Experimentally acquired microscopy images are unavoidably affected by the presence of noise and other unwanted signals, which degrade their quality and might hide relevant features. With the recent increase in image acquisition rate, modern denoising and restoration solutions become necessary. This study focuses on image decomposition and denoising of microscopy images through a workflow based on total variation (TV), addressing images obtained from various microscopy techniques, including atomic force microscopy (AFM), scanning tunneling microscopy (STM), and scanning electron microscopy (SEM). Our approach consists in restoring an image by extracting its unwanted signal components and subtracting them from the raw one, or by denoising it. We evaluate the performance of TV-$L^1$, Huber-ROF, and TGV-$L^1$ in achieving this goal in distinct study cases. Huber-ROF proved to be the most flexible one, while TGV-$L^1$ is the most suitable for denoising. Our results suggest a wider applicability of this method in microscopy, restricted not only to STM, AFM, and SEM images. The Python code used for this study is publicly available as part of AiSurf. It is designed to be integrated into experimental workflows for image acquisition or can be used to denoise previously acquired images.
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…
Fluorescence microscopy has enabled a dramatic development in modern biology. Due to its inherently weak signal, fluorescence microscopy is not only much noisier than photography, but also presented with Poisson-Gaussian noise where Poisson noise, or shot noise, is the dominating noise source. To get clean fluorescence microscopy images, it is highly desirable to have effective denoising algorithms and datasets that are specifically designed to denoise fluorescence microscopy images. While such algorithms exist, no such datasets are available. In this paper, we fill this gap by constructing a …
Max-Planck Institute of Molecular Cell Biology and Genetics（马克斯·普朗克分子细胞生物学与遗传学研究所）；Center for Systems Biology Dresden (CSBD)（德累斯顿系统生物学中心）；Fondazione Human Technopole（人类技术城基金会）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）
Many microscopy applications are limited by the total amount of usable light and are consequently challenged by the resulting levels of noise in the acquired images. This problem is often addressed via (supervised) deep learning based denoising. Recently, by making assumptions about the noise statistics, self-supervised methods have emerged. Such methods are trained directly on the images that are to be denoised and do not require additional paired training data. While achieving remarkable results, self-supervised methods can produce high-frequency artifacts and achieve inferior results compar…
In computer-aided diagnosis (CAD) focused on microscopy, denoising improves the quality of image analysis. In general, the accuracy of this process may depend both on the experience of the microscopist and on the equipment sensitivity and specificity. A medical image could be corrupted by both intrinsic noise, due to the device limitations, and, by extrinsic signal perturbations during image acquisition. Nowadays, CAD deep learning applications pre-process images with image denoising models to reinforce learning and prediction. In this work, an innovative and lightweight deep multiscale convol…
A Zero-Shot Deep Image Prior Framework for Denoising and Deconvolution in Fluorescence Microscopy
Wenzhou Key Laboratory of Biomedical Imaging（温州生物医学成像重点实验室）；Zhejiang Key Laboratory of Soft Matter Biomedical Materials（浙江软物质生物医学材料重点实验室）；Wenzhou Institute, University of Chinese Academy of Sciences（中国科学院大学温州研究院）；Postgraduate Training Base Alliance of Wenzhou Medical University（温州医学院研究生联合培养基地联盟）
AICES Graduate School, RWTH Aachen University（亚琛工业大学 AICES 研究生院）；University of Münster（明斯特大学）
Nowadays, modern electron microscopes deliver images at atomic scale. The precise atomic structure encodes information about material properties. Thus, an important ingredient in the image analysis is to locate the centers of the atoms shown in micrographs as precisely as possible. Here, we consider scanning transmission electron microscopy (STEM), which acquires data in a rastering pattern, pixel by pixel. Due to this rastering combined with the magnification to atomic scale, movements of the specimen even at the nanometer scale lead to random image distortions that make precise atom localiza…
Automating Parameter Selection in Deep Image Prior for Fluorescence Microscopy Image Denoising via Similarity-Based Parameter Transfer
