非负低秩张量逼近及其在多维图像中的应用
Nonnegative Low Rank Tensor Approximation and its Application to Multi-dimensional Images
摘要：
本文的主要目的是开发一种新算法，用于计算许多多维成像应用中出现的非负张量的非负低秩张量近似。非负性是图像数据采集中的一个重要性质，因为每个像素值都表示非零光强。我们的方法是不同于经典的非负张量分解（NTF），它要求每个分解矩阵和/或张量是非负的。本文确定了一个非负的低Tucker秩张量来逼近给定的非负张量。我们提出了一个交替投影算法计算这种非负的低秩张量近似，这是被称为NLRT。证明了流形投影方法的收敛性。合成数据和多维图像的实验结果表明，NLRT的性能优于国家的最先进的NTF方法。
英文摘要：
The main aim of this paper is to develop a new algorithm for computing nonnegative low rank tensor approximation for nonnegative tensors that arise in many multi-dimensional imaging applications. Nonnegativity is one of the important property as each pixel value refers to nonzero light intensity in image data acquisition. Our approach is different from classical nonnegative tensor factorization (NTF) which requires each factorized matrix and/or tensor to be nonnegative. In this paper, we determine a nonnegative low Tucker rank tensor to approximate a given nonnegative tensor. We propose an alternating projections algorithm for computing such nonnegative low rank tensor approximation, which is referred to as NLRT. The convergence of the proposed manifold projection method is established. Experimental results for synthetic data and multi-dimensional images are presented to demonstrate the performance of NLRT is better than state-of-the-art NTF methods.
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