2014/07/16 by Fei Zhu, Zhu, Fei, Paul Honeiné +3
Engineering · #Advanced Image Fusion Techniques #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Information Theory (cs.IT) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural and Evolutionary Computing (cs.NE) #Remote-Sensing Image Classification #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1407.4420
openalex publication_date 2014/07/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The nonnegative matrix factorization (NMF) is widely used in signal and image processing, including bio-informatics, blind source separation and hyperspectral image analysis in remote sensing. A great challenge arises when dealing with a nonlinear formulation of the NMF. Within the framework of kernel machines, the models suggested in the literature do not allow the representation of the factorization matrices, which is a fallout of the curse of the pre-image. In this paper, we propose a novel kernel-based model for the NMF that does not suffer from the pre-image problem, by investigating the estimation of the factorization matrices directly in the input space. For different kernel functions, we describe two schemes for iterative algorithms: an additive update rule based on a gradient descent scheme and a multiplicative update rule in the same spirit as in the Lee and Seung algorithm. Within the proposed framework, we develop several extensions to incorporate constraints, including sparseness, smoothness, and spatial regularization with a total-variation-like penalty. The effectiveness of the proposed method is demonstrated with the problem of unmixing hyperspectral images, using well-known real images and results with state-of-the-art techniques.