Institute for Applied Medical Informatics, Institute of Computational Neuroscience, Center for Biomedical Artificial Intelligence (bAIome), University Medical Center Hamburg-Eppendorf, Germany（应用医学信息学研究所、计算神经科学研究所、生物医学人工智能中心（bAIome）、汉堡-埃彭多夫大学医学中心，德国）；Institute for Biomedical Imaging, Hamburg University of Technology, Hamburg, Germany（生物医学成像研究所、汉堡技术大学、汉堡，德国）；Department of Biomedical Imaging, University Medical Center Hamburg-Eppendorf, Germany（生物医学成像系、汉堡-埃彭多夫大学医学中心，德国）；Fraunhofer Research Institution for Individualized Medical Technology（弗劳恩霍夫个性化医疗技术研究机构）；Institute of Medical Microbiology, Virology and Hygiene, University Medical Center Hamburg-Eppendorf, Germany（医学微生物学研究所、病毒学与卫生学、汉堡-埃彭多夫大学医学中心，德国）；Institute of Biochemistry and Molecular Cell Biology, University Medical Center Hamburg-Eppendorf, Germany（生物化学与分子细胞生物学研究所、汉堡-埃彭多夫大学医学中心，德国）
Recently, much progress has been made in unsupervised denoising learning. However, existing methods more or less rely on some assumptions on the signal and/or degradation model, which limits their practical performance. How to construct an optimal criterion for unsupervised denoising learning without any prior knowledge on the degradation model is still an open question. Toward answering this question, this work proposes a criterion for unsupervised denoising learning based on the optimal transport theory. This criterion has favorable properties, e.g., approximately maximal preservation of the…
University of California San Diego（加州大学圣迭戈分校）；National Taiwan University（台湾大学）；University of Macau（澳门大学）；National Taiwan University Hospital and College of Medicine（台湾大学医学院附设医院暨医学院）
As the rapid growth of high-speed and deep-tissue imaging in biomedical research, it is urgent to find a robust and effective denoising method to retain morphological features for further texture analysis and segmentation. Conventional denoising filters and models can easily suppress perturbative noises in high contrast images. However, for low photon budget multi-photon images, high detector gain will not only boost signals, but also bring huge background noises. In such stochastic resonance regime of imaging, sub-threshold signals may be detectable with the help of noises. Therefore, a denoi…
Decomposition-Guided Curvelet Thresholding for Sharp-to-Soft CT Kernel Conversion
AGH University of Krakow（克拉科夫AGH科技大学）；Sano Centre for Computational Medicine（萨诺计算医学中心）；Jagiellonian University（雅盖隆大学）；Wroclaw University of Science and Technology（弗罗茨瓦夫理工大学）
The Technion - Israel Institute of Technology（以色列理工学院）
The problem of Poisson denoising appears in various imaging applications, such as low-light photography, medical imaging and microscopy. In cases of high SNR, several transformations exist so as to convert the Poisson noise into an additive i.i.d. Gaussian noise, for which many effective algorithms are available. However, in a low SNR regime, these transformations are significantly less accurate, and a strategy that relies directly on the true noise statistics is required. A recent work by Salmon et al. took this route, proposing a patch-based exponential image representation model based on GM…
Self2Seg: Single-Image Self-Supervised Joint Segmentation and Denoising
University of Innsbruck（因斯布鲁克大学）；VASCage-Research Centre on Vascular Ageing and Stroke（VASCage血管衰老与中风研究中心）；MRC Laboratory of Molecular Biology（医学研究委员会分子生物学实验室）；Institut Pascal（帕斯卡尔研究所）；Université Clermont Auvergne（克莱蒙奥弗涅大学）；Institut de Mathématiques de Bordeaux（波尔多数学研究所）
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Cryo-electron microscopy (EM) single particle reconstruction is an entirely general technique for 3D structure determination of macromolecular complexes. However, because the images are taken at low electron dose, it is extremely hard to visualize the individual particle with low contrast and high noise level. In this paper, we propose a novel approach called multi-frequency vector diffusion maps (MFVDM) to improve the efficiency and accuracy of cryo-EM 2D image classification and denoising. This framework incorporates different irreducible representations of the estimated alignment between si…
Center for Systems Biology（系统生物学中心）；Max Planck Institute of Molecular Cell Biology and Genetics（马克斯·普朗克分子细胞生物学与遗传学研究所）；Max Planck Institute for Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）
Microscopy image analysis often requires the segmentation of objects, but training data for this task is typically scarce and hard to obtain. Here we propose DenoiSeg, a new method that can be trained end-to-end on only a few annotated ground truth segmentations. We achieve this by extending Noise2Void, a self-supervised denoising scheme that can be trained on noisy images alone, to also predict dense 3-class segmentations. The reason for the success of our method is that segmentation can profit from denoising, especially when performed jointly within the same network. The network becomes a de…
