Analysis sparse representation for nonnegative signals based on determinant measure by DC programming
type: Item
instance of: scholarly article
title: Analysis sparse representation for nonnegative signals based on determinant measure by DC programming
zbMATH Open document ID: 1407.94041
DOI: 10.1155/2018/2685745
author: Yujie Li
author: Benying Tan
author: Atsunori Kanemura
author: Shuxue Ding
author: Wuhui Chen
published in: Complexity
publication date: 2019-02-18T00:00:00Z
review text: Summary: Analysis sparse representation has recently emerged as an alternative approach to the synthesis sparse model. Most existing algorithms typically employ the \(\ell_0\)-norm, which is generally NP-hard. Other existing algorithms employ the \(\ell_1\)-norm to relax the \(\ell_0\)-norm, which sometimes cannot promote adequate sparsity. Most of these existing algorithms focus on general signals and are not suitable for nonnegative signals. However, many signals are necessarily nonnegative such as spectral data. In this paper, we present a novel and efficient analysis dictionary learning algorithm for nonnegative signals with the determinant-type sparsity measure which is convex and differentiable. The analysis sparse representation can be cast in three subproblems, sparse coding, dictionary update, and signal update, because the determinant-type sparsity measure would result in a complex nonconvex optimization problem, which cannot be easily solved by standard convex optimization methods. Therefore, in the proposed algorithms, we use a Difference of Convex (DC) programming scheme for solving the nonconvex problem. According to our theoretical analysis and simulation study, the main advantage of the proposed algorithm is its greater dictionary learning efficiency, particularly compared with state-of-the-art algorithms. In addition, our proposed algorithm performs well in image denoising.
Mathematics Subject Classification ID: 94A12
Mathematics Subject Classification ID: 94A08
zbMATH DE Number: 7024534
zbMATH Keywords: analysis sparse representation
zbMATH Keywords: nonnegative signals
zbMATH Keywords: analysis dictionary learning algorithm
zbMATH Keywords: sparse coding
zbMATH Keywords: dictionary update
zbMATH Keywords: and signal update
zbMATH Keywords: complex nonconvex optimization problem
zbMATH Keywords: difference of convex (DC) programming
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/2685745
OpenAlex ID: W2799712260
cites work: Sparse Approximate Solutions to Linear Systems
cites work: From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
cites work: Learning Multiscale Sparse Representations for Image and Video Restoration
cites work: Compressed sensing
cites work: Linear convergence of adaptively iterative thresholding algorithms for compressed sensing
cites work: Extensions of compressed sensing
cites work: Sparsity and incoherence in compressive sampling
cites work: Analysis K-SVD: A Dictionary-Learning Algorithm for the Analysis Sparse Model
cites work: Computing Sparse Representations of Multidimensional Signals Using Kronecker Bases
cites work: Manifold optimization-based analysis dictionary learning with an \(\ell_{1/2}\)-norm regularizer
cites work: Greedy-like algorithms for the cosparse analysis model
cites work: Performance Guarantees of the Thresholding Algorithm for the Cosparse Analysis Model
cites work: Nonnegative matrix factorization for spectral data analysis
cites work: Reconstruction of reflectance spectra using robust nonnegative matrix factorization
cites work: Sparse and Redundant Representations
cites work: Sparse Image and Signal Processing
cites work: The cosparse analysis model and algorithms
cites work: Learning Sparsifying Transforms
cites work: Analysis Operator Learning and its Application to Image Reconstruction
cites work: Learning to Sense Sparse Signals: Simultaneous Sensing Matrix and Sparsifying Dictionary Optimization
cites work: Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ 1 minimization
cites work: Blind Spectral Unmixing Based on Sparse Nonnegative Matrix Factorization
cites work: Efficient Nonnegative Matrix Factorization by DC Programming and DCA
cites work: The DC (Difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems
cites work: Q3093232
cites work: Comparing Measures of Sparsity
description: scientific article; zbMATH DE number 7024534