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 stabilization and optimal control of the Cucker-Smale model

Abstract: This article is mainly based on the work [7], and it is dedicated to the 60th anniversary of B. Bonnard, held in Dijon in June 2012. We focus on a controlled Cucker--Smale model in finite dimension. Such dynamics model self-organization and consensus emergence in a group of agents. We explore how it is possible to control this model in order to enforce or facilitate pattern formation or convergence to consensus. In particular, we are interested in designing control strategies that are componentwise sparse in the sense that they require a small amount of external intervention, and also time sparse in the sense that such strategies are not chattering in time. These sparsity features are desirable in view of practical issues. We first show how very simple sparse feedback strategies can be designed with the use of a variational principle, in order to steer the system to consensus. These feedbacks are moreover optimal in terms of decay rate of some functional, illustrating the general principle according to which ''sparse is better''. We then combine these results with local controllability properties to get global controllability results. Finally, we explore the sparsity properties of the optimal control minimizing a combination of the distance from consensus and of a norm of the control.

Image Reconstruction for Electrical Capacitance Tomography Based on Sparse Representation

Abstract: Image reconstruction for electrical capacitance tomography (ECT) is a nonlinear problem A generalized inverse operator is usually ill-posed (unbounded) and ill-conditioned (with a large norm) Therefore, the solutions for ECT are not unique and highly sensitive to the measurement noise To improve the image quality, a new image reconstruction algorithm for ECT based on sparse representation is proposed An unconventional basis, ie, an extended sensitivity matrix consisting of some normalized capacitance vectors corresponding to the base permittivity elements is designed as an expansion frame The permittivity distributions to be reconstructed can have a natural sparse representation based on the new basis and can be represented as a linear combination of the base elements Another sparsity regularization method-the standard Landweber iteration with a threshold is also conducted for comparison The proposed algorithm has been evaluated by both simulation (with and without noise) and experimental results for different permittivity distributions

Classification on the Monogenic Scale Space: Application to Target Recognition in SAR Image

Abstract: This paper introduces a novel classification strategy based on the monogenic scale space for target recognition in Synthetic Aperture Radar (SAR) image. The proposed method exploits monogenic signal theory, a multidimensional generalization of the analytic signal, to capture the characteristics of SAR image, e.g., broad spectral information and simultaneous spatial localization. The components derived from the monogenic signal at different scales are then applied into a recently developed framework, sparse representation-based classification (SRC). Moreover, to deal with the data set, whose target classes are not linearly separable, the classification via kernel combination is proposed, where the multiple components of the monogenic signal are jointly considered into a unifying framework for target recognition. The novelty of this paper comes from: 1) the development of monogenic feature via uniformly downsampling, normalization, and concatenation of the components at various scales; 2) the development of score-level fusion for SRCs; and 3) the development of composite kernel learning for classification. In particular, the comparative experimental studies under nonliteral operating conditions, e.g., structural modifications, random noise corruption, and variations in depression angle, are performed. The comparative experimental studies of various algorithms, including the linear support vector machine and the kernel version, the SRC and the variants, kernel SRC, kernel linear representation, and sparse representation of monogenic signal, are performed too. The feasibility of the proposed method has been successfully verified using Moving and Stationary Target Acquiration and Recognition database. The experimental results demonstrate that significant improvement for recognition accuracy can be achieved by the proposed method in comparison with the baseline algorithms.

Spectral–Spatial Adaptive Sparse Representation for Hyperspectral Image Denoising

Abstract: In this paper, a novel spectral–spatial adaptive sparse representation (SSASR) method is proposed for hyperspectral image (HSI) denoising. The proposed SSASR method aims at improving noise-free estimation for noisy HSI by making full use of highly correlated spectral information and highly similar spatial information via sparse representation, which consists of the following three steps. First, according to spectral correlation across bands, the HSI is partitioned into several nonoverlapping band subsets. Each band subset contains multiple continuous bands with highly similar spectral characteristics. Then, within each band subset, shape-adaptive local regions consisting of spatially similar pixels are searched in spatial domain. This way, spectral–spatial similar pixels can be grouped. Finally, the highly correlated and similar spectral–spatial information in each group is effectively used via the joint sparse coding, in order to generate better noise-free estimation. The proposed SSASR method is evaluated by different objective metrics in both real and simulated experiments. The numerical and visual comparison results demonstrate the effectiveness and superiority of the proposed method.