Nonnegative Matrix Factorization applied to reordered pixels of single images based on patches to achieve structured nonnegative dictionaries

TL;DR

This paper introduces a novel method for creating structured, nonnegative image dictionaries by applying NMF to reordered pixel patches, balancing reconstruction quality with preservation of image parts.

Contribution

It presents a new approach combining pixel patch reordering with NMF to produce structured, nonnegative dictionaries that retain image parts and sign structure.

Findings

NMF-based dictionaries preserve sign structure and image parts.

SVD achieves higher PSNR but loses sign and detail.

NMF offers a parts-based, interpretable representation.

Abstract

Recent improvements in computing allow for the processing and analysis of very large datasets in a variety of fields. Often the analysis requires the creation of low-rank approximations to the datasets leading to efficient storage. This article presents and analyzes a novel approach for creating nonnegative, structured dictionaries using NMF applied to reordered pixels of single, natural images. We reorder the pixels based on patches and present our approach in general. We investigate our approach when using the Singular Value Decomposition (SVD) and Nonnegative Matrix Factorizations (NMF) as low-rank approximations. Peak Signal-to-Noise Ratio (PSNR) and Mean Structural Similarity Index (MSSIM) are used to evaluate the algorithm. We report that while the SVD provides the best reconstructions, its dictionary of vectors lose both the sign structure of the original image and details of localized image content. In contrast, the dictionaries produced using NMF preserves the sign structure of the original image matrix and offer a nonnegative, parts-based dictionary.