To solve inverse problems, plug-and-play (PnP) methods replace the proximal step in a convex optimization algorithm with a call to an application-specific denoiser, often implemented using a deep neural network (DNN). Although such methods yield accurate solutions, they can be improved. For example, denoisers are usually designed/trained to remove white Gaussian noise, but the denoiser input error in PnP algorithms is usually far from white or Gaussian. Approximate message passing (AMP) methods provide white and Gaussian denoiser input error, but only when the forward operator is sufficiently random. In this work, for Fourier-based forward operators, we propose a PnP algorithm based on generalized expectation-consistent (GEC) approximation -- a close cousin of AMP -- that offers predictable error statistics at each iteration, as well as a new DNN denoiser that leverages those statistics. We apply our approach to magnetic resonance (MR) image recovery and demonstrate its advantages over existing PnP and AMP methods.
Nanyang Technological University（南洋理工大学）；Delft University of Technology（代尔夫特理工大学）
State-of-the-art image denoisers exploit various types of deep neural networks via deterministic training. Alternatively, very recent works utilize deep reinforcement learning for restoring images with diverse or unknown corruptions. Though deep reinforcement learning can generate effective policy networks for operator selection or architecture search in image restoration, how it is connected to the classic deterministic training in solving inverse problems remains unclear. In this work, we propose a novel image denoising scheme via Residual Recovery using Reinforcement Learning, dubbed R3L. W…
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…
Thresholding of Curvelet Coefficients, for image denoising, drains out subtle signal component in noise subspace. This produces ringing artifacts near edges and granular effect in the denoised image. We found the noise sensitivity of Curvelet phases (in contrast to their magnitude) reduces with higher noise level. Thus, we preserved the phase of the coefficients below threshold at coarser scale and estimated their magnitude by Joint Bilateral Filtering (JBF) technique from the thresholded and noisy coefficients. In the finest scale, we apply Bilateral Filter (BF) to keep edge information. Furt…
Plug-and-play (PnP) methods that employ application-specific denoisers have been proposed to solve inverse problems, including MRI reconstruction. However, training application-specific denoisers is not feasible for many applications due to the lack of training data. In this work, we propose a PnP-inspired recovery method that does not require data beyond the single, incomplete set of measurements. The proposed method, called recovery with a self-calibrated denoiser (ReSiDe), trains the denoiser from the patches of the image being recovered. The denoiser training and a call to the denoising su…
Fingerprint image denoising is a very important step in fingerprint identification. to improve the denoising effect of fingerprint image,we have designs a fingerprint denoising algorithm based on deep encoder-decoder network,which encoder subnet to learn the fingerprint features of noisy images.the decoder subnet reconstructs the original fingerprint image based on the features to achieve denoising, while using the dilated convolution in the network to increase the receptor field without increasing the complexity and improve the network inference speed. In addition, feature fusion at different…
Washington University in St. Louis（圣路易斯华盛顿大学）；Department of Electrical and Systems Engineering（电气与系统工程系）；Department of Computer Science and Engineering（计算机科学与工程系）
Regularization by denoising (RED) is a widely-used framework for solving inverse problems by leveraging image denoisers as image priors. Recent work has reported the state-of-the-art performance of RED in a number of imaging applications using pre-trained deep neural nets as denoisers. Despite the recent progress, the stable convergence of RED algorithms remains an open problem. The existing RED theory only guarantees stability for convex data-fidelity terms and nonexpansive denoisers. This work addresses this issue by developing a new monotone RED (MRED) algorithm, whose convergence does not …
This paper proposes a non-data-driven deep neural network for spectral image recovery problems such as denoising, single hyperspectral image super-resolution, and compressive spectral imaging reconstruction. Unlike previous methods, the proposed approach, dubbed Mixture-Net, implicitly learns the prior information through the network. Mixture-Net consists of a deep generative model whose layers are inspired by the linear and non-linear low-rank mixture models, where the recovered image is composed of a weighted sum between the linear and non-linear decomposition. Mixture-Net also provides a lo…
