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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.


Papers
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Proceedings ArticleDOI
20 Jun 2011
TL;DR: A novel approach for intrinsic image decomposition using a reflectance sparsity prior that is based on a simple observation: neighboring pixels usually have the same reflectance if their chromaticities are the same or very similar, and derives a sparse representation of reflectance components using data-driven edge-avoiding-wavelets.
Abstract: Intrinsic image decomposition is an important problem that targets the recovery of shading and reflectance components from a single image. While this is an ill-posed problem on its own, we propose a novel approach for intrinsic image decomposition using a reflectance sparsity prior that we have developed. Our method is based on a simple observation: neighboring pixels usually have the same reflectance if their chromaticities are the same or very similar. We formalize this sparsity constraint on local reflectance, and derive a sparse representation of reflectance components using data-driven edge-avoiding-wavelets. We show that the reflectance component of natural images is sparse in this representation. We also propose and formulate a novel global reflectance sparsity constraint. Using this sparsity prior and global constraints, we formulate a l 1 -regularized least squares minimization problem for intrinsic image decomposition that can be solved efficiently. Our algorithm can successfully extract intrinsic images from a single image, without using other reflection or color models or any user interaction. The results on challenging scenes demonstrate the power of the proposed technique.

158 citations

Journal ArticleDOI
TL;DR: A time-scale approach to the decomposition and aggregation of dynamic networks with dense and sparse connections with weak coupling properties is developed.
Abstract: This paper develops a time-scale approach to the decomposition and aggregation of dynamic networks with dense and sparse connections. Two parameters are used to characterize time-scale and weak coupling properties. Bounds in terms of these parameters determine when there are two time-scales in sparse networks. Simplified models of the slow and fast subsystems are proposed and physical interpretations are provided. The results are illustrated with a 2000-node power network.

158 citations

Journal ArticleDOI
TL;DR: In this article, an image based rendering technique based on light field reconstruction from a limited set of perspective views acquired by cameras was developed, which utilizes sparse representation of epipolar-plane images (EPI) in shearlet transform domain.
Abstract: In this article we develop an image based rendering technique based on light field reconstruction from a limited set of perspective views acquired by cameras. Our approach utilizes sparse representation of epipolar-plane images (EPI) in shearlet transform domain. The shearlet transform has been specifically modified to handle the straight lines characteristic for EPI. The devised iterative regularization algorithm based on adaptive thresholding provides high-quality reconstruction results for relatively big disparities between neighboring views. The generated densely sampled light field of a given 3D scene is thus suitable for all applications which require light field reconstruction. The proposed algorithm compares favorably against state of the art depth image based rendering techniques and shows superior performance specifically in reconstructing scenes containing semi-transparent objects.

157 citations

Journal ArticleDOI
TL;DR: This paper considers the sparse linear regression model with a l1-norm penalty, also known as the least absolute shrinkage and selection operator (LASSO), for estimating sparse brain connectivity, a well-known decoding algorithm in the compressed sensing (CS).
Abstract: Partial correlation is a useful connectivity measure for brain networks, especially, when it is needed to remove the confounding effects in highly correlated networks. Since it is difficult to estimate the exact partial correlation under the small-n large-p situation, a sparseness constraint is generally introduced. In this paper, we consider the sparse linear regression model with a l1-norm penalty, also known as the least absolute shrinkage and selection operator (LASSO), for estimating sparse brain connectivity. LASSO is a well-known decoding algorithm in the compressed sensing (CS). The CS theory states that LASSO can reconstruct the exact sparse signal even from a small set of noisy measurements. We briefly show that the penalized linear regression for partial correlation estimation is related to CS. It opens a new possibility that the proposed framework can be used for a sparse brain network recovery. As an illustration, we construct sparse brain networks of 97 regions of interest (ROIs) obtained from FDG-PET imaging data for the autism spectrum disorder (ASD) children and the pediatric control (PedCon) subjects. As validation, we check the network reproducibilities by leave-one-out cross validation and compare the clustered structures derived from the brain networks of ASD and PedCon.

157 citations

Proceedings ArticleDOI
TL;DR: This paper presents the first 3D discrete curvelet transform, an extension to the 2D transform described in Candes et al..1, and describes three different implementations: in-core, out-of-core and MPI-based parallel implementations.
Abstract: In this paper, we present the first 3D discrete curvelet transform. This transform is an extension to the 2D transform described in Candes et al..1 The resulting curvelet frame preserves the important properties, such as parabolic scaling, tightness and sparse representation for singularities of codimension one. We describe three different implementations: in-core, out-of-core and MPI-based parallel implementations. Numerical results verify the desired properties of the 3D curvelets and demonstrate the efficiency of our implementations.

157 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023193
2022454
2021641
2020924
20191,208
20181,371