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.

Structured Priors for Sparse-Representation-Based Hyperspectral Image Classification

Abstract: Pixelwise classification, where each pixel is assigned to a predefined class, is one of the most important procedures in hyperspectral image (HSI) analysis. By representing a test pixel as a linear combination of a small subset of labeled pixels, a sparse representation classifier (SRC) gives rather plausible results compared with that of traditional classifiers such as the support vector machine. Recently, by incorporating additional structured sparsity priors, the second-generation SRCs have appeared in the literature and are reported to further improve the performance of HSI. These priors are based on exploiting the spatial dependences between the neighboring pixels, the inherent structure of the dictionary, or both. In this letter, we review and compare several structured priors for sparse-representation-based HSI classification. We also propose a new structured prior called the low-rank (LR) group prior, which can be considered as a modification of the LR prior. Furthermore, we will investigate how different structured priors improve the result for the HSI classification.

A new sparse grid based method for uncertainty propagation

Abstract: Current methods for uncertainty propagation suffer from their limitations in providing accurate and efficient solutions to high-dimension problems with interactions of random variables. The sparse grid technique, originally invented for numerical integration and interpolation, is extended to uncertainty propagation in this work to overcome the difficulty. The concept of Sparse Grid Numerical Integration (SGNI) is extended for estimating the first two moments of performance in robust design, while the Sparse Grid Interpolation (SGI) is employed to determine failure probability by interpolating the limit-state function at the Most Probable Point (MPP) in reliability analysis. The proposed methods are demonstrated by high-dimension mathematical examples with notable variate interactions and one multidisciplinary rocket design problem. Results show that the use of sparse grid methods works better than popular counterparts. Furthermore, the automatic sampling, special interpolation process, and dimension-adaptivity feature make SGI more flexible and efficient than using the uniform sample based metamodeling techniques.

Parallel and distributed sparse optimization

Abstract: This paper proposes parallel and distributed algorithms for solving very large-scale sparse optimization problems on computer clusters and clouds. Modern datasets usually have a large number of features or training samples, and they are usually stored in a distributed manner. Motivated by the need of solving sparse optimization problems with large datasets, we propose two approaches including (i) distributed implementations of prox-linear algorithms and (ii) GRock, a parallel greedy block coordinate descent method. Different separability properties of the objective terms in the problem enable different data distributed schemes along with their corresponding algorithm implementations. We also establish the convergence of GRock and explain why it often performs exceptionally well for sparse optimization. Numerical results on a computer cluster and Amazon EC2 demonstrate the efficiency and elasticity of our algorithms.

Reconstruction of Graph Signals Through Percolation from Seeding Nodes

Abstract: New schemes to recover signals defined in the nodes of a graph are proposed. Our focus is on reconstructing bandlimited graph signals, which are signals that admit a sparse representation in a frequency domain related to the structure of the graph. Most existing formulations focus on estimating an unknown graph signal by observing its value on a subset of nodes. By contrast, in this paper, we study the problem of inducing a known graph signal using as input a graph signal that is nonzero only for a small subset of nodes. The sparse signal is then percolated (interpolated) across the graph using a graph filter. Alternatively, one can interpret graph signals as network states and study graph-signal reconstruction as a network-control problem where the target class of states is represented by bandlimited signals. Three setups are investigated. In the first one, a single simultaneous injection takes place on several nodes in the graph. In the second one, successive value injections take place on a single node. The third one is a generalization where multiple nodes inject multiple signal values. For noiseless settings, conditions under which perfect reconstruction is feasible are given, and the corresponding schemes to recover the desired signal are specified. Scenarios leading to imperfect reconstruction, either due to insufficient or noisy signal value injections, are also analyzed. Moreover, connections with classical interpolation in the time domain are discussed. Specifically, for time-varying signals, where the ideal interpolator after uniform sampling is a (low-pass) filter, our proposed approach and the reconstruction of a sampled signal coincide. Nevertheless, for general graph signals, we show that these two approaches differ. The last part of the paper presents numerical experiments that illustrate the results developed through synthetic and real-world signal reconstruction problems.