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 Correlation (FRC) is often used, but is little known outside of these fields. Here we show that the FRC can equally well be applied to natural images, e.g. the Google Open Images dataset. We then define a loss function based on the FRC, show that it is analytically differentiable, and use it to train a U-net for denoising of images. This FRC-based loss function allows the network to train faster and achieve similar or better results than when using L1- or L2- based losses. We also investigate the properties and limitations of neural network denoising with the FRC analysis.
University of Goettingen（哥廷根大学）；Statistical and Applied Mathematical Science Institute（统计与应用数学科学研究所）
We consider the very challenging task of restoring images (i) which have a large number of missing pixels, (ii) whose existing pixels are corrupted by noise and (iii) the ideal image to be restored contains both cartoon and texture elements. The combination of these three properties makes this inverse problem a very difficult one. The solution proposed in this manuscript is based on directional global three-part decomposition (DG3PD) [ThaiGottschlich2016] with directional total variation norm, directional G-norm and $\ell_\infty$-norm in curvelet domain as key ingredients of the model. Image d…
The recently developed transformer networks have achieved impressive performance in image denoising by exploiting the self-attention (SA) in images. However, the existing methods mostly use a relatively small window to compute SA due to the quadratic complexity of it, which limits the model's ability to model long-term image information. In this paper, we propose the spatial-frequency attention network (SFANet) to enhance the network's ability in exploiting long-range dependency. For spatial attention module (SAM), we adopt dilated SA to model long-range dependency. In the frequency attention …
Northeastern University at Qinhuangdao（东北大学秦皇岛分校）；Univ Bretagne-Sud（南布列塔尼大学）；Northeastern University（东北大学）；Tianjin University（天津大学）
Following the pioneering works of Rudin, Osher and Fatemi on total variation (TV) and of Buades, Coll and Morel on non-local means (NL-means), the last decade has seen a large number of denoising methods mixing these two approaches, starting with the nonlocal total variation (NLTV) model. The present article proposes an analysis of the NLTV model for image denoising as well as a number of improvements, the most important of which being to apply the denoising both in the space domain and in the Fourier domain, in order to exploit the complementarity of the representation of image data in both d…
Nonlocal image representation has been successfully used in many image-related inverse problems including denoising, deblurring and deblocking. However, a majority of reconstruction methods only exploit the nonlocal self-similarity (NSS) prior of the degraded observation image, it is very challenging to reconstruct the latent clean image. In this paper we propose a novel model for image denoising via group sparsity residual and external NSS prior. To boost the performance of image denoising, the concept of group sparsity residual is proposed, and thus the problem of image denoising is transfor…
Hyperspectral images (HSIs) usually suffer from different types of pollution. This severely reduces the quality of HSIs and limits the accuracy of subsequent processing tasks. HSI denoising can be modeled as a low-rank tensor denoising problem. Tensor nuclear norm (TNN) induced by tensor singular value decomposition plays an important role in this problem. In this letter, we first reconsider three inconspicuous but crucial phenomenons in TNN. In the Fourier transform domain of HSIs, different frequency slices (FS) contain different information; different singular values (SVs) of each FS also r…
Princeton University（普林斯顿大学）；University of Central Florida（中佛罗里达大学）
The problem of image restoration in cryo-EM entails correcting for the effects of the Contrast Transfer Function (CTF) and noise. Popular methods for image restoration include `phase flipping', which corrects only for the Fourier phases but not amplitudes, and Wiener filtering, which requires the spectral signal to noise ratio. We propose a new image restoration method which we call `Covariance Wiener Filtering' (CWF). In CWF, the covariance matrix of the projection images is used within the classical Wiener filtering framework for solving the image restoration deconvolution problem. Our estim…
Ministry of Industry and Information Technology Key Lab of Micro-Nano Optoelectronic Information System（工业和信息化部微纳光电信息系统重点实验室）；Guangdong Provincial Key Laboratory of Semiconductor Optoelectronic Materials and Intelligent Photonic System（广东省半导体光电材料与智能光子系统重点实验室）；Harbin Institute of Technology（哈尔滨工业大学）；School of Electronics and Information Engineering（电子与信息工程学院）；Zhejiang Provincial Key Laboratory of Intelligent Vehicle Electronics Research（浙江省智能车辆电子研究所）；Hangzhou Dianzi University（杭州电子科技大学）；School of Science and Engineering（科学与工程学院）；The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）；Key Laboratory of Photonic Technology for Integrated Sensing and Communication, Ministry of Education（教育部光电一体化感知与通信技术重点实验室）；Guangdong University of Technology（广东工业大学）
Recovering a signal from its Fourier intensity underlies many important applications, including lensless imaging and imaging through scattering media. Conventional algorithms for retrieving the phase suffer when noise is present but display global convergence when given clean data. Neural networks have been used to improve algorithm robustness, but efforts to date are sensitive to initial conditions and give inconsistent performance. Here, we combine iterative methods from phase retrieval with image statistics from deep denoisers, via regularization-by-denoising. The resulting methods inherit …
Decomposing an image through Fourier, DCT or wavelet transforms is still a common approach in digital image processing, in number of applications such as denoising. In this context, data-driven dictionaries and in particular exploiting the redundancy withing patches extracted from one or several images allowed important improvements. This paper proposes an original idea of constructing such an image-dependent basis inspired by the principles of quantum many-body physics. The similarity between two image patches is introduced in the formalism through a term akin to interaction terms in quantum …
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…
imec（比利时微电子研究中心）；Ghent University（根特大学）；Harbin Institute of Technology (Shenzhen)（哈尔滨工业大学（深圳））
Spatial-Spectral Total Variation (SSTV) can quantify local smoothness of image structures, so it is widely used in hyperspectral image (HSI) processing tasks. Essentially, SSTV assumes a sparse structure of gradient maps calculated along the spatial and spectral directions. In fact, these gradient tensors are not only sparse, but also (approximately) low-rank under FFT, which we have verified by numerical tests and theoretical analysis. Based on this fact, we propose a novel TV regularization to simultaneously characterize the sparsity and low-rank priors of the gradient map (LRSTV). The new r…
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…
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 …
