Sparse Low-Rank Matrix Approximation for Data Compression

Junhui Hou, Lap Pui Chau, Nadia Magnenat-Thalmann, Ying He

Research output: Journal article publicationJournal articleAcademic researchpeer-review

27 Citations (Scopus)

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 l0-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.

Original languageEnglish
Article number7368899
Pages (from-to)1043-1054
Number of pages12
JournalIEEE Transactions on Circuits and Systems for Video Technology
Volume27
Issue number5
DOIs
Publication statusPublished - May 2017
Externally publishedYes

Keywords

  • Data compression
  • low-rank matrix
  • optimization
  • orthogonal transform
  • sparsity

ASJC Scopus subject areas

  • Media Technology
  • Electrical and Electronic Engineering

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