Center for Systems Biology Dresden（德累斯顿系统生物学中心）；Max-Planck Institute (CBG)（马克斯·普朗克分子细胞生物学与遗传学研究所）；School of Computer Science（计算机科学学院）；University of Birmingham（伯明翰大学）；Fondazione Human Technopole（人类技术基金会）
Deep Learning based methods have emerged as the indisputable leaders for virtually all image restoration tasks. Especially in the domain of microscopy images, various content-aware image restoration (CARE) approaches are now used to improve the interpretability of acquired data. Naturally, there are limitations to what can be restored in corrupted images, and like for all inverse problems, many potential solutions exist, and one of them must be chosen. Here, we propose DivNoising, a denoising approach based on fully convolutional variational autoencoders (VAEs), overcoming the problem of havin…
In fluorescence microscopy live-cell imaging, there is a critical trade-off between the signal-to-noise ratio and spatial resolution on one side, and the integrity of the biological sample on the other side. To obtain clean high-resolution (HR) images, one can either use microscopy techniques, such as structured-illumination microscopy (SIM), or apply denoising and super-resolution (SR) algorithms. However, the former option requires multiple shots that can damage the samples, and although efficient deep learning based algorithms exist for the latter option, no benchmark exists to evaluate the…
In this paper, we propose a new model to segment cells in phase contrast microscopy images. Cell images collected from the similar scenario share a similar background. Inspired by this, we separate cells from the background in images by formulating the problem as a low-rank and structured sparse matrix decomposition problem. Then, we propose the inverse diffraction pattern filtering method to further segment individual cells in the images. This is a deconvolution process that has a much lower computational complexity when compared to the other restoration methods. Experiments demonstrate the e…
Universidad Politécnica de Madrid（马德里理工大学）；Centre national de la recherche scientifique (CNRS)（法国国家科学研究中心）；Interdisciplinary Institute for Neuroscience (IINS)（跨学科神经科学研究所）；University of Bordeaux（波尔多大学）；Mechanobiology Institute（机械生物学研究所）；National University of Singapore（新加坡国立大学）
Microscopy images often suffer from high levels of noise, which can hinder further analysis and interpretation. Content-aware image restoration (CARE) methods have been proposed to address this issue, but they often require large amounts of training data and suffer from over-fitting. To overcome these challenges, we propose a novel framework for few-shot microscopy image denoising. Our approach combines a generative adversarial network (GAN) trained via contrastive learning (CL) with two structure preserving loss terms (Structural Similarity Index and Total Variation loss) to further improve t…
Indian Institute of Technology Guwahati（印度理工学院古瓦哈蒂分校）；UiT The Arctic University of Norway（挪威特罗姆瑟大学（UiT 挪威北极大学））；Indian Institute of Technology Dhanbad（印度理工学院丹巴德分校）
Scanning acoustic microscopy (SAM) has been employed since microscopic images are widely used for biomedical or materials research. Acoustic imaging is an important and well-established method used in nondestructive testing (NDT), bio-medical imaging, and structural health monitoring.The imaging is frequently carried out with signals of low amplitude, which might result in leading that are noisy and lacking in details of image information. In this work, we attempted to analyze SAM images acquired from low amplitude signals and employed a block matching filter over time domain signals to obtain…
Zero-Shot Image Denoising for High-Resolution Electron Microscopy
School of Information Science and Technology, ShanghaiTech University（上海科技大学信息科学与技术学院）；Lingang Laboratory（临港实验室）；School of Physical Science and Technology, ShanghaiTech University（上海科技大学物理科学与技术学院）；School of Software, Tsinghua University（清华大学软件学院）；School of Biomedical Engineering and Institute of Medical Robotics, Shanghai Jiao Tong University（上海交通大学生物医学工程学院与医学机器人研究所）
University of Notre Dame（圣母大学）；California Institute of Technology（加州理工学院）；Indiana University（印第安纳大学）
Fluorescence lifetime imaging microscopy (FLIM) systems are limited by their slow processing speed, low signal-to-noise ratio (SNR), and expensive and challenging hardware setups. In this work, we demonstrate applying a denoising convolutional network to improve FLIM SNR. The network will be integrated with an instant FLIM system with fast data acquisition based on analog signal processing, high SNR using high-efficiency pulse-modulation, and cost-effective implementation utilizing off-the-shelf radio-frequency components. Our instant FLIM system simultaneously provides the intensity, lifetime…
Denoising diffusion models for high-resolution microscopy image restoration
