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Title: Sparse low-rank matrix approximation for data compression
Authors: Hou, Junhui
Chau, Lap-Pui
Magnenat-Thalmann, Nadia
He, Ying
Keywords: Optimization
DRNTU::Engineering::Computer science and engineering
Data Compression
DRNTU::Engineering::Electrical and electronic engineering
Issue Date: 2017
Source: Hou, J., Chau, L. P., Magnenat-Thalmann, N., & He, Y. (2017). Sparse Low-Rank Matrix Approximation for Data Compression. IEEE Transactions on Circuits and Systems for Video Technology, 27(5), 1043-1054. doi:10.1109/TCSVT.2015.2513698
Series/Report no.: IEEE Transactions on Circuits and Systems for Video Technology
Abstract: Low-rank matrix approximation (LRMA) is a powerful technique for signal processing and pattern analysis. However, its potential for data compression has not yet been fully investigated. In this paper, we propose sparse LRMA (SLRMA), an effective computational tool for data compression. SLRMA extends conventional LRMA by exploring both the intra and inter coherence of data samples simultaneously. With the aid of prescribed orthogonal transforms (e.g., discrete cosine/wavelet transform and graph transform), SLRMA decomposes a matrix into a product of two smaller matrices, where one matrix is made up of extremely sparse and orthogonal column vectors and the other consists of the transform coefficients. Technically, we formulate SLRMA as a constrained optimization problem, i.e., minimizing the approximation error in the least-squares sense regularized by the 0-norm and orthogonality, and solve it using the inexact augmented Lagrangian multiplier method. Through extensive tests on real-world data, such as 2D image sets and 3D dynamic meshes, we observe that: 1) SLRMA empirically converges well; 2) SLRMA can produce approximation error comparable to LRMA but in a much sparse form; and 3) SLRMA-based compression schemes significantly outperform the state of the art in terms of rate–distortion performance.
ISSN: 1051-8215
DOI: 10.1109/TCSVT.2015.2513698
Schools: School of Computer Science and Engineering 
School of Electrical and Electronic Engineering 
Rights: © 2017 Institute of Electrical and Electronics Engineers (IEEE). This is the author created version of a work that has been peer reviewed and accepted for publication by IEEE Transactions on Circuits and Systems for Video Technology, Institute of Electrical and Electronics Engineers (IEEE). It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [].
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:EEE Journal Articles
SCSE Journal Articles

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