We present a novel algorithm for blind denoising of images corrupted by mixed impulse, Poisson, and Gaussian noises. The algorithm starts by applying the Anscombe variance-stabilizing transformation to convert the Poisson into white Gaussian noise. Then it applies a combinatorial optimization technique to denoise the mixed impulse Gaussian noise using proximal algorithms. The result is then processed by the inverse Anscombe transform. We compare our algorithm to state of the art methods on standard images, and show its superior performance in various noise conditions.
Technical University of Munich（慕尼黑工业大学）；University of Siegen（锡根大学）
While variational methods have been among the most powerful tools for solving linear inverse problems in imaging, deep (convolutional) neural networks have recently taken the lead in many challenging benchmarks. A remaining drawback of deep learning approaches is their requirement for an expensive retraining whenever the specific problem, the noise level, noise type, or desired measure of fidelity changes. On the contrary, variational methods have a plug-and-play nature as they usually consist of separate data fidelity and regularization terms. In this paper we study the possibility of replaci…
University of Massachusetts Medical School（马萨诸塞大学医学院）；The University of Akron（阿克伦大学）
Noise is a major issue while transferring images through all kinds of electronic communication. One of the most common noise in electronic communication is an impulse noise which is caused by unstable voltage. In this paper, the comparison of known image denoising techniques is discussed and a new technique using the decision based approach has been used for the removal of impulse noise. All these methods can primarily preserve image details while suppressing impulsive noise. The principle of these techniques is at first introduced and then analysed with various simulation results using MATLAB…
PPORLD-EDNetLDCT: A Proximal Policy Optimization-Based Reinforcement Learning Framework for Adaptive Low-Dose CT Denoising
Department of Computer Science and Engineering, United International University, Dhaka 1212, Bangladesh（United International University）；Faculty of Science and Technology, Charles Darwin University, Casuarina, NT 0909, Australia（Charles Darwin University）；Faculty of Science and Information Technology, Charles Darwin University, Sydney, NSW, Australia（Charles Darwin University）
This paper evaluates four algorithms for denoising raw Electrooculography (EOG) data based on the Signal to Noise Ratio (SNR). The SNR is computed using the eigenvalue method. The filtering algorithms are a) Finite Impulse Response (FIR) bandpass filters, b) Stationary Wavelet Transform, c) Empirical Mode Decomposition (EMD) d) FIR Median Hybrid Filters. An EOG dataset has been prepared where the subject is asked to perform letter cancelation test on 20 subjects.
The motivation of this paper is to introduce a novel framework for the restoration of images corrupted by mixed Gaussian-impulse noise. To this aim, first, an adaptive curvelet thresholding criterion is proposed which tries to adaptively remove the perturbations appeared during denoising process. Then, a new statistical regularization term, called joint adaptive statistical prior (JASP), is established which enforces both the local and nonlocal statistical consistencies, simultaneously, in a unified manner. Furthermore, a novel technique for mixed Gaussian plus impulse noise removal using JASP…
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…
University of Freiburg（弗莱堡大学）；BIOSS Centre for Biological Signalling Studies（BIOSS生物信号研究中心）；Graz University of Technology（格拉茨工业大学）
In this paper we study an algorithm for solving a minimization problem composed of a differentiable (possibly non-convex) and a convex (possibly non-differentiable) function. The algorithm iPiano combines forward-backward splitting with an inertial force. It can be seen as a non-smooth split version of the Heavy-ball method from Polyak. A rigorous analysis of the algorithm for the proposed class of problems yields global convergence of the function values and the arguments. This makes the algorithm robust for usage on non-convex problems. The convergence result is obtained based on the \KL ine…
Beijing Institute of Technology（北京理工大学）；University of Cambridge（剑桥大学）；Shanghai Jiao Tong University（上海交通大学）；Beijing Normal University（北京师范大学）
Plug-and-Play (PnP) is a non-convex optimization framework that combines proximal algorithms, for example, the alternating direction method of multipliers (ADMM), with advanced denoising priors. Over the past few years, great empirical success has been obtained by PnP algorithms, especially for the ones that integrate deep learning-based denoisers. However, a key challenge of PnP approaches is the need for manual parameter tweaking as it is essential to obtain high-quality results across the high discrepancy in imaging conditions and varying scene content. In this work, we present a class of t…
We consider the problem of estimating a vector from its noisy measurements using a prior specified only through a denoising function. Recent work on plug-and-play priors (PnP) and regularization-by-denoising (RED) has shown the state-of-the-art performance of estimators under such priors in a range of imaging tasks. In this work, we develop a new block coordinate RED algorithm that decomposes a large-scale estimation problem into a sequence of updates over a small subset of the unknown variables. We theoretically analyze the convergence of the algorithm and discuss its relationship to the trad…
This paper deals with impulse noise removal from color images. The proposed noise removal algorithm employs a novel approach with morphological filtering for color image denoising; that is, detection of corrupted pixels and removal of the detected noise by means of morphological filtering. With the help of computer simulation we show that the proposed algorithm can effectively remove impulse noise. The performance of the proposed algorithm is compared in terms of image restoration metrics and processing speed with that of common successful algorithms.
