A novel patch-based nonlinear matrix completion algorithm for image analysis through convolutional neural network

doi:10.1016/j.neucom.2020.01.037

A novel patch-based nonlinear matrix completion algorithm for image analysis through convolutional neural network

2020-05-01

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DOI：10.1016/j.neucom.2020.01.037

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Matrix completion is extensively studied due to its wide applications in science and technology. In this paper, we concentrate our study on the matrix completion problem for image analysis tasks due to their immense importance and pervasive use in many fields. A rich collection of models has been proposed to capture both linear and nonlinear relationships latent in a matrix. Even though nonlinear models possess more powerful matrix completion capabilities than their linear counterparts, these models generally carry higher model complexity and tuning difficulties. To take advantage of the superior discriminative power offered by nonlinear models while curbing its deployment overheads, this paper proposes a novel nonlinear matrix completion model utilizing a deep learning-based approach. In contrast to existing nonlinear models, the new model carefully explores and exploits spatial locality among adjacent matrix elements exhibited in patches of various sizes and locations in a target matrix. Building upon this idea, a new patch-based nonlinear matrix completion algorithm is designed. The algorithm leverages a convolutional neural network to learn the predictive relationship between a matrix element and its surrounding elements through an end-to-end trainable fashion, leading to a capable and easy-to-deploy nonlinear matrix completion solution. To identify an optimal patch size suited for tackling a given matrix completion task without exhaustively enumerating all candidate patch sizes, the new algorithm is coupled with a fast stochastic search procedure, yielding a good trade-off between computational efficiency and accuracy. Extensive experiments are conducted to validate the effectiveness and advantages of the proposed algorithm for nonlinear matrix completion problem in comparison with a series of state-of-the-art algorithms. Experimental results consistently demonstrate the superiority of the new algorithm in completing images with a variety of random and textual noises. (C) 2020 Published by Elsevier B.V.

Keywords:

Nonlinear matrix completion

Laplace distribution

Patch-based completion algorithm

Deep convolutional neural network

A novel patch-based nonlinear matrix completion algorithm for image analysis through convolutional neural network

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