Frankfurt Institute for Advanced Studies (FIAS)（法兰克福高级研究所）；Goethe University Frankfurt（法兰克福大学）；Institute of Physical and Theoretical Chemistry（物理与理论化学研究所）
Fluorescence microscopy is a key driver to promote discoveries of biomedical research. However, with the limitation of microscope hardware and characteristics of the observed samples, the fluorescence microscopy images are susceptible to noise. Recently, a few self-supervised deep learning (DL) denoising methods have been proposed. However, the training efficiency and denoising performance of existing methods are relatively low in real scene noise removal. To address this issue, this paper proposed self-supervised image denoising method Noise2SR (N2SR) to train a simple and effective image den…
We leverage deep learning techniques to jointly denoise and super-resolve biomedical images acquired with fluorescence microscopy. We develop a deep learning algorithm based on the networks and method described in the recent W2S paper to solve a joint denoising and super-resolution problem. Specifically, we address the restoration of SIM images from widefield images. Our TensorFlow model is trained on the W2S dataset of cell images and is made accessible online in this repository: https://github.com/mchatton/w2s-tensorflow. On test images, the model shows a visually-convincing denoising and in…
Photoacoustic imaging is a new imaging technology in recent years, which combines the advantages of high resolution and rich contrast of optical imaging with the advantages of high penetration depth of acoustic imaging. Photoacoustic imaging has been widely used in biomedical fields, such as brain imaging, tumor detection and so on. The signal-to-noise ratio (SNR) of image signals in photoacoustic imaging is generally low due to the limitation of laser pulse energy, electromagnetic interference in the external environment and system noise. In order to solve the problem of low SNR of photoacous…
Indian Institute of Technology Madras（印度理工学院马德拉斯分校）；Robert Bosch Center for Data Science and AI（罗伯特·博世数据科学与人工智能中心）
Deep convolutional neural networks (CNNs) for video denoising are typically trained with supervision, assuming the availability of clean videos. However, in many applications, such as microscopy, noiseless videos are not available. To address this, we propose an Unsupervised Deep Video Denoiser (UDVD), a CNN architecture designed to be trained exclusively with noisy data. The performance of UDVD is comparable to the supervised state-of-the-art, even when trained only on a single short noisy video. We demonstrate the promise of our approach in real-world imaging applications by denoising raw vi…
Google Research（谷歌研究院）；Fondazione Human Technopole（人类技术城基金会）
Image denoising and artefact removal are complex inverse problems admitting multiple valid solutions. Unsupervised diversity restoration, that is, obtaining a diverse set of possible restorations given a corrupted image, is important for ambiguity removal in many applications such as microscopy where paired data for supervised training are often unobtainable. In real world applications, imaging noise and artefacts are typically hard to model, leading to unsatisfactory performance of existing unsupervised approaches. This work presents an interpretable approach for unsupervised and diverse imag…
Deep Denoising For Scientific Discovery: A Case Study In Electron Microscopy
Center for Data Science, New York University（纽约大学数据科学中心）；School for Engineering of Matter, Transport, and Energy, ASU（亚利桑那州立大学物质、运输与能源工程学院）；Department of Statistics and Data Science, Cornell University（康奈尔大学统计与数据科学系）；Indian Institute of Technology Madras（印度马德拉斯理工学院）；Howard Hughes Medical Institute（霍华德·休斯医学研究所）；Courant Institute of Mathematical Sciences, NYU（纽约大学柯朗数学科学研究所）
Denoising extreme low light images is a challenging task due to the high noise level. When the illumination is low, digital cameras increase the ISO (electronic gain) to amplify the brightness of captured data. However, this in turn amplifies the noise, arising from read, shot, and defective pixel sources. In the raw domain, read and shot noise are effectively modelled using Gaussian and Poisson distributions respectively, whereas defective pixels can be modeled with impulsive noise. In extreme low light imaging, noise removal becomes a critical challenge to produce a high quality, detailed im…
Deep Joint Denoising and Detection for Enhanced Intracellular Particle Analysis
Erasmus University Medical Center（伊拉斯姆斯大学医学中心）；Utrecht University（乌得勒支大学）；University of New South Wales (UNSW)（新南威尔士大学）；NVIDIA Corporation（英伟达公司）；SURFsara
We present a new convolutional neural network (CNN) based ImageJ plugin for fluorescence microscopy image denoising with an average improvement of 7.5 dB in peak signal-to-noise ratio (PSNR) and denoising instantly within 80 msec.
