Phase retrieval is the nonlinear inverse problem of recovering a true signal from its Fourier magnitude measurements. It arises in many applications such as astronomical imaging, X-Ray crystallography, microscopy, and more. The problem is highly ill-posed due to the phase-induced ambiguities and the large number of possible images that can fit to the given measurements. Thus, there's a rich history of enforcing structural priors to improve solutions including sparsity priors and deep-learning-based generative models. However, such priors are often limited in their representational capacity or generalizability to slightly different distributions. Recent advancements in using denoisers as regularizers for non-convex optimization algorithms have shown promising performance and generalization. We present a way of leveraging the prior implicitly learned by a denoiser to solve phase retrieval problems by incorporating it in a classical alternating minimization framework. Compared to performant denoising-based algorithms for phase retrieval, we showcase competitive performance with Fourier measurements on in-distribution images and notable improvement on out-of-distribution images.
Harbin Institute of Technology（哈尔滨工业大学）；Peng Cheng Lab（鹏城实验室）；Tomorrow Advancing Life
The success of deep denoisers on real-world color photographs usually relies on the modeling of sensor noise and in-camera signal processing (ISP) pipeline. Performance drop will inevitably happen when the sensor and ISP pipeline of test images are different from those for training the deep denoisers (i.e., noise discrepancy). In this paper, we present an unpaired learning scheme to adapt a color image denoiser for handling test images with noise discrepancy. We consider a practical training setting, i.e., a pre-trained denoiser, a set of test noisy images, and an unpaired set of clean images.…
Plug-and-Play (PnP) methods solve ill-posed inverse problems through iterative proximal algorithms by replacing a proximal operator by a denoising operation. When applied with deep neural network denoisers, these methods have shown state-of-the-art visual performance for image restoration problems. However, their theoretical convergence analysis is still incomplete. Most of the existing convergence results consider nonexpansive denoisers, which is non-realistic, or limit their analysis to strongly convex data-fidelity terms in the inverse problem to solve. Recently, it was proposed to train th…
Instituto de Telecomunicações（电信研究所）；Instituto Superior Técnico（高等技术学院）
The recently proposed plug-and-play (PnP) framework allows leveraging recent developments in image denoising to tackle other, more involved, imaging inverse problems. In a PnP method, a black-box denoiser is plugged into an iterative algorithm, taking the place of a formal denoising step that corresponds to the proximity operator of some convex regularizer. While this approach offers flexibility and excellent performance, convergence of the resulting algorithm may be hard to analyze, as most state-of-the-art denoisers lack an explicit underlying objective function. In this paper, we propose a …
Hunan University of Science and Technology（湖南科技大学）；Nanjing First Hospital, Nanjing Medical University（南京医科大学附属南京第一医院）；University of Macau（澳门大学）；Nanjing University of Posts and Telecommunications（南京邮电大学）
Compressive sensing (CS) based computed tomography (CT) image reconstruction aims at reducing the radiation risk through sparse-view projection data. It is usually challenging to achieve satisfying image quality from incomplete projections. Recently, the nonconvex ${L_ {1/2}} $-norm has achieved promising performance in sparse recovery, while the applications on imaging are unsatisfactory due to its nonconvexity. In this paper, we develop a ${L_ {1/2}} $-regularized nonlocal self-similarity (NSS) denoiser for CT reconstruction problem, which integrates low-rank approximation with group sparse …
Recent frameworks, such as the so-called plug-and-play, allow us to leverage the developments in image denoising to tackle other, and more involved, problems in image processing. As the name suggests, state-of-the-art denoisers are plugged into an iterative algorithm that alternates between a denoising step and the inversion of the observation operator. While these tools offer flexibility, the convergence of the resulting algorithm may be difficult to analyse. In this paper, we plug a state-of-the-art denoiser, based on a Gaussian mixture model, in the iterations of an alternating direction me…
We introduce a new class of iterative image reconstruction algorithms for radio interferometry, at the interface of convex optimization and deep learning, inspired by plug-and-play methods. The approach consists in learning a prior image model by training a deep neural network (DNN) as a denoiser, and substituting it for the handcrafted proximal regularization operator of an optimization algorithm. The proposed AIRI (``AI for Regularization in radio-interferometric Imaging'') framework, for imaging complex intensity structure with diffuse and faint emission from visibility data, inherits the r…
The Plug-and-Play (PnP) framework makes it possible to integrate advanced image denoising priors into optimization algorithms, to efficiently solve a variety of image restoration tasks generally formulated as Maximum A Posteriori (MAP) estimation problems. The Plug-and-Play alternating direction method of multipliers (ADMM) and the Regularization by Denoising (RED) algorithms are two examples of such methods that made a breakthrough in image restoration. However, while the former method only applies to proximal algorithms, it has recently been shown that there exists no regularization that exp…
The Technion - Israel Institute of Technology（以色列理工学院）
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 f…
Phase retrieval refers to the problem of recovering an image from the magnitudes of its complex-valued linear measurements. Since the problem is ill-posed, the recovery requires prior knowledge on the unknown image. We present DOLPH as a new deep model-based architecture for phase retrieval that integrates an image prior specified using a diffusion model with a nonconvex data-fidelity term for phase retrieval. Diffusion models are a recent class of deep generative models that are relatively easy to train due to their implementation as image denoisers. DOLPH reconstructs high-quality solutions …
Bayesian imaging using Plug & Play priors: when Langevin meets Tweedie
University of Oxford（牛津大学）；Institut Universitaire de France（法国大学研究院）；Heriot-Watt University（赫瑞瓦特大学）；Maxwell Institute for Mathematical Sciences（麦克斯韦数学科学研究所）
本文针对贝叶斯成像中 Plug & Play (PnP) 先验方法缺乏收敛证明的问题，提出了两种可证明收敛的算法 PnP-ULA 和 PnP-SGD，并建立了详细的收敛保证，适用于图像去模糊、修复和去噪等任务。
Alternating direction method of multiplier (ADMM) is a widely used algorithm for solving constrained optimization problems in image restoration. Among many useful features, one critical feature of the ADMM algorithm is its modular structure which allows one to plug in any off-the-shelf image denoising algorithm for a subproblem in the ADMM algorithm. Because of the plug-in nature, this type of ADMM algorithms is coined the name "Plug-and-Play ADMM". Plug-and-Play ADMM has demonstrated promising empirical results in a number of recent papers. However, it is unclear under what conditions and by …
University of Electronic Science and Technology of China（电子科技大学）；Southwestern University of Finance and Economics（西南财经大学）；Xi’an Jiaotong University（西安交通大学）
Multi-dimensional images, such as color images and multi-spectral images, are highly correlated and contain abundant spatial and spectral information. However, real-world multi-dimensional images are usually corrupted by missing entries. By integrating deterministic low-rankness prior to the data-driven deep prior, we suggest a novel regularized tensor completion model for multi-dimensional image completion. In the objective function, we adopt the newly emerged tensor nuclear norm (TNN) to characterize the global low-rankness prior of the multi-dimensional images. We also formulate an implicit…
Blind Super-Resolution via Meta-learning and Markov Chain Monte Carlo Simulation
College of Electronic Engineering, National University of Defense Technology（国防科技大学电子工程学院）；College of Electronic Engineering, Beihang University（北京航空航天大学电子工程学院）；Imperial College London（伦敦帝国学院）；University of Modena and Reggio Emilia（摩德纳-雷焦艾米利亚大学）
