Poisson noise is an inherent signal-dependent distortion commonly encountered in low-dose medical imaging and microscopic imaging, which poses significant challenges for image restoration models, particularly in balancing effective noise removal and fine detail preservation. In this paper, we propose a Poisson image denoising method that integrates high-order total variation (HOTV) regularization with low-rank regularization. The proposed method combines the advantages of HOTV regularization to avoid staircase artifacts and low-rank prior to retain a large amount of image details. We then employ an alternating minimization method to solve the proposed Poisson image denoising model with the combination of Chambolle's dual projection algorithm and the non-negative Garrote thresholding algorithm. Experiments on natural and medical images validate the efficacy of our method, demonstrating its superiority over multiple state-of-the-art Poisson denoising approaches in both quantitative metrics and visual perception.
Citation: Binbin Hao, Zixuan Fang, Jing Pan, Jianguang Zhu. Poisson image denoising via high-order total variation and low-rank minimization[J]. AIMS Mathematics, 2026, 11(10): 25795-25817. doi: 10.3934/math.20261387
Poisson noise is an inherent signal-dependent distortion commonly encountered in low-dose medical imaging and microscopic imaging, which poses significant challenges for image restoration models, particularly in balancing effective noise removal and fine detail preservation. In this paper, we propose a Poisson image denoising method that integrates high-order total variation (HOTV) regularization with low-rank regularization. The proposed method combines the advantages of HOTV regularization to avoid staircase artifacts and low-rank prior to retain a large amount of image details. We then employ an alternating minimization method to solve the proposed Poisson image denoising model with the combination of Chambolle's dual projection algorithm and the non-negative Garrote thresholding algorithm. Experiments on natural and medical images validate the efficacy of our method, demonstrating its superiority over multiple state-of-the-art Poisson denoising approaches in both quantitative metrics and visual perception.
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Figures(10) / Tables(8)
Binbin Hao, Zixuan Fang, Jing Pan, Jianguang Zhu. Poisson image denoising via high-order total variation and low-rank minimization[J]. AIMS Mathematics, 2026, 11(10): 25795-25817. doi: 10.3934/math.20261387
Flowchart of the proposed model for Poisson image denoising
Test images: (a) Cameraman ($ 256\times256 $), (b) Barbara ($ 256\times256 $), (c) Boat ($ 256\times256 $), (d) Einstein ($ 256\times256 $), (e) Brain ($ 442\times442 $), (f) Liver ($ 320\times320 $). "Brain" and "Liver" are resized to $ 256\times256 $ for all experiments
PSNR values versus regularization parameters $ \lambda_1 $ and $ \lambda_2 $, and penalty parameters $ \alpha_1 $ and $ \alpha_2 $, under different noise levels for different images
The recovery results of different methods with peak = 15 on Cameraman
The recovery results of different methods with peak = 30 on Barbara
The recovery results of different methods with peak = 100 on Boat
The recovery results of different methods with peak = 155 on Einstein
The recovery results of different methods with peak = 15 on Brain
The recovery results of different methods with peak = 30 on Liver
The convergence curves of PSNR and SSIM relative to the iterations under the noise level peak = 15 and peak = 100
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