Analysis-operator guided simultaneous tensor decomposition and completion

Abstract

Most of low-rank tensor approximation problems are NP-hard. Hence a great number of synthesis tensor decomposition approximation have been proposed. In this paper, we instead present an analysis-operator guided tensor decomposition. The proposed method first employs the classical Field-of-Experts (FoE) filters to produce multi-view features such that forming a higher-order tensor, and then do simultaneous tensor decomposition and completion (STDC). The multi-view features are obtained by convolving the target image with high-frequency FoE filters along different directions and scales. The proposed method is solved efficiently by alternating direction of multipliers method (ADMM). Experiments are conducted to demonstrate the superior performance of our method to state-of-the-art tensor completion methods.