  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.
