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.
翻译:本文的主要目的是为在许多多维成像应用中产生的非阴性低等级的非阴性低压抗拉近似值开发一种新的计算算法。 非负性是重要属性之一,因为每个像素值在图像数据采集中都指非零光强度。我们的方法不同于传统的非阴性抗拉因子化(NTF),它要求每个因素化矩阵和(或)微值为非负性。在本文中,我们确定一个非阴性低塔克低等级的抗拉值,接近给定的非阴性抗拉值。我们提出了计算这种非阴性低级别高压近似值的交替预测算法,称为NLRT。拟议的多重投影法的趋同性已经确立。 合成数据和多维图像的实验结果被展示,以证明NLRT的性能比最先进的NTF方法要好。