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This paper demonstrates that combining low-resolution images at different scales, achieved through sensors with different pixel sizes, resolves ambiguities in super-resolution tasks. They prove that using pairwise coprime pixel sizes results in a stable inverse system, enabling efficient super-resolution reconstruction via Fourier domain techniques or iterative least squares. The authors provide a mathematical analysis of the noise-resolution tradeoff and validate their approach with 1D and 2D experiments using CCD hardware binning.
Super-resolution is possible without image priors by cleverly combining low-resolution images at different scales, unlocking a stable inverse system for reconstruction.
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.
