Abstract. Deep learning-based image denoising models demonstrate remarkable performance, but their lack of robustness analysis remains a significant concern. A major issue is that these models are susceptible to adversarial attacks, where small, carefully crafted perturbations to input data can cause them to fail. Surprisingly, perturbations specifically crafted for one model can easily transfer across various models, including convolutional neural networks, transformers, unfolding models, and plug-and-play models, leading to failures in those models as well. Such high adversarial transferability is not observed in classification models. We analyze the possible underlying reasons behind the high adversarial transferability through a series of hypotheses and validation experiments. By characterizing the manifolds of Gaussian noise and adversarial perturbations using the concept of a typical set and the asymptotic equipartition property, we prove that adversarial samples deviate slightly from the typical set of the original input distribution, causing the models to fail. Based on these insights, we propose a novel adversarial defense method: the out-of-distribution typical set sampling (TSS) training strategy. TSS training strategy not only significantly enhances the model’s robustness but also marginally improves denoising performance compared to the original model.

The rapid development of deep learning has significantly advanced Synthetic Aperture Radar (SAR) despeckling techniques. However, as the uncertainty and vulnerability of the network structure is ignited by the fuse of adversarial attacks, its authenticity and widespread applicability are subsequently drawn into question. This study examines the robustness and performance of deep learning-based image despeckling models under a denoising-PGD adversarial attack. Furthermore, we investigate the impact of varying feature extraction approaches on model performance, with the goal of providing reliable guidelines for model training.

Multiplicative noise removal problems have attracted much attention in recent years. Unlike additive noise removal problems, multiplicative noise destroys almost all information of the original image, especially for texture images. In this paper, a fractional-order nonlinear diffusion model is proposed to denoise the texture images corrupted by multiplicative noise. In the model, a gray level indicator is introduced to remove multiplicative noise and preserve structure details for texture images. By virtue of the discrete Fourier transform, the model is solved by an iterative scheme in the frequency domain. Then an algorithm in the spatial domain is developed based on the definition of the Grünwald--Letnikov fractional-order derivative. Inspired by the discrepancy principle used for additive noise, we develop a new stopping criterion based on the mean and variance of the noise. Numerical examples are presented to demonstrate the effectiveness and efficiency of the proposed method. Experimental results show that the proposed model can handle multiplicative noise removal and texture preservation quite well.

Multiplicative noise removal is a challenging task in image processing. Inspired by the impressive performance of nonlinear diffusion models in additive noise removal, we address this problem in the view of nonlinear diffusion equation theories rather than the traditional variation methods. We develop a nonlinear diffusion filter denoising framework, which considers not only the information of the gradient of the image, but also the information of gray levels of the image. Furthermore, under this framework, we propose a doubly degenerate diffusion model for multiplicative noise removal, which is analyzed with respect to some of its properties and behavior in denoising process. In numerical aspects, we present an efficient scheme which uses a stabilization by fast explicit diffusion for the implementation of the multiplicative noise removal model. Finally, the experimental results illustrate effectiveness and efficiency of the proposed model.

This paper introduces a class of adaptive Perona-Malik (PM) diffusion, which combines the PM equation with the heat equation. The PM equation provides a potential algorithm for image segmentation, noise removal, edge detection, and image enhancement. However, the defect of traditional PM model is tending to cause the staircase effect and create new features in the processed image. Utilizing the edge indicator as a variable exponent, we can adaptively control the diffusion mode, which alternates between PM diffusion and Gaussian smoothing in accordance with the image feature. Computer experiments indicate that the present algorithm is very efficient for edge detection and noise removal.