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Nonnegative Low Rank Tensor Approximation and its Application to Multi-dimensional Images

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Document pages: 23 pages

Abstract: The main aim of this paper is to develop a new algorithm for computingNonnegative Low Rank Tensor (NLRT) approximation for nonnegative tensors thatarise in many multi-dimensional imaging applications. Nonnegativity is one ofthe important property as each pixel value refer to nonzero light intensity inimage data acquisition. Our approach is different from classical nonnegativetensor factorization (NTF) which has been studied for many years. For a givennonnegative tensor, the classical NTF approach is to determine nonnegative lowrank tensor by computing factor matrices or tensors (for example, CPD findsfactor matrices while Tucker decomposition finds core tensor and factormatrices), such that the distance between this nonnegative low rank tensor andgiven tensor is as small as possible. The proposed NLRT approach is differentfrom the classical NTF. It determines a nonnegative low rank tensor withoutusing decompositions or factorization methods. The minimized distance by theproposed NLRT method can be smaller than that by the NTF method, and it impliesthat the proposed NLRT method can obtain a better low rank tensorapproximation. The proposed NLRT approximation algorithm is derived by usingthe alternating averaged projection on the product of low rank matrix manifoldsand non-negativity property. We show the convergence of the alternatingprojection algorithm. Experimental results for synthetic data andmulti-dimensional images are presented to demonstrate the performance of theproposed NLRT method is better than that of existing NTF methods.

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