Combined new nonnegative matrix factorization algorithms with two-dimensional nonnegative matrix factorization for image processing

HU Li-ying

doi:10.1007/s11042-015-2837-5

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Combined new nonnegative matrix factorization algorithms with two-dimensional nonnegative matrix factorization for image processing

2015-08-08

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HU Li-ying *

Gongde Guo

Changfeng Ma

DOI：10.1007/s11042-015-2837-5

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Abstract

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In recent years, nonnegative matrix factorization (NMF) has attracted significant amount of attentions in image processing, text mining, speech processing and related fields. Although NMF has been applied in several application successfully, its simple application on image processing has a few caveats. For example, NMF costs considerable computational resources when performing on large databases. In this paper, we propose two enhanced NMF algorithms for image processing to save the computational costs. One is modified rank-one residue iteration (MRRI) algorithm, the other is element-wisely residue iteration (ERI) algorithm. Here we combine CAPG (a NMF algorithm proposed by Lin), MRRI and ERI with two-dimensional nonnegative matrix factorization (2DNMF) for image processing. The main difference between NMF and 2DNMF is that the former first aligns images into one-dimensional (1D) vectors and then represents them with a set of 1D bases, while the latter regards images as 2D matrices and represents them with a set of 2D bases. The three combined algorithms are named CAPG-2DNMF, MRRI-2DNMF and ERI-2DNMF. The computational complexity and convergence analyses of proposed algorithms are also presented in this paper. Three public databases are used to test the three NMF algorithms and the three combinations, the results of which show the enhancement performance of our proposed algorithms (MRRI and ERI algorithms) over the CAPG algorithm. MRRI and ERI have similar performance. The three combined algorithms have better image reconstruction quality and less running time than their corresponding 1DNMF algorithms under the same compression ratio. We also do some experiments on a real-captured image database and get similar conclusions.

Keywords:

Nonnegative matrix factorization (NMF)

Two-dimensional nonnegative matrix factorization (2DNMF)

Rank-one residue iteration (RRI)

Element-wisely residue iteration (ERI)

Image processing

Compression ratio

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