Multiscale Super Resolution without Image Priors

2026-04-23

AI Summary

This work addresses the inherent ill-posedness and ambiguity of translational super-resolution at a single scale by proposing a multi-scale super-resolution method that requires no image priors. By leveraging low-resolution images acquired with incommensurate pixel pitches—such as those from different sensors or optical zoom settings—the approach constructs a well-posed reconstruction system. A stable solution is achieved through iterative least-squares optimization in the Fourier domain. Theoretical analysis demonstrates that incommensurate sampling guarantees the existence of a stable inverse for the system and reveals a fundamental trade-off between noise amplification and achievable reconstruction resolution. Experiments on both one-dimensional and two-dimensional scenarios successfully recover high-resolution images, validating the method’s efficacy and its practical potential for deployment on conventional imaging hardware, such as CCD sensors supporting pixel binning.

Technology Category

• Machine Learning: Multi-instance/Multi-view Learning
• Computer Vision: Multi-modal Vision
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• super-resolution
• multiscale imaging
• image ambiguity
• pixel size
• translation invariance

Innovation

• multiscale super-resolution
• coprime pixel sizes
• Fourier domain reconstruction
• least squares estimation
• hardware binning