Reconstruction-Aware Distribution Matching for Inverse Problems with Unpaired Data

2026-10-05

AI Summary

This study addresses the challenge of accurately constraining forward operators in unpaired settings, where relying solely on degraded-domain distribution matching proves insufficient. To overcome this limitation, we propose a reconstruction-aware distribution matching framework that employs a differentiable plug-and-play (PnP) algorithm to map degraded observations into the clean domain. By minimizing the distributional discrepancy between recovered and ground-truth clean images, the proposed approach optimizes operator estimation beyond conventional single-domain degradation matching. Introducing reconstruction consistency as an auxiliary constraint significantly enhances the recovery of invisible components. Experimental results on point spread function (PSF) calibration and blind super-resolution tasks demonstrate that our method yields more precise operator estimates than single-domain degradation matching, substantially narrowing the performance gap with ground-truth baselines.

Abstract

Recovering the forward operator of an imaging system from unpaired data avoids both calibration hardware and the clean/degraded pairs that supervision requires-pairs that, for a real lens, are often impossible to acquire. Existing unpaired approaches that explicitly estimate the forward operator by distribution matching evaluate a candidate only through the measurements it generates, whose distribution should match that of the real ones. Components suppressed by the operator are barely present in the degraded images, and therefore barely constrain the operator under such a criterion. Yet inversion precisely tries to recover them. As a result, two operators that are nearly indistinguishable as forward models can invert very differently. We address this by adding a comparison on the clean side: real degraded images, once restored, should be distributed like clean ones. Restorations are computed by a differentiable plug-and-play algorithm parameterized by the operator being learned. On spatially varying PSF calibration and blind super-resolution, the method recovers more accurate operators than degraded-side matching alone, and closes much of the gap to restoration with the true operator.

Problem

• inverse problems
• unpaired data
• forward operator estimation
• distribution matching

Innovation

• Unpaired Data
• Distribution Matching
• Inverse Problems
• Differentiable Plug-and-Play
• Forward Operator Recovery