint to the least squares representation-based patch representation in order to obtain stable reconstruction weights, especially when the noise level of the input LR image is high. Experiments are carried out on the benchmark FEI face database and CMU+MIT face database. Visual and quantitative comparisons show that the proposed face image super-resolution method yields superior reconstruction results when the input LR face image is contaminated by strong noise.

Image inpainting via sparse representation

Abstract: This paper proposes a novel patch-wise image inpainting algorithm using the image signal sparse representation over a redundant dictionary, which merits in both capabilities to deal with large holes and to preserve image details while taking less risk. Different from all existing works, we consider the problem of image inpainting from the view point of sequential incomplete signal recovery under the assumption that the every image patch admits a sparse representation over a redundant dictionary. To ensure the visually plausibility and consistency constraints between the filled hole and the surroundings, we propose to construct a redundant signal dictionary by directly sampling from the intact source region of current image. Then we sequentially compute the sparse representation for each incomplete patch at the boundary of the hole and recover it until the whole hole is filled. Experimental results show that this approach can efficiently fill in the hole with visually plausible information, and take less risk to introduce unwanted objects or artifacts.