University of Athens（雅典大学）；University of Peloponnese（伯罗奔尼撒大学）
The goal of this paper is the development of a novel approach for the problem of Noise Removal, based on the theory of Reproducing Kernels Hilbert Spaces (RKHS). The problem is cast as an optimization task in a RKHS, by taking advantage of the celebrated semiparametric Representer Theorem. Examples verify that in the presence of gaussian noise the proposed method performs relatively well compared to wavelet based technics and outperforms them significantly in the presence of impulse or mixed noise. A more detailed version of this work has been published in the IEEE Trans. Im. Proc. : P. Boubou…
Image restoration problems are typically ill-posed requiring the design of suitable priors. These priors are typically hand-designed and are fully instantiated throughout the process. In this paper, we introduce a novel framework for handling inverse problems related to image restoration based on elements from the half quadratic splitting method and proximal operators. Modeling the proximal operator as a convolutional network, we defined an implicit prior on the image space as a function class during training. This is in contrast to the common practice in literature of having the prior to be f…
This paper considers the constrained total variation (TV) denoising problem for complex-valued images. We extend the definition of TV seminorms for real-valued images to dealing with complex-valued ones. In particular, we introduce two types of complex TV in both isotropic and anisotropic forms. To solve the constrained denoising problem, we adopt a dual approach and derive an accelerated gradient projection algorithm. We further generalize the proposed denoising algorithm as a key building block of the proximal gradient scheme to solve a vast class of complex constrained optimization problems…
We describe a novel method for training high-quality image denoising models based on unorganized collections of corrupted images. The training does not need access to clean reference images, or explicit pairs of corrupted images, and can thus be applied in situations where such data is unacceptably expensive or impossible to acquire. We build on a recent technique that removes the need for reference data by employing networks with a "blind spot" in the receptive field, and significantly improve two key aspects: image quality and training efficiency. Our result quality is on par with state-of-t…
Helmholtz Center Munich（慕尼黑亥姆霍兹中心）；Technische Universität München（慕尼黑工业大学）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
We consider total variation minimization for manifold valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with $\ell^p$-type data terms in the manifold case. These algorithms are based on iterative geodesic averaging which makes them easily applicable to a large class of data manifolds. As an application, we consider denoising images which take their values in a manifold. We apply our algorithms to diffusion tensor images, interferometric SAR images as well as sphere and cylinder valued images. For the class of Cartan-Had…
Beijing Institute of Technology（北京理工大学）；University of Cambridge（剑桥大学）
Plug-and-play (PnP) is a non-convex framework that combines ADMM or other proximal algorithms with advanced denoiser priors. Recently, PnP has achieved great empirical success, especially with the integration of deep learning-based denoisers. However, a key problem of PnP based approaches is that they require manual parameter tweaking. It is necessary to obtain high-quality results across the high discrepancy in terms of imaging conditions and varying scene content. In this work, we present a tuning-free PnP proximal algorithm, which can automatically determine the internal parameters includin…
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…
The Ohio State University（俄亥俄州立大学）；The University of Maryland（马里兰大学）
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 …
Tensor completion is a technique of filling missing elements of the incomplete data tensors. It being actively studied based on the convex optimization scheme such as nuclear-norm minimization. When given data tensors include some noises, the nuclear-norm minimization problem is usually converted to the nuclear-norm `regularization' problem which simultaneously minimize penalty and error terms with some trade-off parameter. However, the good value of trade-off is not easily determined because of the difference of two units and the data dependence. In the sense of trade-off tuning, the noisy te…
Deep Equilibrium Convolutional Sparse Coding for Hyperspectral Image Denoising
School of Computer Science and Engineering, Nanjing University of Science and Technology（南京理工大学计算机科学与工程学院）；College of Computer Science, Zhejiang University（浙江大学计算机科学学院）
Nanjing Forestry University（南京林业大学）；University of Michigan（密歇根大学）；FXPAL inc.（FX帕洛阿尔托实验室公司）；Zhejiang A&F University（浙江农林大学）；University of Calgary（卡尔加里大学）；Chinese Academy of Sciences（中国科学院）；University of Chinese Academy of Sciences（中国科学院大学）；FX Palo Alto Laboratory Inc.（FX帕洛阿尔托实验室公司）
Sliding-window based low-rank matrix approximation (LRMA) is a technique widely used in hyperspectral images (HSIs) denoising or completion. However, the uncertainty quantification of the restored HSI has not been addressed to date. Accurate uncertainty quantification of the denoised HSI facilitates to applications such as multi-source or multi-scale data fusion, data assimilation, and product uncertainty quantification, since these applications require an accurate approach to describe the statistical distributions of the input data. Therefore, we propose a prior-free closed-form element-wise …
Wangxuan Institute of Computer Technology, Peking University（北京大学王选计算机研究所）；York University（约克大学）
