$\mathrm{S}^3$-PnP: Plug-and-Play Denoising for Scientific Imaging with Self-Supervised Score Priors

Yukun Cui; Jiangshe Zhang; Shuang Xu; Lilun Deng; Haowen Bai; Tao Feng; Haotong Qin; Konrad Schindler

cs.CVOct 13, 2026

$\mathrm{S}^3$ -PnP: Plug-and-Play Denoising for Scientific Imaging with Self-Supervised Score Priors

Authors: Yukun Cui, Jiangshe Zhang, Shuang Xu, Lilun Deng, Haowen Bai, Tao Feng, Haotong Qin, Konrad Schindler, +1 more

Organizations: Xi’an Jiaotong University · Northwestern Polytechnical University · Nanyang Technological University · Tsinghua University · Hong Kong Polytechnic University · ETH Zürich

Abstract

Modern image restoration methods increasingly rely on large-scale supervised training, yet clean targets are often prohibitively difficult to obtain in scientific imaging modalities such as hyperspectral imaging (HSI) and magnetic resonance imaging (MRI). Plug-and-play ADMM (PnP-ADMM) with pretrained diffusion priors offers a promising alternative, but the learned prior distribution can mismatch both the target scientific image distribution and the distribution of ADMM denoiser inputs induced by dual feedback. To mitigate these mismatches, we propose $\mathrm{S}^3$ -PnP, a self-supervised plug-and-play restoration framework that learns a score prior directly from observation-derived ADMM intermediate states, without clean training targets or externally pretrained weights. Specifically, the learned score corrects the input to the analytical prior update, combining observation-driven corrections with analytical regularization. We further analyze the convergence and reconstruction error of the corrected ADMM algorithm assuming an ideal score and quadratic data fidelity. Experiments on reference-guided HSI restoration, single-image HSI denoising, and MRI denoising demonstrate consistent improvements over competing methods.

Figures & tables

Figure 1: Two sources of mismatch when using pretrained image priors in scientific imaging: differences between the pretraining and target image domains, and differences between score-model training inputs and ADMM denoiser inputs.

Figure 2: Training and inference of S 3 -PnP. Purple arrows indicate full-space learning with $P_{s}=0$ , $P_{g}=I$ , and $\beta_{s}=0$ . Orange arrows indicate structure-guided learning: $D_{s}$ is trained and frozen, and its correction is enabled to collect a new state training set for $D_{g}$ . At inference, active corrections are evaluated at the same ADMM input and combined before a single analytical prior update. Snowflakes denote frozen networks.

	Gaussian Mean				Mixed Mean
Method	PSNR $\uparrow$	SSIM $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$
R-PNN + HIR-Diff	30.83	0.7226	8.80	22.55	29.83	0.7139	11.44	31.40
HIR-Diff + SwinIR	32.42	0.7431	7.00	19.42	29.76	0.6776	11.33	34.18
HIR-Diff + R-PNN	35.32	0.9199	6.08	15.35	33.12	0.8995	9.75	29.67
PWRCTV + PLRDiff	36.13	0.8675	6.23	21.54	32.76	0.7747	13.59	153.69
PWRCTV + SwinIR	35.55	0.8773	4.66	14.65	33.80	0.8403	9.90	160.43

Table 1: Reference-guided HSI restoration on Dongying. Best in bold; second best underlined.

	Gaussian Mean				Mixed Mean
Method	PSNR $\uparrow$	SSIM $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$
BM4D	33.95	0.8214	3.61	9.18	24.56	0.4833	17.50	68.67
HLRTF	34.94	0.7733	3.07	8.97	31.23	0.7944	27.69	117.96
RCTV	28.59	0.5180	7.34	19.50	34.01	0.8741	5.49	16.13
DDS2M	39.97	0.9504	1.40	4.21	29.79	0.8536	13.12	53.51
LRTFR	37.24	0.9020	1.78	6.17	30.84	0.8442	27.00	114.55

Table 2: Single-image HSI denoising on Qingpu. Best in bold; second best underlined.

Method	3%		5%		7%		T1		T2		FLAIR
	BrainWeb						M4Raw
	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM
Noise2Self	31.22	0.8613	30.40	0.8396	29.49	0.7952	29.10	0.8537	28.17	0.8095	28.94	0.8150
Noise2Void	32.11	0.8810	30.40	0.8522	29.23	0.8110	31.24	0.8671	30.45	0.8392	30.80	0.8288
Noisier2Noise	34.38	0.8964	31.37	0.8341	28.90	0.7410	31.18	0.8675	30.55	0.8435	31.17	0.8356
R2R	34.02	0.8011	32.03	0.7879	29.50	0.7292	30.82	0.8552	30.48	0.8329	30.97	0.8187

Table 3: MRI denoising. Best in bold; second best underlined.

