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.

Sparse Representation for 3D Shape Estimation: A Convex Relaxation Approach

Abstract: We investigate the problem of estimating the 3D shape of an object defined by a set of 3D landmarks, given their 2D correspondences in a single image. A successful approach to alleviating the reconstruction ambiguity is the 3D deformable shape model and a sparse representation is often used to capture complex shape variability. But the model inference is still challenging due to the nonconvexity in the joint optimization of shape and viewpoint. In contrast to prior work that relies on an alternating scheme whose solution depends on initialization, we propose a convex approach to addressing this challenge and develop an efficient algorithm to solve the proposed convex program. We further propose a robust model to handle gross errors in the 2D correspondences. We demonstrate the exact recovery property of the proposed method, the advantage compared to several nonconvex baselines and the applicability to recover 3D human poses and car models from single images.

A New Discriminative Sparse Representation Method for Robust Face Recognition via $l_{2}$ Regularization

Abstract: Sparse representation has shown an attractive performance in a number of applications. However, the available sparse representation methods still suffer from some problems, and it is necessary to design more efficient methods. Particularly, to design a computationally inexpensive, easily solvable, and robust sparse representation method is a significant task. In this paper, we explore the issue of designing the simple, robust, and powerfully efficient sparse representation methods for image classification. The contributions of this paper are as follows. First, a novel discriminative sparse representation method is proposed and its noticeable performance in image classification is demonstrated by the experimental results. More importantly, the proposed method outperforms the existing state-of-the-art sparse representation methods. Second, the proposed method is not only very computationally efficient but also has an intuitive and easily understandable idea. It exploits a simple algorithm to obtain a closed-form solution and discriminative representation of the test sample. Third, the feasibility, computational efficiency, and remarkable classification accuracy of the proposed $l_{2}$ regularization-based representation are comprehensively shown by extensive experiments and analysis. The code of the proposed method is available at http://www.yongxu.org/lunwen.html .

Image Decomposition and Separation Using Sparse Representations: An Overview

Abstract: This paper gives essential insights into the use of sparsity and morphological diversity in image decomposition and source separation by reviewing our recent work in this field. The idea to morphologically decompose a signal into its building blocks is an important problem in signal processing and has far-reaching applications in science and technology. Starck , proposed a novel decomposition method-morphological component analysis (MCA)-based on sparse representation of signals. MCA assumes that each (monochannel) signal is the linear mixture of several layers, the so-called morphological components, that are morphologically distinct, e.g., sines and bumps. The success of this method relies on two tenets: sparsity and morphological diversity. That is, each morphological component is sparsely represented in a specific transform domain, and the latter is highly inefficient in representing the other content in the mixture. Once such transforms are identified, MCA is an iterative thresholding algorithm that is capable of decoupling the signal content. Sparsity and morphological diversity have also been used as a novel and effective source of diversity for blind source separation (BSS), hence extending the MCA to multichannel data. Building on these ingredients, we will provide an overview the generalized MCA introduced by the authors in and as a fast and efficient BSS method. We will illustrate the application of these algorithms on several real examples. We conclude our tour by briefly describing our software toolboxes made available for download on the Internet for sparse signal and image decomposition and separation.

Generalized spectral bounds for sparse LDA

Abstract: We present a discrete spectral framework for the sparse or cardinality-constrained solution of a generalized Rayleigh quotient. This NP-hard combinatorial optimization problem is central to supervised learning tasks such as sparse LDA, feature selection and relevance ranking for classification. We derive a new generalized form of the Inclusion Principle for variational eigenvalue bounds, leading to exact and optimal sparse linear discriminants using branch-and-bound search. An efficient greedy (approximate) technique is also presented. The generalization performance of our sparse LDA algorithms is demonstrated with real-world UCI ML benchmarks and compared to a leading SVM-based gene selection algorithm for cancer classification.

Video anomaly detection and localisation based on the sparsity and reconstruction error of auto-encoder

Abstract: A fast and accurate video anomaly detection and localisation method is presented. The speed and localisation accuracy are two ongoing challenges in real-world anomaly detection. We introduce two novel cubic-patch-based anomaly detector where one works based on power of an auto-encoder (AE) on reconstituting an input video patch and another one is based on the power of sparse representation of an input video patch. It is found that if an AE is efficiently trained on all normal patches, the anomaly patch in testing phase has a more reconstruction error than a normal patch. Also if a sparse AE is learned based on normal training patches, we expect that the given patch to AE is represented sparsely. If the representation is not enough sparse it is considered as a good candidate to be anomaly. For being more fast, these two detectors are combined as a cascade classifier. First, all small patches on test video frame are scanned, those which have not enough sparse representation are resized and sent to next detector for more careful evaluation. The experiment results show that the method mentioned here has a better performance especially in run-time measure than state-of-the-art methods on two UMN and UCSD benchmarks.