论文标题
非负低等级张量近似及其应用于多维图像
Nonnegative Low Rank Tensor Approximation and its Application to Multi-dimensional Images
论文作者
论文摘要
本文的主要目的是开发一种新算法，用于计算在许多多维成像应用中出现的非负张量的非负级张量近似值。非阴性是重要属性之一，因为每个像素值是指图像数据采集中的非零光强度。我们的方法与经典的非负张量分解（NTF）不同，后者要求每个分解的矩阵和/或张量为非负数。在本文中，我们确定了一个非负低塔克等级张量，以近似给定的非负张量。我们提出了一种用于计算这种非负秩量张量近似的交替投影算法，该算法称为NLRT。建立了所提出的歧管投影方法的收敛性。提出了合成数据和多维图像的实验结果，以证明NLRT的性能优于最新的NTF方法。
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.
