Resolving Blind Inverse Problems under Dynamic Range Compression via Structured Forward Operator Modeling

TL;DR

CaMB-Diff significantly outperforms state-of-the-art zero-shot baselines in terms of both signal fidelity and physical consistency and empirically validate the effectiveness of the proposed CaMB parameterization in accurately modeling the unknown forward operator.

Abstract

Recovering radiometric fidelity from unknown dynamic range compression (UDRC), such as low-light enhancement and HDR reconstruction, is a challenging blind inverse problem, due to the unknown forward model and irreversible information loss introduced by compression. To address this challenge, we first identify monotonicity as the fundamental physical invariant shared across UDRC tasks. Leveraging this insight, we introduce the \textbf{cascaded monotonic Bernstein} (CaMB) operator to parameterize the unknown forward model. CaMB enforces monotonicity as a hard architectural inductive bias, constraining optimization to physically consistent mappings and enabling robust and stable operator estimation. We further integrate CaMB with a plug-and-play diffusion framework, proposing \textbf{CaMB-Diff}. Within this framework, the diffusion model serves as a powerful geometric prior for structural and semantic recovery, while CaMB explicitly models and corrects radiometric distortions through a physically grounded forward operator. Extensive experiments on a variety of zero-shot UDRC tasks, including low-light enhancement, low-field MRI enhancement, and HDR reconstruction, demonstrate that CaMB-Diff significantly outperforms state-of-the-art zero-shot baselines in terms of both signal fidelity and physical consistency. Moreover, we empirically validate the effectiveness of the proposed CaMB parameterization in accurately modeling the unknown forward operator.

Figures (10)

• Figure 1: Illustration of unknown dynamic range compression (UDRC), which arises from a mismatch between the signal span (yellow) and the sensor’s effective response region (blue).
• Figure 2: Overview of the CaMB-Diff: We solve unknown dynamic range compression (UDRC) via joint zero-shot optimization within the reverse diffusion sampling process. a. The diffusion model progressively refines the latent image through reverse-time sampling. b. At each sampling step, the estimated image is passed through the CaMB-parameterized forward model $\mathcal{M}_{\boldsymbol{\Theta}}$ to produce a predicted measurement, which is matched to the observed measurement via a data-fidelity loss, while the image is simultaneously regularized by the diffusion prior through a prior loss. c. CaMB is constructed by cascading monotonic Bernstein polynomials, enforcing physical monotonicity by design and enabling robust estimation of the unknown radiometric mapping.
• Figure 3: Qualitative comparison of low-light image enhancement on the LOLv1, LOLv2-real, and LOLv2-synthetic benchmarks.
• Figure 4: Qualitative comparison of low-field MRI enhancement on the HCP dataset.
• Figure 5: Qualitative comparison of HDR reconstruction on the ImageNet dataset.

Theorems & Definitions (7)

• Corollary 3.2
• Lemma 2.1: Monotonicity / Safety
• proof
• Lemma 2.2: Dense Approximation / Completeness
• proof
• Theorem 2.3: Deep Universality of CaMB
• proof