Neighbor embedding based single-image super-resolution using Semi-Nonnegative Matrix Factorization

Abstract

This paper describes a novel method for single-image superresolution (SR) based on a neighbor embedding technique which uses Semi-Nonnegative Matrix Factorization (SNMF). Each low-resolution (LR) input patch is approximated by a linear combination of nearest neighbors taken from a dictionary. This dictionary stores low-resolution and corresponding high-resolution (HR) patches taken from natural images and is thus used to infer the HR details of the super-resolved image. The entire neighbor embedding procedure is carried out in a feature space. Features which are either the gradient values of the pixels or the mean-subtracted luminance values are extracted from the LR input patches, and from the LR and HR patches stored in the dictionary. The algorithm thus searches for the K nearest neighbors of the feature vector of the LR input patch and then computes the weights for approximating the input feature vector. The use of SNMF for computing the weights of the linear approximation is shown to have a more stable behavior than the use of LLE and lead to significantly higher PSNR values for the super-resolved images.

Super-resolution: a comprehensive survey

“…Then, a MAP sparse-representation based algorithm has been applied to these parts. A similar technique has been used in [553].…”

“…Manifold Manifold based methods [151] (2004), [206], [207], [310], [311], [327], [329], [343], [382], [386], [403], [404], [469], [495], [521], [553], [561], [568], [569], [570] assume that the HR and LR images form manifolds with similar local geometries in two distinct feature spaces [343]. Similar to PCA, these methods are also usually used for dimensionality reduction.…”

“…-Locally Linear Embedding (LLE) [151] (2004), [207], [206], [344], [553], [561], [597]. -Locality Preserving Projections (LPP) [310], [311], [327], [329], [382], [461], [495].…”

Image Quality Assessment by Upsampling Methods Based on Spatial Spectrum Extrapolation

“…The problem in (2.7) is known in the literature as non-negative least squares As an alternative and possibly faster solver of (2.7), in [73] we also proposed to use Semi-nonnegative Matrix Factorization (SNMF) [76]. In fact, SNMF is a method to perform a factorization of a matrix, where, dierently from full Nonnegative Matrix Factorization (NMF) [74], only one factor is constrained to have positive values.…”

A convex optimization approach for image resolution enhancement from compressed representations

“…Recently proposed superresolution techniques like those presented in [3], [4], [5] are based on the building of patch dictionaries from training sets of uncompressed images to provide a sparse representation in a suitable domain. In particular in [5], a convex optimization approach is used to solve the resulting problem.…”