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.

Joint Within-Class Collaborative Representation for Hyperspectral Image Classification

Abstract: Representation-based classification has gained great interest recently. In this paper, we extend our previous work in collaborative representation-based classification to spatially joint versions. This is due to the fact that neighboring pixels tend to belong to the same class with high probability. Specifically, neighboring pixels near the test pixel are simultaneously represented via a joint collaborative model of linear combinations of labeled samples, and the weights for representation are estimated by an l 2 -minimization derived closed-form solution. Experimental results confirm that the proposed joint within-class collaborative representation outperforms other state-of-the-art techniques, such as joint sparse representation and support vector machines with composite kernels.

Learning Sparse Representations of High Dimensional Data on Large Scale Dictionaries

Abstract: Learning sparse representations on data adaptive dictionaries is a state-of-the-art method for modeling data. But when the dictionary is large and the data dimension is high, it is a computationally challenging problem. We explore three aspects of the problem. First, we derive new, greatly improved screening tests that quickly identify codewords that are guaranteed to have zero weights. Second, we study the properties of random projections in the context of learning sparse representations. Finally, we develop a hierarchical framework that uses incremental random projections and screening to learn, in small stages, a hierarchically structured dictionary for sparse representations. Empirical results show that our framework can learn informative hierarchical sparse representations more efficiently.

Adaptive compressive ghost imaging based on wavelet trees and sparse representation

Abstract: Compressed sensing is a theory which can reconstruct an image almost perfectly with only a few measurements by finding its sparsest representation. However, the computation time consumed for large images may be a few hours or more. In this work, we both theoretically and experimentally demonstrate a method that combines the advantages of both adaptive computational ghost imaging and compressed sensing, which we call adaptive compressive ghost imaging, whereby both the reconstruction time and measurements required for any image size can be significantly reduced. The technique can be used to improve the performance of all computational ghost imaging protocols, especially when measuring ultra-weak or noisy signals, and can be extended to imaging applications at any wavelength.