Matching Particle-Arrival Rates for Low-Count Image Denoising

Huazhen Liu; Zipei Yan; Jizhou Li

eess.IVOct 23, 2026

Matching Particle-Arrival Rates for Low-Count Image Denoising

Authors: Huazhen Liu, Zipei Yan, Jizhou Li

Organizations: Department of Electronic Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong.

Abstract

Low-count imaging arises when limited illumination or dose yields only a few detected particles in microscopy, such as photons or electrons, causing measurements to be dominated by signal-dependent Poisson shot noise. Supervised denoisers typically require paired clean and noisy observations, whereas many self-supervised approaches exploit spatial or temporal redundancy without directly estimating the underlying particle-arrival process. We introduce PARM, a self-supervised denoising framework based on particle-arrival-rate matching. By modeling particle accumulation over exposure as a Poisson counting process, PARM identifies the conditional particle-arrival-rate field with the posterior mean of the latent clean rate. Poisson thinning then splits each observation into complementary lower-exposure views that provide self-supervised rate targets for one another. In implementation, the network estimates the normalized spatial allocation of the conditional rate, while the observed total count determines its global particle mass. Experiments on synthetic data, natural-video sequences corrupted with Poisson noise, and real low-dose electron microscopy demonstrate leading or competitive performance while effectively preserving fine structures. PARM therefore provides a statistically grounded approach to low-count image denoising when clean references are unavailable.

Figures & tables

Fig. 1: Illustration of the exposure-indexed Poisson rate formulation. Conditioned on the clean image $X=x$ , particle counts follow $Y_{\tau}\mid X=x\sim\operatorname{Poisson}(\lambda_{0}\tau x)$ . The circles indicate count distributions at effective exposures $p\tau$ , $q\tau$ , and $\tau$ . Poisson thinning decomposes $Y_{\tau}$ into complementary views $A$ and $B$ , where $q=1-p$ , $A+B=Y_{\tau}$ , and $A\perp B\mid X$ . Conditioned on $X$ , these views follow the count distributions associated with effective exposures $p\tau$ and $q\tau$ , respectively. At pixel $i$ , the conditional particle-arrival-rate field component $v_{\tau,i}(y)=\mathbb{E}[\lambda_{0}X_{i}\mid Y_{\tau}=y]$ governs transitions toward higher count states. Exposure-normalized counts have conditional mean $\lambda_{0}x_{i}$ , while their conditional variance decreases with exposure.

Fig. 2: Synthetic Cameraman benchmark for 2D and 3D Poisson denoising. (a) Original Cameraman image and the "2"-shaped cropping trajectory used to generate the synthetic stack. (b) Illustration of the resulting ordered synthetic dataset, where consecutive patches contain smoothly varying spatial content. (c) 2D single-frame Poisson denoising comparison at $\Lambda=2$ . PARM suppresses particle noise while retaining object boundaries and local intensity transitions. (d) 3D stack-based Poisson denoising comparison at $\Lambda=0.25$ . The red box highlights the camera. PARM shows lower visible particle fluctuations and sharper local transitions in this region. The magnified insets and line profiles further show the preservation of local transitions and structural peaks. PSNR values are annotated on the reconstructions in (c) and (d).

$\Lambda$	2	1	0.5	0.25	0.125	0.0625
Method	PSNR (dB) / SSIM
VBM4D	25.08 / 0.796	22.71 / 0.732	20.46 / 0.643	18.72 / 0.549	17.15 / 0.450	15.67 / 0.361
N2V	20.96 / 0.527	20.12 / 0.498	18.99 / 0.435	18.27 / 0.383	16.98 / 0.298	16.16 / 0.238
SHINE	18.13 / 0.405	17.84 / 0.400	16.91 / 0.376	15.64 / 0.292	14.43 / 0.215	12.61 / 0.121
UDVD	22.93 / 0.736	21.82 / 0.700	20.63 / 0.657	19.40 / 0.587	18.34 / 0.524	17.37 / 0.450
bit2bit	25.40 / 0.781	23.24 / 0.703	22.35 / 0.683	22.03 / 0.678	20.49 / 0.582	19.01 / 0.487

TABLE I: Quantitative comparison for the 3D stack-based Cameraman experiment. PSNR and SSIM are averaged over all extracted images at each particle level. Bold and underlined values indicate the best and second-best results, respectively, among all methods except PARM(Sup.). PARM(Sup.) is shown only as a supervised reference and is excluded from this ranking. Results are averaged over 5 independent noise realizations.

Fig. 3: Qualitative comparison on the Coastguard sequence under synthetic Poisson noise at $\Lambda=2$ . Red and yellow boxes mark fine-structure regions, with enlarged views shown beside each reconstruction. In the red region, PARM resolves the thin tree trunks more clearly, whereas other methods merge or obscure them. In the yellow region, PARM recovers the sail with a recognizable shape and boundary.

