Sparse Low-Rank Matrix Approximation for Data Compression

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 the literature. In this paper, we propose sparse lowrank matrix approximation (SLRMA), an effective computational tool for data compression. SLRMA extends the 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 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 ℓ0norm and orthogonality, and solve it using the inexact augmented Lagrangian multiplier method. Through extensive tests on realworld data, such as 2D image sets and 3D dynamic meshes, we observe that (i) SLRMA empirically converges well; (ii) SLRMA can produce approximation error comparable to LRMA but in a much sparse form; (iii) SLRMA-based compression schemes significantly outperform the state-of-the-art in terms of ratedistortion performance.

Towards Real-Time Service from Remote Sensing: Compression of Earth Observatory Video Data via Long-Term Background Referencing

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“…A 2D bounding box with size 10 × 10 is generated, the longest edge of within the bounding box is used to the splitting direction, and the median of the points within the bounding box is applied to be separation point. Assuming that the coordinates of the point being queried is (9,7), the coordinates of the points at which the k-d tree is generated are (2,3),(4,7), (5,4), (9,6),(8,1), (7,2). m indicates splitting direction and n represents the coordinate of separation point in <m,n> .…”

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