Figure 3: Qualitative comparisons on Dongying (GNI), Qingpu (G50), BrainWeb (T1, 7% noise), and M4Raw (T1), from top to bottom. Enlarged regions and corresponding error maps are shown below each reconstruction.

Figure 4: PSNR gains over analytical ADMM at the same prior setting, varying

\tau

in (a)–(b) and

c

in (c)–(d). In (b), solid curves denote structure-guided correction and the dashed curve denotes full-space correction at

\tau=0.105

; the horizontal axis scales their respective reference gains. BrainWeb results average three development slices per condition.

Figure 5: Controlled experiments with

64\times 64

Gaussian states and ideal scores. (a)–(c) Wide-spectrum fidelity; (d) near-matched fidelity with a theoretical lower bound on error reduction. The relative prior strength

\gamma=b/a_{t}

is fixed at

0.15

in (a)–(b) and

0.1

in (d). Shading in (c)–(d) indicates pointwise 95% confidence intervals.

Appendix figures & tables20 assets

Supplementary material from the paper’s appendix.

Appendix

Stage	Operation	Output size	Parameters
Input	State, guide, and condition maps	$(r+4)\times H\times W$	–
Conditioning	MLP: $129\to 128\to 128$	$128$	33,152
Input projection	$3\times 3$ convolution	$48\times H\times W$	$432r+1{,}776$
Encoder block 1	Residual block	$48\times H\times W$	47,952
Downsampling	$4\times 4$ convolution, stride 2	$96\times\frac{H}{2}\times\frac{W}{2}$	73,824
Encoder block 2	Residual block	$96\times\frac{H}{2}\times\frac{W}{2}$	178,848

Appendix

Table 4: Architecture of one correction network.

r

is the number of state channels, and

H\times W

is the input spatial size. Parameter counts include all trainable weights and biases.

Condition	$K$	$\rho$	$\tau$	$d$	$\beta_{s}$	$\beta_{g}$	$N_{s}$	$N_{g}$
G10	4	1	0.105	0.10	0	1	–	5000
G30	8	8	0.105	0.10	0	1	–	5000
GNI	8	4	0.105	0.10	0	1	–	5000
Mix35	8	8	0.070	0.10	0.75	1.25	10000	5000
Mix55	8	4	0.070	0.10	0.75	1.25	5000	5000
Mix55-G30	8	4	0.070	0.10	0.50	0.50	5000	5000

Appendix

Table 5: HiPandas solver and correction parameters.

Condition	$K$	$\rho$	$d$	$\beta_{s}$	$\beta_{g}$	$N_{s}$	$N_{g}$
Qingpu G30	30	2	0.1	0	0.5	–	5000
Qingpu G50	30	2	0.1	0	0.75	–	6000
Qingpu G70	30	2	0.1	0	0.75	–	5000
Qingpu M30	30	2	0.1	0.125	0.5	2000	2000
Qingpu M50	30	2	0.1	0.375	0.75	3000	3000
Qingpu M70	30	2	0.1	0.1875	0.75	2000	2000

Appendix

Table 6: HSI denoising solver and correction parameters.

Condition	$K$	$\rho$	$c$	$a$	$J$	$\gamma_{\sigma}$	$d$	$\beta$	$N_{g}$	$\eta_{k}$
T1, 3%	30	2	0.1875	0.20	20	1	0.10	0.25	5000	1
T1, 5%	30	2	0.1875	0.20	20	1	0.10	0.50	5000	1
T1, 7%	30	2	0.1875	0.20	20	1	0.10	0.50	5000	1
T2, 3%	30	2	0.1875	0.20	20	1	0.10	0.25	5000	1
T2, 5%	30	2	0.1875	0.20	20	1	0.10	0.50	5000	1
T2, 7%	30	2	0.1875	0.20	20	1	0.10	0.75	5000	1

Appendix

Table 7: BrainWeb solver and correction parameters.

Contrast	$K$	$\rho$	$c$	$a$	$J$	$\gamma_{\sigma}$	$d$	$\beta$	$N_{g}$	$\eta_{k}$
T1	30	2	$0.03125\to 0.015625$	$0.350\to 0.175$	20	1.25	0.20	1.00	5000	$[(k-15)/15]_{0}^{1}$
T2	30	2	0.09375	0.175	20	1.25	0.10	0.50	5000	$\mathbf{1}_{\{k\geq 10\}}$
FLAIR	30	2	0.125	0.050	20	1.25	0.10	0.50	5000	1

Appendix

Table 8: M4Raw solver and correction parameters.