Center for Systems Biology Dresden (CSBD)（德累斯顿系统生物学中心）；Max-Planck Institute of Molecular Cell Biology and Genetics（马克斯·普朗克分子细胞生物学与遗传学研究所）
Deep learning (DL) has arguably emerged as the method of choice for the detection and segmentation of biological structures in microscopy images. However, DL typically needs copious amounts of annotated training data that is for biomedical projects typically not available and excessively expensive to generate. Additionally, tasks become harder in the presence of noise, requiring even more high-quality training data. Hence, we propose to use denoising networks to improve the performance of other DL-based image segmentation methods. More specifically, we present ideas on how state-of-the-art sel…
TOOPLOOX（TOOPLOOX 公司）；Wrocław University of Science and Technology（弗罗茨瓦夫科技大学）
Image quality is a nebulous concept with different meanings to different people. To quantify image quality a relative difference is typically calculated between a corrupted image and a ground truth image. But what metric should we use for measuring this difference? Ideally, the metric should perform well for both natural and scientific images. The structural similarity index (SSIM) is a good measure for how humans perceive image similarities, but is not sensitive to differences that are scientifically meaningful in microscopy. In electron and super-resolution microscopy, the Fourier Ring Corre…
MPI-CBG/PKS (CSBD)（马克斯·普朗克分子细胞生物学与遗传学研究所/普朗克计算生物学中心（德累斯顿系统生物学中心））；Brno University of Technology（布尔诺理工大学）
Today, Convolutional Neural Networks (CNNs) are the leading method for image denoising. They are traditionally trained on pairs of images, which are often hard to obtain for practical applications. This motivates self-supervised training methods such as Noise2Void~(N2V) that operate on single noisy images. Self-supervised methods are, unfortunately, not competitive with models trained on image pairs. Here, we present 'Probabilistic Noise2Void' (PN2V), a method to train CNNs to predict per-pixel intensity distributions. Combining these with a suitable description of the noise, we obtain a compl…
Institute of Computer Science, University of Tartu（塔尔图大学计算机科学研究所）；Wellcome Sanger Institute（惠康桑格研究所）；PerkinElmer Cellular Technologies（珀金埃尔默细胞技术公司）
Biomedical images are noisy. The imaging equipment itself has physical limitations, and the consequent experimental trade-offs between signal-to-noise ratio, acquisition speed, and imaging depth exacerbate the problem. Denoising is, therefore, an essential part of any image processing pipeline, and convolutional neural networks are currently the method of choice for this task. One popular approach, Noise2Noise, does not require clean ground truth, and instead, uses a second noisy copy as a training target. Self-supervised methods, like Noise2Self and Noise2Void, relax data requirements by lear…
Tensor decomposition has proven to be a strong tool in various 3D image processing tasks such as denoising and super-resolution. In this context, we recently proposed a canonical polyadic decomposition (CPD) based algorithm for single image super-resolution (SISR). The algorithm has shown to be an order of magnitude faster than popular optimization-based techniques. In this work, we investigated the added value brought by Tucker decomposition. While CPD allows a joint implementation of the denoising and deconvolution steps of the SISR model, with Tucker decomposition the denoising is realized …
Decomposition of digital signals and images into other basis or dictionaries than time or space domains is a very common approach in signal and image processing and analysis. Such a decomposition is commonly obtained using fixed transforms (e.g., Fourier or wavelet) or dictionaries learned from example databases or from the signal or image itself. In this work, we investigate in detail a new approach of constructing such a signal or image-dependent bases inspired by quantum mechanics tools, i.e., by considering the signal or image as a potential in the discretized Schroedinger equation. To ill…