Identifying an appropriate underlying graph kernel that reflects pairwise similarities is critical in many recent graph spectral signal restoration schemes, including image denoising, dequantization, and contrast enhancement. Existing graph learning algorithms compute the most likely entries of a properly defined graph Laplacian matrix $\mathbf{L}$, but require a large number of signal observations $\mathbf{z}$'s for a stable estimate. In this work, we assume instead the availability of a relevant feature vector $\mathbf{f}_i$ per node $i$, from which we compute an optimal feature graph via op…
Commonwealth Scientific and Industrial Research Organisation（澳大利亚联邦科学与工业研究组织）
Natural images tend to mostly consist of smooth regions with individual pixels having highly correlated spectra. This information can be exploited to recover hyperspectral images of natural scenes from their incomplete and noisy measurements. To perform the recovery while taking full advantage of the prior knowledge, we formulate a composite cost function containing a square-error data-fitting term and two distinct regularization terms pertaining to spatial and spectral domains. The regularization for the spatial domain is the sum of total-variation of the image frames corresponding to all spe…
A Convex Functional for Image Denoising based on Patches with Constrained Overlaps and its vectorial application to Low Dose Differential Phase Tomography
the Ludwig Maximilians University, Physics Departement, 85748 Garching, Germany（慕尼黑大学物理系）；Ludwig Maximilians University, Departement of Clinical Radiology,80336 Munich, Germany（慕尼黑大学临床放射学系）
Denoising images contaminated by the mixture of additive white Gaussian noise (AWGN) and impulse noise (IN) is an essential but challenging problem. The presence of impulsive disturbances inevitably affects the distribution of noises and thus largely degrades the performance of traditional AWGN denoisers. Existing methods target to compensate the effects of IN by introducing a weighting matrix, which, however, is lack of proper priori and thus hard to be accurately estimated. To address this problem, we exploit the Pareto distribution as the priori of the weighting matrix, based on which an ac…
Deep LoRA-Unfolding Networks for Image Restoration
School of Computer Science and Technology, Harbin Institute of Technology (Shenzhen)（计算机科学与技术学院，哈尔滨工业大学（深圳））；Institute of Image Communication and Network Engineering, Shanghai Jiao Tong University（图像通信与网络工程院，上海交通大学）；School of Intelligence Science and Technology, Nanjing University（智能科学与技术学院，南京大学）；School of Electronics and Information Engineering, Harbin Institute of Technology (Shenzhen)（电子与信息工程学院，哈尔滨工业大学（深圳））
Noise reduction is one the most important and still active research topic in low-level image processing due to its high impact on object detection and scene understanding for computer vision systems. Recently, we can observe a substantial increase of interest in the application of deep learning algorithms in many computer vision problems due to its impressive capability of automatic feature extraction and classification. These methods have been also successfully applied in image denoising, significantly improving the performance, but most of the proposed approaches were designed for Gaussian n…
Yonsei University（延世大学）；Chungnam National University（忠南国立大学）
Regularization-based image restoration has remained an active research topic in computer vision and image processing. It often leverages a guidance signal captured in different fields as an additional cue. In this work, we present a general framework for image restoration, called deeply aggregated alternating minimization (DeepAM). We propose to train deep neural network to advance two of the steps in the conventional AM algorithm: proximal mapping and ?- continuation. Both steps are learned from a large dataset in an end-to-end manner. The proposed framework enables the convolutional neural n…
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…
Learning Cocoercive Conservative Denoisers via Helmholtz Decomposition for Poisson Inverse Problems
School of Mathematical Sciences, East China Normal University（东华大学数学系）；School of Mathematical Sciences, Key Laboratory of MEA (Ministry of Education), Shanghai Key Laboratory of PMMP, East China Normal University（东华大学数学系）；Institute for Advanced Study, Beijing Normal-Hong Kong Baptist University（北京师范大学-香港 Baptist大学高级研究院）；School of Mathematics and Statistics, Guangzhou Nanfang College（广州南方学院数学系）
UIUC（伊利诺伊大学厄巴纳-香槟分校）；University of Oxford（牛津大学）；Megvii Research（旷视研究院）；Stony Brook（石溪大学）
Discriminative learning-based image denoisers have achieved promising performance on synthetic noises such as Additive White Gaussian Noise (AWGN). The synthetic noises adopted in most previous work are pixel-independent, but real noises are mostly spatially/channel-correlated and spatially/channel-variant. This domain gap yields unsatisfied performance on images with real noises if the model is only trained with AWGN. In this paper, we propose a novel approach to boost the performance of a real image denoiser which is trained only with synthetic pixel-independent noise data dominated by AWGN.…
The University of Hong Kong（香港大学）；Shenzhen Institute of Research and Innovation, The University of Hong Kong（香港大学深圳研究院）
Hyperspectral imaging with high spectral resolution plays an important role in finding objects, identifying materials, or detecting processes. The decrease of the widths of spectral bands leads to a decrease in the signal-to-noise ratio (SNR) of measurements. The decreased SNR reduces the reliability of measured features or information extracted from HSIs. Furthermore, the image degradations linked with various mechanisms also result in different types of noise, such as Gaussian noise, impulse noise, deadlines, and stripes. This paper introduces a fast and parameter-free hyperspectral image mi…
