Image denoising is a well-known and well studied problem, commonly targeting a minimization of the mean squared error (MSE) between the outcome and the original image. Unfortunately, especially for severe noise levels, such Minimum MSE (MMSE) solutions may lead to blurry output images. In this work we propose a novel stochastic denoising approach that produces viable and high perceptual quality results, while maintaining a small MSE. Our method employs Langevin dynamics that relies on a repeated application of any given MMSE denoiser, obtaining the reconstructed image by effectively sampling from the posterior distribution. Due to its stochasticity, the proposed algorithm can produce a variety of high-quality outputs for a given noisy input, all shown to be legitimate denoising results. In addition, we present an extension of our algorithm for handling the inpainting problem, recovering missing pixels while removing noise from partially given data.
PPFM: Image denoising in photon-counting CT using single-step posterior sampling Poisson flow generative models
KTH Royal Institute of Technology（皇家理工学院）；Karolinska University Hospital（卡罗林斯卡大学医院）；University of Wisconsin School of Medicine and Public Health（威斯康星大学麦迪逊分校医学与公共卫生学院）；GE HealthCare（GE医疗）；Rensselaer Polytechnic Institute（伦斯勒理工学院）
Many interesting tasks in image restoration can be cast as linear inverse problems. A recent family of approaches for solving these problems uses stochastic algorithms that sample from the posterior distribution of natural images given the measurements. However, efficient solutions often require problem-specific supervised training to model the posterior, whereas unsupervised methods that are not problem-specific typically rely on inefficient iterative methods. This work addresses these issues by introducing Denoising Diffusion Restoration Models (DDRM), an efficient, unsupervised posterior sa…
Variational Denoising Network: Toward Blind Noise Modeling and Removal
Xi’an Jiaotong University（西安交通大学）；Hong Kong Polytechnic University（香港理工大学）；Alibaba Group（阿里巴巴集团）；The Macau University of Science and Technology（澳门科技大学）
In this paper, we propose a new image denoising method, tailored to specific classes of images, assuming that a dataset of clean images of the same class is available. Similarly to the non-local means (NLM) algorithm, the proposed method computes a weighted average of non-local patches, which we interpret under the importance sampling framework. This viewpoint introduces flexibility regarding the adopted priors, the noise statistics, and the computation of Bayesian estimates. The importance sampling viewpoint is exploited to approximate the minimum mean squared error (MMSE) patch estimates, us…
Regularization by denoising: Bayesian model and Langevin-within-split Gibbs sampling
Institut Denis Poisson, University of Orléans（德尼·泊松研究所，奥尔良大学）；University of Toulouse, IRIT/INP-ENSEEIHT, CNRS（图卢兹大学，法国国家信息与自动化研究所/国立高等电子、电子技术、计算机与机械学院，法国国家科学研究中心）
本文提出一种基于去噪正则化（RED）的图像反演贝叶斯框架，并设计了内含Langevin Monte Carlo步骤的分裂Gibbs采样算法，通过去模糊等任务验证了其有效性。
Posterior sampling via Langevin dynamics based on generative priors
Elmore Family School of Electrical and Computer Engineering, Purdue University（普渡大学埃尔莫尔家族电气与计算机工程学院）；H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology（佐治亚理工学院H·米尔顿·斯图尔特工业与系统工程学院）；Department of Mathematics, Duke University（杜克大学数学系）；Department of Physics and Department of Chemistry, Duke University（杜克大学物理系与化学系）
Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希-亚历山大大学）；Massachusetts Institute of Technology（麻省理工学院）；Tufts School of Medicine（塔夫茨医学院）
Optical coherence tomography angiography (OCTA) is a novel and clinically promising imaging modality to image retinal and sub-retinal vasculature. Based on repeated optical coherence tomography (OCT) scans, intensity changes are observed over time and used to compute OCTA image data. OCTA data are prone to noise and artifacts caused by variations in flow speed and patient movement. We propose a novel iterative maximum a posteriori signal recovery algorithm in order to generate OCTA volumes with reduced noise and increased image quality. This algorithm is based on previous work on probabilistic…
Confocal microscopy is essential for histopathologic cell visualization and quantification. Despite its significant role in biology, fluorescence confocal microscopy suffers from the presence of inherent noise during image acquisition. Non-local patch-wise Bayesian mean filtering (NLB) was until recently the state-of-the-art denoising approach. However, classic denoising methods have been outperformed by neural networks in recent years. In this work, we propose to exploit the strengths of NLB in the framework of Bayesian deep learning. We do so by designing a convolutional neural network and t…
Low-dose computed tomography (LDCT) is an important topic in the field of radiology over the past decades. LDCT reduces ionizing radiation-induced patient health risks but it also results in a low signal-to-noise ratio (SNR) and a potential compromise in the diagnostic performance. In this paper, to improve the LDCT denoising performance, we introduce the conditional denoising diffusion probabilistic model (DDPM) and show encouraging results with a high computational efficiency. Specifically, given the high sampling cost of the original DDPM model, we adapt the fast ordinary differential equat…