Figure 6: Wide-spectrum convergence and stability. (a)–(c) Original ADMM trajectories across dimensions at

\gamma=0.15

. (d) Additional correction strengths at

64\times 64

;

\beta>1

lies outside the theorem’s range. Growing runs stop at a prescribed numerical safety threshold. Panel (d) uses wider axis ranges.

Figure 7: Reconstruction error under wide-spectrum fidelity. Each panel fixes the state dimension; lower curves indicate better restoration. The gray curve is analytical ADMM (

\beta=0

). Markers denote evaluated prior strengths, connecting segments are visual guides, and shading shows pointwise 95% intervals computed across independent test matrices. All panels share the same vertical scale.

	G10				G30				GNI
Method	PSNR $\uparrow$	SSIM $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$
PLRDiff + HIR-Diff	34.52	0.8215	6.73	16.49	32.20	0.8115	8.96	20.36	31.01	0.7670	12.73	23.66
PLRDiff + PWRCTV	38.10	0.9445	5.42	12.22	33.43	0.9156	9.02	18.93	32.73	0.9082	12.05	21.31
SwinIR + HIR-Diff	33.88	0.8512	4.69	22.02	27.79	0.4978	10.21	33.18	27.18	0.4962	12.66	35.11
SwinIR + PWRCTV	31.66	0.7815	8.33	65.58	21.16	0.3662	29.96	422.81	22.62	0.4464	31.18	489.23
R-PNN + HIR-Diff	33.80	0.8068	6.22	17.49	29.10	0.6743	9.28	25.03	29.59	0.6866	10.90	25.12

Appendix

Table 9: Reference-guided HSI restoration on Dongying under Gaussian/GNI noise.

	Mix35				Mix55				Mix55-G30
Method	PSNR $\uparrow$	SSIM $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$
PLRDiff + HIR-Diff	30.90	0.7649	12.30	26.04	30.70	0.7687	13.35	35.69	31.63	0.7997	11.03	34.60
PLRDiff + PWRCTV	32.58	0.9079	11.79	23.82	32.13	0.9000	12.92	34.07	32.82	0.9059	10.94	33.24
SwinIR + HIR-Diff	27.88	0.5443	12.53	34.58	27.62	0.5328	13.47	43.14	28.20	0.5456	11.84	42.82
SwinIR + PWRCTV	25.43	0.5544	27.50	393.81	23.98	0.4886	29.39	662.34	22.44	0.4233	30.17	685.00
R-PNN + HIR-Diff	30.52	0.7378	10.72	25.12	29.48	0.7004	12.24	34.86	29.48	0.7036	11.36	34.20

Appendix

Table 10: Reference-guided HSI restoration on Dongying under mixed noise.

	G30				G50				G70
Method	PSNR $\uparrow$	SSIM $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$
BM4D	36.44	0.8936	2.60	6.72	33.64	0.8194	3.65	9.29	31.77	0.7511	4.58	11.54
HLRTF	40.70	0.9427	1.28	3.66	34.39	0.7927	2.81	8.10	29.74	0.5845	5.11	15.13
RCTV	33.03	0.7311	4.10	10.87	27.95	0.4866	7.36	19.66	24.79	0.3364	10.55	27.95
DDS2M	41.57	0.9645	1.12	3.49	39.87	0.9507	1.40	4.21	38.47	0.9361	1.68	4.95
LRTFR	38.73	0.9235	1.39	5.11	37.11	0.9000	1.78	6.22	35.89	0.8826	2.17	7.17

Appendix

Table 11: Single-image HSI denoising on Qingpu under Gaussian noise.

	M30				M50				M70
Method	PSNR $\uparrow$	SSIM $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$
BM4D	22.54	0.3971	23.26	91.66	25.36	0.5140	15.60	61.07	25.77	0.5388	13.63	53.29
HLRTF	35.60	0.9123	27.83	115.44	30.84	0.8113	27.54	117.36	27.25	0.6595	27.70	121.07
RCTV	36.83	0.9183	3.88	11.74	33.64	0.8730	5.51	16.32	31.55	0.8311	7.07	20.32
DDS2M	29.88	0.8430	13.20	53.63	29.78	0.8552	13.12	53.49	29.70	0.8625	13.05	53.41
LRTFR	32.70	0.8733	27.13	112.10	30.62	0.8417	26.95	114.20	29.20	0.8176	26.94	117.34

Appendix

Table 12: Single-image HSI denoising on Qingpu under mixed noise.