Score-Based Turbo Message Passing for Plug-and-Play Compressive Image Recovery
Department of Information Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong SAR（信息工程系，香港中文大学（深圳校区））；National Key Lab. of Wireless Commun., Uni. of Electronic Sci. and Tech. of China, Chengdu, China（无线通信国家重点实验室，电子科技大学，成都，中国）
Positron Emission Tomography (PET) is an essential technique in many clinical applications that allows for quantitative imaging at the molecular level. This study aims to develop a denoising method using novel dilated convolutional neural network to recover full-count images from low-count images. We adopted similar hierarchal structure from the conventional uNet and incorporated dilated kernels in each convolution to allow the network to observe larger, and perhaps, more robust, features within the image. Our dNet were trained alongside a uNet for comparison. Our 2.5D model used a training se…
Technion Israel Institute of Technology（以色列理工学院）；Google Research（谷歌研究院）
Inverse problems in image processing are typically cast as optimization tasks, consisting of data-fidelity and stabilizing regularization terms. A recent regularization strategy of great interest utilizes the power of denoising engines. Two such methods are the Plug-and-Play Prior (PnP) and Regularization by Denoising (RED). While both have shown state-of-the-art results in various recovery tasks, their theoretical justification is incomplete. In this paper, we aim to bridge between RED and PnP, enriching the understanding of both frameworks. Towards that end, we reformulate RED as a convex op…
Washington University in St. Louis（圣路易斯华盛顿大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Department of Computer Science and Engineering, Washington University in St. Louis（圣路易斯华盛顿大学计算机科学与工程系）；Department of Electrical and Systems Engineering, Washington University in St. Louis（圣路易斯华盛顿大学电气与系统工程系）
Regularization by denoising (RED) is a recently developed framework for solving inverse problems by integrating advanced denoisers as image priors. Recent work has shown its state-of-the-art performance when combined with pre-trained deep denoisers. However, current RED algorithms are inadequate for parallel processing on multicore systems. We address this issue by proposing a new asynchronous RED (ASYNC-RED) algorithm that enables asynchronous parallel processing of data, making it significantly faster than its serial counterparts for large-scale inverse problems. The computational complexity…
YOND: Practical Blind Raw Image Denoising Free from Camera-Specific Data Dependency
School of Computer Science and Technology, Beijing Institute of Technology（计算机科学与技术学院，北京理工大学）；School of Artificial Intelligence, Beijing Normal University（人工智能学院，北京师范大学）
The vast majority of image recovery tasks are ill-posed problems. As such, methods that are based on optimization use cost functions that consist of both fidelity and prior (regularization) terms. A recent line of works imposes the prior by the Regularization by Denoising (RED) approach, which exploits the good performance of existing image denoising engines. Yet, the relation of RED to explicit prior terms is still not well understood, as previous work requires too strong assumptions on the denoisers. In this paper, we make two contributions. First, we show that the RED gradient can be seen a…
As quotidian use of sophisticated cameras surges, people in modern society are more interested in capturing fine-quality images. However, the quality of the images might be inferior to people's expectations due to the noise contamination in the images. Thus, filtering out the noise while preserving vital image features is an essential requirement. Current existing denoising methods have their own assumptions on the probability distribution in which the contaminated noise is sampled for the method to attain its expected denoising performance. In this paper, we utilize our recent Gramian-based f…
Washington University in St. Louis（圣路易斯华盛顿大学）；University of California, Riverside（加州大学河滨分校）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
The plug-and-play priors (PnP) and regularization by denoising (RED) methods have become widely used for solving inverse problems by leveraging pre-trained deep denoisers as image priors. While the empirical imaging performance and the theoretical convergence properties of these algorithms have been widely investigated, their recovery properties have not previously been theoretically analyzed. We address this gap by showing how to establish theoretical recovery guarantees for PnP/RED by assuming that the solution of these methods lies near the fixed-points of a deep neural network. We also pre…
Fudan University（复旦大学）；Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University（复旦大学类脑智能科学与技术研究院）；Huashan Hospital, Fudan University（复旦大学附属华山医院）
