Topic
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.
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TL;DR: Experimental results demonstrate the superiority of SPSTFM in capturing surface reflectance changes on both categories of images, and the model was compared with other related algorithms on two types of data: images primarily with phenology change and images mainly with land-cover type change.
Abstract: This paper presents a novel model for blending remote sensing data of high spatial resolution (HSR), taken at infrequent intervals, with those available frequently but at low spatial resolution (LSR) in the context of monitoring and predicting changes in land usage and phenology. Named “SParse-representation-based SpatioTemporal reflectance Fusion Model” (SPSTFM), the model has been developed for predicting HSR surface reflectances through data blending with LSR scenes. Remarkably, this model forms a unified framework for fusing remote sensing images with temporal reflectance changes, phenology change (e.g., seasonal change of vegetation), or type change (e.g., conversion of farmland to built-up area), by establishing correspondences between structures within HSR images of given areas and their corresponding LSR images. Such corresponding relationship is achieved by means of the sparse representation, specifically by jointly training two dictionaries generated from HSR and LSR difference image patches and sparse coding at the reconstruction stage. SPSTFM was tested using both a simulated data set and an actual data set of Landsat Enhanced Thematic Mapper Plus-Moderate Resolution Imaging Spectroradiometer acquisitions. It was also compared with other related algorithms on two types of data: images primarily with phenology change and images primarily with land-cover type change. Experimental results demonstrate the superiority of SPSTFM in capturing surface reflectance changes on both categories of images.
311 citations
TL;DR: The robustness of this approach under various types of distortions, such as deformation, noise, outliers, rotation, and occlusion, greatly outperforms the state-of-the-art methods, especially when the data is badly degraded.
Abstract: In previous work on point registration, the input point sets are often represented using Gaussian mixture models and the registration is then addressed through a probabilistic approach, which aims to exploit global relationships on the point sets. For non-rigid shapes, however, the local structures among neighboring points are also strong and stable and thus helpful in recovering the point correspondence. In this paper, we formulate point registration as the estimation of a mixture of densities, where local features, such as shape context, are used to assign the membership probabilities of the mixture model. This enables us to preserve both global and local structures during matching. The transformation between the two point sets is specified in a reproducing kernel Hilbert space and a sparse approximation is adopted to achieve a fast implementation. Extensive experiments on both synthesized and real data show the robustness of our approach under various types of distortions, such as deformation, noise, outliers, rotation, and occlusion. It greatly outperforms the state-of-the-art methods, especially when the data is badly degraded.
311 citations
TL;DR: The proposed unconventional random feature extraction is simple, yet by leveraging the sparse nature of texture images, the approach outperforms traditional feature extraction methods which involve careful design and complex steps and leads to significant improvements in classification accuracy and reductions in feature dimensionality.
Abstract: Inspired by theories of sparse representation and compressed sensing, this paper presents a simple, novel, yet very powerful approach for texture classification based on random projection, suitable for large texture database applications. At the feature extraction stage, a small set of random features is extracted from local image patches. The random features are embedded into a bag--of-words model to perform texture classification; thus, learning and classification are carried out in a compressed domain. The proposed unconventional random feature extraction is simple, yet by leveraging the sparse nature of texture images, our approach outperforms traditional feature extraction methods which involve careful design and complex steps. We have conducted extensive experiments on each of the CUReT, the Brodatz, and the MSRC databases, comparing the proposed approach to four state-of-the-art texture classification methods: Patch, Patch-MRF, MR8, and LBP. We show that our approach leads to significant improvements in classification accuracy and reductions in feature dimensionality.
310 citations
Book•
01 Jan 1971
TL;DR: A particular computation algorithm for the method without reorthogonalization is shown to have remarkably good error properties, and this suggests that this variant of the Lanczos process is likely to become an extremely useful algorithm for finding several extreme eigenvalues, and their eigenvectors if needed, of very large sparse symmetric matrices.
Abstract: Several methods are available for computing eigenvalues and eigenvectors of large sparse matrices, but as yet no outstandingly good algorithm is generally known. For the symmetric matrix case one of the most elegant algorithms theoretically is the method of minimized iterations developed by Lanczos in 1950. This method reduces the original matrix to tri-diagonal form from which the eigensystem can easily be found. The method can be used iteratively, and here the convergence properties and different possible eigenvalue intervals are first considered assuming infinite precision computation. Next rounding error analyses are given for the method both with and without re-orthogonalization. It is shown that the method has been unjustly neglected, in fact a particular computation algorithm for the method without reorthogonalization is shown to have remarkably good error properties. As well as this the algorithm is very fast and can be programmed to require very little store compared with other comparable methods, and this suggests that this variant of the Lanczos process is likely to become an extremely useful algorithm for finding several extreme eigenvalues, and their eigenvectors if needed, of very large sparse symmetric matrices.
310 citations
TL;DR: A novel dictionary learning method, called Dictionary Learning with Group Sparsity and Graph Regularization (DL-GSGR), where the geometrical structure of atoms is modeled as the graph regularization and the group coherence of learned dictionary can be enforced small enough such that any signal can be group sparse coded effectively.
Abstract: Recently, sparse representation has attracted a lot of interest in various areas. However, the standard sparse representation does not consider the intrinsic structure, i.e., the nonzero elements occur in clusters, called group sparsity. Furthermore, there is no dictionary learning method for group sparse representation considering the geometrical structure of space spanned by atoms. In this paper, we propose a novel dictionary learning method, called Dictionary Learning with Group Sparsity and Graph Regularization (DL-GSGR). First, the geometrical structure of atoms is modeled as the graph regularization. Then, combining group sparsity and graph regularization, the DL-GSGR is presented, which is solved by alternating the group sparse coding and dictionary updating. In this way, the group coherence of learned dictionary can be enforced small enough such that any signal can be group sparse coded effectively. Finally, group sparse representation with DL-GSGR is applied to 3-D medical image denoising and image fusion. Specifically, in 3-D medical image denoising, a 3-D processing mechanism (using the similarity among nearby slices) and temporal regularization (to perverse the correlations across nearby slices) are exploited. The experimental results on 3-D image denoising and image fusion demonstrate the superiority of our proposed denoising and fusion approaches.
310 citations