	G30				G50				G70
Method	PSNR $\uparrow$	SSIM $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$
BM4D	35.02	0.8637	2.54	5.58	32.40	0.7786	3.49	7.57	30.66	0.7046	4.32	9.28
HLRTF	39.91	0.9502	1.25	3.29	34.77	0.8508	2.25	5.86	30.51	0.6857	3.84	9.86
RCTV	33.03	0.7797	3.48	7.65	27.97	0.5534	6.25	13.88	24.79	0.3981	9.01	20.04
DDS2M	39.75	0.9448	1.22	3.35	38.07	0.9250	1.47	4.02	36.61	0.9001	1.73	4.73
LRTFR	35.57	0.8309	1.61	5.70	34.18	0.7808	1.98	6.77	33.26	0.7510	2.31	7.54

Appendix

Table 13: Single-image HSI denoising on Xiong’an under Gaussian noise.

	M30				M50				M70
Method	PSNR $\uparrow$	SSIM $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$
BM4D	22.38	0.3987	18.29	43.57	24.96	0.5014	12.33	28.99	25.21	0.5095	10.85	25.93
HLRTF	33.61	0.8941	24.44	81.55	30.12	0.8326	24.06	81.94	27.70	0.7451	24.21	83.75
RCTV	34.86	0.8863	3.77	9.16	31.92	0.8267	5.28	12.47	30.00	0.7754	6.75	15.83
DDS2M	29.05	0.8231	10.05	26.26	28.93	0.8250	9.92	26.17	28.81	0.8212	9.81	26.11
LRTFR	29.98	0.7704	23.74	79.14	28.30	0.7195	23.51	80.07	27.23	0.6901	23.48	81.42

Appendix

Table 14: Single-image HSI denoising on Xiong’an under mixed noise.

T1
	T1 3%		T1 5%		T1 7%
Method	PSNR $\uparrow$	SSIM $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$
Noise2Void	35.41	0.9062	34.88	0.9425	32.97	0.8833
Noise2Self	33.17	0.7933	33.23	0.9600	30.81	0.7435
Noisier2Noise	37.49	0.9261	34.52	0.9049	31.90	0.7828
R2R	36.20	0.8040	34.83	0.8113	32.26	0.7534

Appendix

Table 15: MRI denoising on BrainWeb across nine contrast–noise conditions.

	T1		T2		FLAIR
Method	PSNR $\uparrow$	SSIM $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$
Noise2Void	31.24	0.8671	30.45	0.8392	30.80	0.8288
Noise2Self	29.10	0.8537	28.17	0.8095	28.94	0.8150
Noisier2Noise	31.18	0.8675	30.55	0.8435	31.17	0.8356
R2R	30.82	0.8552	30.48	0.8329	30.97	0.8187
Noise2Score	31.23	0.8444	30.48	0.8139	31.00	0.7975

Appendix

Table 16: MRI denoising on M4Raw across three contrasts.

Figure 8: Reference-guided HSI restoration on Dongying: G30 (top) and Mix55 (bottom).

Figure 9: Single-image HSI denoising on Qingpu: G30 (top) and G50 (bottom).

Figure 10: Single-image HSI denoising on Xiong’an: G70 (top) and M70 (bottom).

Figure 11: MRI denoising on BrainWeb (T2, 7% noise).

Figure 12: MRI denoising on M4Raw: T2, T2, and FLAIR from top to bottom.

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SP $^3$ : Spherical Priors for Plug-and-Play Restoration

Sean Man, Ron Raphaeli, Matan Kleiner, Or Ronai

Technion – Israel Institute of Technology · Independent Researcher

Image Restoration

Open paper AskPDF arXiv

In this paper, we introduce SP

^3

, a novel Plug-and-Play algorithm that accelerates maximum a posteriori image restoration by replacing denoisers with Spherical Encoders (SE) as generative priors. SP

^3

approximates the intractable proximal prior step by utilizing the SE tightly structured latent space as a robust projection onto the natural image manifold. Alternating this projection with a closed-form data-consistency step, via Half-Quadratic Splitting, achieves stable convergence without requiring gradient computation during inference. This unique formulation unlocks "anytime" restoration capabilities, producing sharp, plausible images from the first iteration. Evaluations across a variety of image restoration tasks demonstrate that SP

^3

achieves perceptual quality comparable to state-of-the-art zero-shot diffusion and flow methods while being

3

630\times

faster.

Abstract

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