Guided Nonlocal Patch Regularization and Efficient Filtering-Based Inversion for Multiband Fusion

TL;DR

This paper introduces a novel nonlocal patch regularizer and an efficient FFT-based ADMM algorithm for multiband image fusion, improving reconstruction quality over existing methods.

Contribution

It proposes a new convex regularizer leveraging nonlocal patch similarities guided by high-resolution images, and an efficient filtering-based optimization algorithm for multiband fusion.

Findings

Outperforms state-of-the-art variational methods

Outperforms deep learning techniques in reconstruction quality

Uses FFT-based convolution for computational efficiency

Abstract

In multiband fusion, an image with a high spatial and low spectral resolution is combined with an image with a low spatial but high spectral resolution to produce a single multiband image having high spatial and spectral resolutions. This comes up in remote sensing applications such as pansharpening~(MS+PAN), hyperspectral sharpening~(HS+PAN), and HS-MS fusion~(HS+MS). Remote sensing images are textured and have repetitive structures. Motivated by nonlocal patch-based methods for image restoration, we propose a convex regularizer that (i) takes into account long-distance correlations, (ii) penalizes patch variation, which is more effective than pixel variation for capturing texture information, and (iii) uses the higher spatial resolution image as a guide image for weight computation. We come up with an efficient ADMM algorithm for optimizing the regularizer along with a standard least-squares loss function derived from the imaging model. The novelty of our algorithm is that by expressing patch variation as filtering operations and by judiciously splitting the original variables and introducing latent variables, we are able to solve the ADMM subproblems efficiently using FFT-based convolution and soft-thresholding. As far as the reconstruction quality is concerned, our method is shown to outperform state-of-the-art variational and deep learning techniques.