CLRMA: Compact Low Rank Matrix Approximation for Data Compression

Low rank matrix approximation (LRMA) is a powerful technique for signal processing and pattern analysis. However, the performance of existing LRMA-based compression methods are still limited. In this paper, we propose compact low rank matrix approximation (CLRMA), a very effective tool for data compression, which extends the LRMA by exploring both the intra- and inter-coherence of data samples simultaneously. Technically, under the assistance of prescribed orthogonal transforms (such as such as discrete cosine/wavelet transform and graph transform), the CLRMA decomposes a matrix into a product of two smaller matrices so that one consists of extremely sparse and orthogonal column vectors, and the other is a transformed coefficient matrix for reconstruction. Numerically, we formulate the CLRMA problem by minimizing the $\ell_0$-norm and orthogonality regularized approximation (or reconstruction) error, and solve it by the inexact augmented Lagrangian multiplier method. We demonstrate the efficacy of CLMRA on various types of real-world data, including 3D meshes, image datasets, videos as well as human motion capture data, that is, the proposed CLRMA, in a much more compact form, can produce comparable approximation (or reconstruction) error as LRMA. Moreover, we present a CLRMA-based compression scheme for 3D dynamic meshes, and experimental results show that it outperforms the state-of-the-art scheme to a large extend in terms of compression performance.