Small lesions in magnetic resonance imaging (MRI) images are crucial for clinical diagnosis of many kinds of diseases. However, the MRI quality can be easily degraded by various noise, which can greatly affect the accuracy of diagnosis of small lesion. Although some methods for denoising MR images have been proposed, task-specific denoising methods for improving the diagnosis confidence of small lesions are lacking. In this work, we propose a voxel-wise hybrid residual MLP-CNN model to denoise three-dimensional (3D) MR images with small lesions. We combine basic deep learning architecture, MLP…
Several imaging algorithms including patch-based image denoising, image time series recovery, and convolutional neural networks can be thought of as methods that exploit the manifold structure of signals. While the empirical performance of these algorithms is impressive, the understanding of recovery of the signals and functions that live on manifold is less understood. In this paper, we focus on the recovery of signals that live on a union of surfaces. In particular, we consider signals living on a union of smooth band-limited surfaces in high dimensions. We show that an exponential mapping t…
We introduce a new algorithm for regularized reconstruction of multispectral (MS) images from noisy linear measurements. Unlike traditional approaches, the proposed algorithm regularizes the recovery problem by using a prior specified \emph{only} through a learned denoising function. More specifically, we propose a new accelerated gradient method (AGM) variant of regularization by denoising (RED) for model-based MS image reconstruction. The key ingredient of our approach is the three-dimensional (3D) deep neural net (DNN) denoiser that can fully leverage spationspectral correlations within MS …
Color image denoising is frequently encountered in various image processing and computer vision tasks. One traditional strategy is to convert the RGB image to a less correlated color space and denoise each channel of the new space separately. However, such a strategy can not fully exploit the correlated information between channels and is inadequate to obtain satisfactory results. To address this issue, this paper proposes a new multi-channel optimization model for color image denoising under the nuclear norm minus Frobenius norm minimization framework. Specifically, based on the block-matchin…
Cloud K-SVD is a dictionary learning algorithm that can train at multiple nodes and hereby produce a mutual dictionary to represent low-dimensional geometric structures in image data. We present a novel application of the algorithm as we use it to recover both noiseless and noisy images from overlapping patches. We implement a node network in Kubernetes using Docker containers to facilitate Cloud K-SVD. Results show that Cloud K-SVD can recover images approximately and remove quantifiable amounts of noise from benchmark gray-scaled images without sacrificing accuracy in recovery; we achieve an…
College of Electronic and Optical Engineering & College of Microelectronics, Nanjing University of Posts and Telecommunications（南京邮电大学电子与光学工程学院、微电子学院）；College of Telecommunications & Information Engineering, Nanjing University of Posts and Telecommunications（南京邮电大学通信与信息工程学院）
Recently, low-rank matrix recovery theory has been emerging as a significant progress for various image processing problems. Meanwhile, the group sparse coding (GSC) theory has led to great successes in image restoration (IR) problem with each group contains low-rank property. In this paper, we propose a novel low-rank minimization based denoising model for IR tasks under the perspective of GSC, an important connection between our denoising model and rank minimization problem has been put forward. To overcome the bias problem caused by convex nuclear norm minimization (NNM) for rank approximat…
Quantum Image Denoising: A Framework via Boltzmann Machines, QUBO, and Quantum Annealing
Johns Hopkins University（约翰斯·霍普金斯大学）；NASA Ames Research Center（美国国家航空航天局艾姆斯研究中心）；Research Institute of Advanced Computer Science, USRA（大学空间研究协会高级计算机科学研究所）；NEC Corporation（日本电气股份有限公司）；National Institute of Advanced Industrial Science and Technology (AIST)（日本产业技术综合研究所）
University of Electronic Science and Technology of China（电子科技大学）；Shanghai Jiao Tong University（上海交通大学）
Hyperspectral image (HSI) has some advantages over natural image for various applications due to the extra spectral information. During the acquisition, it is often contaminated by severe noises including Gaussian noise, impulse noise, deadlines, and stripes. The image quality degeneration would badly effect some applications. In this paper, we present a HSI restoration method named smooth and robust low rank tensor recovery. Specifically, we propose a structural tensor decomposition in accordance with the linear spectral mixture model of HSI. It decomposes a tensor into sums of outer matrix v…