Method	VBM4D	N2V	SHINE	UDVD	bit2bit	PARM
	Coastguard
2	24.84 / 0.628	22.47 / 0.502	22.75 / 0.599	24.10 / 0.604	26.40 / 0.746	27.25 / 0.767
1	23.24 / 0.537	19.98 / 0.342	21.24 / 0.513	23.32 / 0.563	25.18 / 0.701	26.26 / 0.723
0.5	21.55 / 0.447	17.55 / 0.193	18.81 / 0.432	22.57 / 0.518	24.58 / 0.654	25.12 / 0.666
0.25	20.17 / 0.375	15.65 / 0.122	17.61 / 0.353	21.72 / 0.472	23.07 / 0.543	23.91 / 0.592
0.125	18.75 / 0.316	10.94 / 0.035	17.39 / 0.320	20.84 / 0.416	19.57 / 0.327	22.33 / 0.471

TABLE II: Quantitative comparison on six noisy video sequences. PSNR (dB) and SSIM are reported for each particle level

\Lambda

. Bold numbers indicate the best result for each metric and setting, and underlined numbers indicate the second-best result. Results are averaged over 5 independent noise realizations.

Fig. 4: Real low-dose electron microscopy denoising on Pt nanoparticle data. ( a ) Representative results at two time points. Numbers on the denoised images denote correlations with a local multi-frame reference. PARM suppresses background noise while retaining lattice-like nanoparticle structures. ( b ) Detailed comparison of local nanoparticle structures and intensity profiles. The region of interest in ( b ) corresponds to the red box in ( a ). Gaussian blur and 50-frame UDVD provide reference comparisons. Gaussian blur suppresses noise but removes particle boundaries, whereas 50-frame UDVD uses longer temporal context but blurs some single-frame details. PARM produces a cleaner single-frame reconstruction while retaining individual nanoparticle contrast. Its intensity profile preserves periodic peaks that the reference methods attenuate or merge. ( c ) Average correlation as a function of the group size used to construct the evaluation reference. The displayed correlations in ( a ) use

G=50

. Error bars in ( c ) denote the sample standard deviation across the four

2\times 2

spatial-subsampling offsets; they do not represent independently acquired microscopy experiments.

Fig. 5: Ablation studies. ( a ) Effect of the base consistency coefficient $\gamma_{0}$ on the 3D Cameraman benchmark. A large coefficient degrades the displayed particle levels; $\gamma_{0}=0.01$ is the default used in the main experiments. ( b ) Effect of temporal stack size on the 3D Cameraman benchmark. Increasing the stack depth generally improves reconstruction quality, with larger depths requiring greater memory and runtime cost. Error bars denote the standard deviation of PSNR over five independently generated noisy realizations.

Dataset \ Platform			CPU	GPU
Name	Resolution	Frames	VBM4D	N2V	SHINE	UDVD	bit2bit	PARM
Cameraman	$128\times 128$	513	3.03	1.00	88.14	9.72	22.52	3.30
Coastguard	$144\times 176$	300	2.51	2.41	53.31	13.15	41.23	10.46
Bus / Miss America	$288\times 352$	150	5.72	3.82	26.44	6.67	22.45	11.02
Flower / Tennis	$240\times 352$	150	5.28	2.31	26.38	6.68	23.25	10.48
Foreman	$288\times 352$	300	11.02	7.6	56.82	13.40	41.50	18.99

TABLE III: Runtime comparison on different video sequences. Runtime is reported in minutes. VBM4D is evaluated on CPU, while N2V, SHINE, UDVD, bit2bit, and PARM are evaluated on GPU.

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Low-dose computed tomography (LDCT) measurements contain mixed Poisson-Gaussian noise. However, most self-supervised methods rely on generic image statistics and do not explicitly model this noise, which may limit their ability to effectively suppress realistic LDCT noise. To address this issue, we propose a physics-driven framework with cross-domain iteration for self-supervised LDCT denoising. The proposed framework proceeds in three main steps. First, a learned sinogram prior and the LDCT noise model guide posterior inference of photon counts, enabling separation of the Poisson and Gaussian components. Second, the separated Poisson and Gaussian components are respectively processed by binomial thinning and Gaussian data thinning to construct two branches, and residual scaling matches each branch's noise level to that of the observation, yielding a training pair with approximately independent noise realizations from one low-dose measurement. Finally, the pair is used to train an image-domain network whose forward-projected outputs update the prior. Through cross-domain iteration, the prior and the training pair are progressively refined while maintaining consistency with CT acquisition physics. Experiments on simulated data from AAPM, LIDC-IDRI, and LoDoPaB-CT and on real LDCT data show consistent gains over the evaluated self-supervised baselines across dose levels, with performance comparable to the evaluated supervised baseline.

Abstract

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