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.

Adaptive Nonlocal Sparse Representation for Dual-Camera Compressive Hyperspectral Imaging

Abstract: Leveraging the compressive sensing (CS) theory, coded aperture snapshot spectral imaging (CASSI) provides an efficient solution to recover 3D hyperspectral data from a 2D measurement. The dual-camera design of CASSI, by adding an uncoded panchromatic measurement, enhances the reconstruction fidelity while maintaining the snapshot advantage. In this paper, we propose an adaptive nonlocal sparse representation (ANSR) model to boost the performance of dual-camera compressive hyperspectral imaging (DCCHI). Specifically, the CS reconstruction problem is formulated as a 3D cube based sparse representation to make full use of the nonlocal similarity in both the spatial and spectral domains. Our key observation is that, the panchromatic image, besides playing the role of direct measurement, can be further exploited to help the nonlocal similarity estimation. Therefore, we design a joint similarity metric by adaptively combining the internal similarity within the reconstructed hyperspectral image and the external similarity within the panchromatic image. In this way, the fidelity of CS reconstruction is greatly enhanced. Both simulation and hardware experimental results show significant improvement of the proposed method over the state-of-the-art.

Maximum Likelihood Estimation-Based Joint Sparse Representation for the Classification of Hyperspectral Remote Sensing Images

Abstract: A joint sparse representation (JSR) method has shown superior performance for the classification of hyperspectral images (HSIs). However, it is prone to be affected by outliers in the HSI spatial neighborhood. In order to improve the robustness of JSR, we propose a maximum likelihood estimation (MLE)-based JSR (MLEJSR) model, which replaces the traditional quadratic loss function with an MLE-like estimator for measuring the joint approximation error. The MLE-like estimator is actually a function of coding residuals. Given some priors on the coding residuals, the MLEJSR model can be easily converted to an iteratively reweighted JSR problem. Choosing a reasonable weight function, the effect of inhomogeneous neighboring pixels or outliers can be dramatically reduced. We provide a theoretical analysis of MLEJSR from the viewpoint of recovery error and evaluate its empirical performance on three public hyperspectral data sets. Both the theoretical and experimental results demonstrate the effectiveness of our proposed MLEJSR method, especially in the case of large noise.

Ship Classification in TerraSAR-X Images With Feature Space Based Sparse Representation

Abstract: Ship classification is the key step in maritime surveillance using synthetic aperture radar (SAR) imagery In this letter, we develop a new ship classification method in TerraSAR-X images based on sparse representation in feature space, in which the sparse representation classification (SRC) method is exploited In particular, to describe the ship more accurately and to reduce the dimension of the dictionary in SRC, we propose to employ a representative feature vector to construct the dictionary instead of utilizing the image pixels directly By testing on a ship data set collected from TerraSAR-X images, we show that the proposed method is superior to traditional methods such as the template matching (TM), K-nearest neighbor (K-NN), Bayes and Support Vector Machines (SVM)

Sparsity-Based Two-Dimensional DOA Estimation for Coprime Array: From Sum–Difference Coarray Viewpoint

Abstract: This paper addresses the issue of two-dimensional (2-D) direction of arrival (DOA) estimation with coprime planar arrays (CPPAs) via sparse representation. Our work differs from the partial spectral search approach [25] , which suppresses the phase ambiguity by searching the common peaks of two subarrays. We focus on the coprime property of CPPA, where the sparse array extension model with sum–difference coarray (SDCA) is derived for larger degrees of freedom (DOFs). Besides, to optimize the selection of regularization parameter, we also construct a new sparse representation algorithm by estimating the errors between the signal and noise parts. Further, an iterative scheme is presented to transform the 2-D grids searching to several times of 1-D searching, where the initial values are obtained by extracting one difference coarray from SDCA. So the proposed method can achieve aperture extension, high estimation performance, and low computational complexity. Besides, the sparse array extension model for multiple-input multiple-output radars is discussed and the Cramer–Rao bound for 2-D DOA estimation with CPPA is also derived in detail. Finally, simulation results demonstrate the effectiveness of proposed method compared to the state-of-the-art methods.

Sparse Tensor Discriminant Color Space for Face Verification

Abstract: As one of the fundamental features, color provides useful information and plays an important role for face recognition. Generally, the choice of a color space is different for different visual tasks. How can a color space be sought for the specific face recognition problem? To address this problem, we propose a sparse tensor discriminant color space (STDCS) model that represents a color image as a third-order tensor in this paper. The model cannot only keep the underlying spatial structure of color images but also enhance robustness and give intuitionistic or semantic interpretation. STDCS transforms the eigenvalue problem to a series of regression problems. Then one spare color space transformation matrix and two sparse discriminant projection matrices are obtained by applying lasso or elastic net on the regression problems. The experiments on three color face databases, AR, Georgia Tech, and Labeled Faces in the Wild face databases, show that both the performance and the robustness of the proposed method outperform those of the state-of-the-art TDCS model.