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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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Journal ArticleDOI
TL;DR: An efficient and robust solution for image set classification which includes the image samples of the set and their affine hull model and jointly optimizes the nearest points as well as their sparse approximations is proposed.
Abstract: We propose an efficient and robust solution for image set classification. A joint representation of an image set is proposed which includes the image samples of the set and their affine hull model. The model accounts for unseen appearances in the form of affine combinations of sample images. To calculate the between-set distance, we introduce the Sparse Approximated Nearest Point (SANP). SANPs are the nearest points of two image sets such that each point can be sparsely approximated by the image samples of its respective set. This novel sparse formulation enforces sparsity on the sample coefficients and jointly optimizes the nearest points as well as their sparse approximations. Unlike standard sparse coding, the data to be sparsely approximated are not fixed. A convex formulation is proposed to find the optimal SANPs between two sets and the accelerated proximal gradient method is adapted to efficiently solve this optimization. We also derive the kernel extension of the SANP and propose an algorithm for dynamically tuning the RBF kernel parameter while matching each pair of image sets. Comprehensive experiments on the UCSD/Honda, CMU MoBo, and YouTube Celebrities face datasets show that our method consistently outperforms the state of the art.

191 citations

Journal ArticleDOI
TL;DR: Extensive experiments on handwritten digit classification, landmark recognition and face recognition demonstrate that the proposed hybrid classifier outperforms ELM and SRC in classification accuracy with outstanding computational efficiency.

190 citations

Journal ArticleDOI
Kangjoo Lee1, Sungho Tak1, Jong Chul Ye1
TL;DR: A new data driven fMRI analysis that is derived solely based upon the sparsity of the signals is proposed that enables estimation of spatially adaptive design matrix as well as sparse signal components that represent synchronous, functionally organized and integrated neural hemodynamics.
Abstract: We propose a novel statistical analysis method for functional magnetic resonance imaging (fMRI) to overcome the drawbacks of conventional data-driven methods such as the independent component analysis (ICA). Although ICA has been broadly applied to fMRI due to its capacity to separate spatially or temporally independent components, the assumption of independence has been challenged by recent studies showing that ICA does not guarantee independence of simultaneously occurring distinct activity patterns in the brain. Instead, sparsity of the signal has been shown to be more promising. This coincides with biological findings such as sparse coding in V1 simple cells, electrophysiological experiment results in the human medial temporal lobe, etc. The main contribution of this paper is, therefore, a new data driven fMRI analysis that is derived solely based upon the sparsity of the signals. A compressed sensing based data-driven sparse generalized linear model is proposed that enables estimation of spatially adaptive design matrix as well as sparse signal components that represent synchronous, functionally organized and integrated neural hemodynamics. Furthermore, a minimum description length (MDL)-based model order selection rule is shown to be essential in selecting unknown sparsity level for sparse dictionary learning. Using simulation and real fMRI experiments, we show that the proposed method can adapt individual variation better compared to the conventional ICA methods.

190 citations

Journal ArticleDOI
TL;DR: Experimental results demonstrate that the proposed CS-MCA model can outperform some benchmarking and state-of-the-art SR-based fusion methods in terms of both visual perception and objective assessment.
Abstract: In this letter, a sparse representation (SR) model named convolutional sparsity based morphological component analysis (CS-MCA) is introduced for pixel-level medical image fusion. Unlike the standard SR model, which is based on single image component and overlapping patches, the CS-MCA model can simultaneously achieve multi-component and global SRs of source images, by integrating MCA and convolutional sparse representation (CSR) into a unified optimization framework. For each source image, in the proposed fusion method, the CSRs of its cartoon and texture components are first obtained by the CS-MCA model using pre-learned dictionaries. Then, for each image component, the sparse coefficients of all the source images are merged and the fused component is accordingly reconstructed using the corresponding dictionary. Finally, the fused image is calculated as the superposition of the fused cartoon and texture components. Experimental results demonstrate that the proposed method can outperform some benchmarking and state-of-the-art SR-based fusion methods in terms of both visual perception and objective assessment.

190 citations

Journal ArticleDOI
TL;DR: A new sparse Bayesian learning method for recovery of block-sparse signals with unknown cluster patterns by introducing a pattern-coupled hierarchical Gaussian prior to characterize the pattern dependencies among neighboring coefficients, where a set of hyperparameters are employed to control the sparsity of signal coefficients.
Abstract: We consider the problem of recovering block-sparse signals whose cluster patterns are unknown a priori. Block-sparse signals with nonzero coefficients occurring in clusters arise naturally in many practical scenarios. However, the knowledge of the block partition is usually unavailable in practice. In this paper, we develop a new sparse Bayesian learning method for recovery of block-sparse signals with unknown cluster patterns. A pattern-coupled hierarchical Gaussian prior is introduced to characterize the pattern dependencies among neighboring coefficients, where a set of hyperparameters are employed to control the sparsity of signal coefficients. The proposed hierarchical model is similar to that for the conventional sparse Bayesian learning. However, unlike the conventional sparse Bayesian learning framework in which each individual hyperparameter is associated independently with each coefficient, in this paper, the prior for each coefficient not only involves its own hyperparameter, but also its immediate neighbor hyperparameters. In doing this way, the sparsity patterns of neighboring coefficients are related to each other and the hierarchical model has the potential to encourage structured-sparse solutions. The hyperparameters are learned by maximizing their posterior probability. We exploit an expectation-maximization (EM) formulation to develop an iterative algorithm that treats the signal as hidden variables and iteratively maximizes a lower bound on the posterior probability. In the M-step, a simple suboptimal solution is employed to replace a gradient-based search to maximize the lower bound. Numerical results are provided to illustrate the effectiveness of the proposed algorithm.

190 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