Photoacoustic (PA) imaging is an emerging hybrid imaging modality that combines rich optical spectroscopic contrast and high ultrasonic resolution and thus holds tremendous promise for a wide range of pre-clinical and clinical applications. Compact and affordable light sources such as light-emitting diodes (LEDs) and laser diodes (LDs) are promising alternatives to bulky and expensive solid-state laser systems that are commonly used as PA light sources. These could accelerate the clinical translation of PA technology. However, PA signals generated with these light sources are readily degraded …
FAU Erlangen-Nürnberg（埃尔朗根-纽伦堡大学）；Siemens Healthcare GmbH（西门子医疗有限公司）；Fraunhofer Institute for Ceramic Technologies and Systems IKTS（弗劳恩霍夫陶瓷技术与系统研究所IKTS）；Ewha Womans University（梨花女子大学）
Self-supervised image denoising techniques emerged as convenient methods that allow training denoising models without requiring ground-truth noise-free data. Existing methods usually optimize loss metrics that are calculated from multiple noisy realizations of similar images, e.g., from neighboring tomographic slices. However, those approaches fail to utilize the multiple contrasts that are routinely acquired in medical imaging modalities like MRI or dual-energy CT. In this work, we propose the new self-supervised training scheme Noise2Contrast that combines information from multiple measured …
Leading denoising methods such as 3D block matching (BM3D) are patch-based. However, they can suffer from frequency domain artefacts and require to specify explicit noise models. We present a patch-based method that avoids these drawbacks. It combines a simple and fast patch reordering with a non-linear smoothing. The smoothing rewards both patch and pixel similarities in a multiplicative way. We perform experiments on real world images with additive white Gaussian noise (AWGN), and on electron microscopy data with a more general additive noise model. Our filter outperforms BM3D in 77% of the …
California Polytechnic State University（加州州立理工大学）；University of Georgia（佐治亚大学）；Providence College（普罗维登斯学院）；University of Colorado Colorado Springs（科罗拉多大学科罗拉多斯普林斯分校）
We extend the blindspot model for self-supervised denoising to handle Poisson-Gaussian noise and introduce an improved training scheme that avoids hyperparameters and adapts the denoiser to the test data. Self-supervised models for denoising learn to denoise from only noisy data and do not require corresponding clean images, which are difficult or impossible to acquire in some application areas of interest such as low-light microscopy. We introduce a new training strategy to handle Poisson-Gaussian noise which is the standard noise model for microscope images. Our new strategy eliminates hyper…
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究所）；University College London（伦敦大学学院）；Q.bio Inc.（Q.bio公司）
Microscopy is a powerful visualization tool in biology, enabling the study of cells, tissues, and the fundamental biological processes; yet, the observed images typically suffer from blur and background noise. In this work, we propose a unifying framework of algorithms for Gaussian image deblurring and denoising. These algorithms are based on deep learning techniques for the design of learnable regularizers integrated into the Wiener-Kolmogorov filter. Our extensive experimentation line showcases that the proposed approach achieves a superior quality of image reconstruction and surpasses the s…
University of Electronic Science and Technology of China（电子科技大学）；Oregon State University（俄勒冈州立大学）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）
Image denoising is often empowered by accurate prior information. In recent years, data-driven neural network priors have shown promising performance for RGB natural image denoising. Compared to classic handcrafted priors (e.g., sparsity and total variation), the "deep priors" are learned using a large number of training samples -- which can accurately model the complex image generating process. However, data-driven priors are hard to acquire for hyperspectral images (HSIs) due to the lack of training data. A remedy is to use the so-called unsupervised deep image prior (DIP). Under the unsuper…
