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

Muyu Liu; Xuanyu Tian; Chenhe Du; Qing Wu; Hongjiang Wei; Yuyao Zhang

cs.CVMar 2, 2026

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

Authors: Muyu Liu, Xuanyu Tian, Chenhe Du, Qing Wu, Hongjiang Wei, Yuyao Zhang

Organizations: ShanghaiTech University · Shanghai Jiao Tong University

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 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 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 & tables

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.

Type	Methods	LOL v1 ( Wei et al., 2018 )					LOL v2 Real ( Yang et al., 2021 )					LOL v2 Synthetic ( Yang et al., 2021 )
Type	Methods	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$	LOE $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$	LOE $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$	LOE $\downarrow$
S	RetinexNet ( Wei et al., 2018 )	18.21	0.7962	0.3195	130.13	445.75	18.12	0.8052	0.3438	142.89	595.90	17.59	0.8123	0.2399	86.30	534.90
	KinD ( Zhang et al., 2019 )	20.38	0.9076	0.1586	63.25	437.55	18.63	0.8821	0.1455	63.08	445.97	17.65	0.8695	0.2599	85.56	436.02
	Restormer ( Zamir et al., 2022 )	22.92	0.9314	0.1655	76.44	134.35	19.04	0.8891	0.2013	72.50	233.57	21.92	0.9183	0.1579	45.51	183.17
	SNR-Net ( Xu et al., 2022 )	25.71	0.9426	0.1422	54.83	188.15	22.11	0.9251	0.1434	52.06	206.59	24.48	0.9528	0.0651	18.61	204.31
	RetinexFormer ( Cai et al., 2023 )	26.20	0.9498	0.1554	65.46	150.06	23.32	0.9234	0.1656	58.00	199.79	26.18	0.9607	0.0744	20.71	186.08

Table 1: Quantitative comparison of low-light image enhancement on the LOLv1, LOLv2-real, and LOLv2-synthetic benchmarks. The method types “S” and “Z” denote Supervised and Zero-shot methods, respectively. For clarity, the best overall results are underlined , while the best zero-shot performance is highlighted in bold .

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.

Method	T1w			T2w
Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
ULFInr ( Islam et al., 2025 )	22.06	0.7172	0.2194	20.26	0.5689	0.2699
PF-SR ( Man et al., 2023 )	21.92	0.7052	0.2126	21.21	0.6542	0.2001
DiffDeuR ( Lin et al., 2024 )	23.17	0.6840	0.2611	23.66	0.8087	0.2620
GDP ( Fei et al., 2023 )	23.42	0.6789	0.2169	23.92	0.7657	0.2278
TAO ( Gou et al., 2023 )	23.61	0.6892	0.2156	24.18	0.7821	0.2094

Table 2: Quantitative comparison of low-field MRI enhancement on the HCP dataset. The best results are highlighted in bold .

Method	ImageNet
Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$
GDP ( Fei et al., 2023 )	16.80	0.7003	0.3016	84.99
TAO ( Gou et al., 2023 )	16.77	0.6692	0.3478	101.28
CaMB-Diff (Ours)	19.95	0.7909	0.2639	70.73

Table 3: Quantitative comparison of HDR Reconstruction on the ImageNet dataset. The best results are highlighted in bold .

Figure 5: Qualitative comparison of HDR reconstruction on the ImageNet dataset.

Forward Model	Num of Params	LOL v1
Forward Model	Num of Params	PSNR	SSIM	LPIPS	FID	LOE
CaMB(N=64 K=1)	63	10.99	0.5165	0.2627	95.60	49.63
CaMB(N=2 K=8)	8	19.94	0.8476	0.2311	87.91	82.41
CaMB(N=3 K=8)	16	20.14	0.8498	0.2171	72.65	82.21
GDP(fx+M)	65537	17.06	0.7145	0.3581	126.39	190.22
TAO(CNNs)	742660	17.18	0.8099	0.4153	127.32	331.13

Table 4: Ablation study on architectural design and parameter efficiency. We evaluate the impact of operator depth (

K

) versus width (degree

N

) on the LOLv1 dataset. Our cascaded design (

N=3,K=8

) achieves superior fidelity with minimal parameters, distinctly outperforming the unstable high-degree variant (

N=64

) and heavy baselines.

Figure 6: Qualitative and Quantitative comparisons of CaMB-Diff with various cascaded designs. While the single high-degree model ( $N=64,K=1$ ) fails to enhance the dark input, our cascaded low-degree design ( $N=3,K=8$ ) effectively recovers the illumination and details.

Figure 7: Convergence Analysis of Operator Estimation. We track the dynamics of the learned forward operator across the reverse diffusion process. (Left) Fidelity Error: Most methods successfully minimize the data consistency objective towards the observed measurement

\boldsymbol{y}

. (Right) Validation Error: A critical generalization gap emerges when evaluating against the ground truth. Unconstrained methods (GDP, TAO) fail to converge to a low validation error. In contrast, CaMB-Diff achieves stable convergence to a minimal error state via a monotonic descent.

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Forward Operator	Low-light Image Enhancement					High Dynamic Range
Forward Operator	PSNR	SSIM	LPIPS	FID	LOE	PSNR	SSIM	LPIPS	FID
Monotonic-MLP	17.94	0.7158	0.3528	237.54	132.95	16.18	0.6245	0.3117	82.80
CaMB	20.14	0.8498	0.2171	72.65	82.21	19.85	0.7909	0.2639	70.73

Appendix

Table 5: Ablation on Operator Architecture: Monotonic-MLP vs. CaMB. We compare our proposed cascaded Bernstein formulation against a standard Multi-Layer Perceptron (MLP) with monotonic constraints (positive weights). The ”Monotonic-MLP” suffers from optimization stiffness, failing to adapt to the diffusion guidance effectively. In contrast, CaMB provides a smoother, more expressive parameterization, yielding significant gains in both signal fidelity (PSNR) and perceptual quality (FID) across Low-light and HDR tasks.

Figure 8: Qualitative ablation of Operator Design on low-light image enhancement(LLIE) and HDR reconstruction(HDR). While the Monotonic-MLP (2nd column) avoids intensity inversion, its piecewise-linear nature struggles to model the smooth transition into saturation, resulting in flat, lifeless highlights. CaMB (3rd column) leverages the smoothness of Bernstein polynomials to approximate the continuous radiometric response, recovering richer details in the overexposed regions.

Figure 9: Additional visual comparisons for low-light image enhancment. We evaluate performance across diverse indoor and outdoor scenes. While GDP often results in under-enhanced contrast and TAO suffers from severe chromatic artifacts (e.g., unnatural color shifts in the statue and cabinet), CaMB-Diff consistently restores natural radiance and accurate colors, closely matching the Ground Truth.

Figure 10: Evolution of the Tweedie Estimate $\boldsymbol{x}_{0|t}$ during Inference. We visualize the trajectory of the posterior mean estimate $\hat{\boldsymbol{x}}_{0|t}$ across the reverse diffusion process, which demonstrates a stable coarse-to-fine recovery, where the global illumination and object geometry are resolved first, followed by the restoration of fine textures in the saturated regions, guided effectively by our proposed CaMB operator.

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