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.

3D Feature Constrained Reconstruction for Low-Dose CT Imaging

Abstract: Low-dose computed tomography (LDCT) images are often highly degraded by amplified mottle noise and streak artifacts. Maintaining image quality under low-dose scan protocols is a well-known challenge. Recently, sparse representation-based techniques have been shown to be efficient in improving such CT images. In this paper, we propose a 3D feature constrained reconstruction (3D-FCR) algorithm for LDCT image reconstruction. The feature information used in the 3D-FCR algorithm relies on a 3D feature dictionary constructed from available high quality standard-dose CT sample. The CT voxels and the sparse coefficients are sequentially updated using an alternating minimization scheme. The performance of the 3D-FCR algorithm was assessed through experiments conducted on phantom simulation data and clinical data. A comparison with previously reported solutions was also performed. Qualitative and quantitative results show that the proposed method can lead to a promising improvement of LDCT image quality.

Fault tolerant preconditioned conjugate gradient for sparse linear system solution

Abstract: In scientific applications that involve dense matrices, checksum encodings have yielded "algorithm-based fault tolerance" (ABFT) in the event of data corruption from either hard or transient (soft) errors in the hardware. However, such checksum-based ABFT techniques have not been developed when sparse matrices are involved, for example, in sparse linear system solution through a method such as preconditioned conjugate gradients (PCG). In this paper, we develop a new sparse checksum encoded algorithm-based fault tolerant PCG, S-ABFT-PCG. Our checksum based approach can be applied to all the key operations in PCG, including sparse matrix-vector multiplication (SpMV), vector operations and the application of a preconditioner through sparse triangular solution. We prove that our approach detects a single error in the matrix and vector elements and in the metadata representing the sparse matrix row or column indices, when the linear system has a coefficient matrix that is symmetric positive definite and strictly diagonally dominant. The overhead of S-ABFT-PCG is proportional to the cost of a few O(n) vector operations, a value that is relatively low compared to the total cost of a PCG iteration with an SpMV and two triangular solutions. However, if an error is detected, then the underlying PCG iteration must be recomputed because our approach does not enable checksum encoded recovery from the error. We compare our S-ABFT-PCG with a classical ABFT-PCG (C-ABFT-PCG) that detects and recovers from a single error in the SpMV kernel, but does not provide fault tolerance for the sparse triangular solution kernel. Our experimental results indicate that in the event of no errors, compared to a PCG with no ABFT, the overheads of S-ABFT-PCG are 11.3% and lower than the 23.1% overheads of C-ABFT-PCG. Furthermore, in the event of a single error in the application of the preconditioner through triangular solution, C-ABFT-PCG suffers from significant increases in iteration counts, leading to performance degradations of 63.2% on average compared to 3.2% on average for S-ABFT-PCG.

Blind deconvolution of images using optimal sparse representations

Abstract: The relative Newton algorithm, previously proposed for quasi-maximum likelihood blind source separation and blind deconvolution of one-dimensional signals is generalized for blind deconvolution of images. Smooth approximation of the absolute value is used as the nonlinear term for sparse sources. In addition, we propose a method of sparsification, which allows blind deconvolution of arbitrary sources, and show how to find optimal sparsifying transformations by supervised learning.

$p$ -Laplacian Regularized Sparse Coding for Human Activity Recognition

Abstract: Human activity analysis in videos has increasingly attracted attention in computer vision research with the massive number of videos now accessible online. Although many recognition algorithms have been reported recently, activity representation is challenging. Recently, manifold regularized sparse coding has obtained promising performance in action recognition, because it simultaneously learns the sparse representation and preserves the manifold structure. In this paper, we propose a generalized version of Laplacian regularized sparse coding for human activity recognition called $p$ -Laplacian regularized sparse coding (pLSC). The proposed method exploits $p$ -Laplacian regularization to preserve the local geometry. The $p$ -Laplacian is a nonlinear generalization of standard graph Laplacian and has tighter isoperimetric inequality. As a result, pLSC provides superior theoretical evidence than standard Laplacian regularized sparse coding with a proper $p$ . We also provide a fast iterative shrinkage-thresholding algorithm for the optimization of pLSC. Finally, we input the sparse codes learned by the pLSC algorithm into support vector machines and conduct extensive experiments on the unstructured social activity attribute dataset and human motion database (HMDB51) for human activity recognition. The experimental results demonstrate that the proposed pLSC algorithm outperforms the manifold regularized sparse coding algorithms including the standard Laplacian regularized sparse coding algorithm with a proper $p$ .