Multiscale Super Resolution without Image Priors

TL;DR

This paper proposes a multiscale super-resolution method that combines images at different scales to resolve ambiguities, using Fourier and iterative techniques validated through experiments with CCD hardware binning.

Contribution

It introduces a multiscale super-resolution approach leveraging scale differences and coprime pixel sizes, with mathematical analysis and practical validation.

Findings

Stable inverse systems with coprime pixel sizes enable super-resolution reconstruction.

Fourier domain and least squares methods efficiently reconstruct high-resolution images.

Experimental validation demonstrates improved resolution over a range of pixel sizes.

Abstract

We address the ambiguities in the super-resolution problem under translation. We demonstrate that combinations of low-resolution images at different scales can be used to make the super-resolution problem well posed. Such differences in scale can be achieved using sensors with different pixel sizes (as demonstrated here) or by varying the effective pixel size through changes in optical magnification (e.g., using a zoom lens). We show that images acquired with pairwise coprime pixel sizes lead to a system with a stable inverse, and furthermore, that super-resolution images can be reconstructed efficiently using Fourier domain techniques or iterative least squares methods. Our mathematical analysis provides an expression for the expected error of the least squares reconstruction for large signals assuming i.i.d. noise that elucidates the noise-resolution tradeoff. These results are validated through both one- and two-dimensional experiments that leverage charge-coupled device (CCD) hardware binning to explore reconstructions over a large range of effective pixel sizes. Finally, two-dimensional reconstructions for a series of targets are used to demonstrate the advantages of multiscale super-resolution, and implications of these results for common imaging systems are discussed.