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While researches on model-based blind single image super-resolution (SISR) have achieved tremendous successes recently, most of them do not consider the image degradation sufficiently. Firstly, they always assume image noise obeys an independent and identically distributed (i.i.d.) Gaussian or Laplacian distribution, which largely underestimates the complexity of real noise. Secondly, previous commonly-used kernel priors (e.g., normalization, sparsity) are not effective enough to guarantee a rational kernel solution, and thus degenerates the performance of subsequent SISR task. To address the above issues, this paper proposes a model-based blind SISR method under the probabilistic framework, which elaborately models image degradation from the perspectives of noise and blur kernel. Specifically, instead of the traditional i.i.d. noise assumption, a patch-based non-i.i.d. noise model is proposed to tackle the complicated real noise, expecting to increase the degrees of freedom of the model for noise representation. As for the blur kernel, we novelly construct a concise yet effective kernel generator, and plug it into the proposed blind SISR method as an explicit kernel prior (EKP). To solve the proposed model, a theoretically grounded Monte Carlo EM algorithm is specifically designed. Comprehensive experiments demonstrate the superiority of our method over current state-of-the-arts on synthetic and real datasets. The source code is available at https://github.com/zsyOAOA/BSRDM., Comment: Accepted by CVPR 2022

Contaminants such as dust, dirt and moisture adhering to the camera lens can greatly affect the quality and clarity of the resulting image or video. In this paper, we propose a video restoration method to automatically remove these contaminants and produce a clean video. Our approach first seeks to detect attention maps that indicate the regions that need to be restored. In order to leverage the corresponding clean pixels from adjacent frames, we propose a flow completion module to hallucinate the flow of the background scene to the attention regions degraded by the contaminants. Guided by the attention maps and completed flows, we propose a recurrent technique to restore the input frame by fetching clean pixels from adjacent frames. Finally, a multi-frame processing stage is used to further process the entire video sequence in order to enforce temporal consistency. The entire network is trained on a synthetic dataset that approximates the physical lighting properties of contaminant artifacts. This new dataset and our novel framework lead to our method that is able to address different contaminants and outperforms competitive restoration approaches both qualitatively and quantitatively., Comment: 10 pages, 11 figures

Low-quality face image restoration is a popular research direction in today's computer vision field. It can be used as a pre-work for tasks such as face detection and face recognition. At present, there is a lot of work to solve the problem of low-quality faces under various environmental conditions. This paper mainly focuses on the restoration of motion-blurred faces. In increasingly abundant mobile scenes, the fast recovery of motion-blurred faces can bring highly effective speed improvements in tasks such as face matching. In order to achieve this goal, a deblurring method for motion-blurred facial image signals based on generative adversarial networks(GANs) is proposed. It uses an end-to-end method to train a sharp image generator, i.e., a processor for motion-blurred facial images. This paper introduce the processing progress of motion-blurred images, the development and changes of GANs and some basic concepts. After that, it give the details of network structure and training optimization design of the image processor. Then we conducted a motion blur image generation experiment on some general facial data set, and used the pairs of blurred and sharp face image data to perform the training and testing experiments of the processor GAN, and gave some visual displays. Finally, MTCNN is used to detect the faces of the image generated by the deblurring processor, and compare it with the result of the blurred image. From the results, the processing effect of the deblurring processor on the motion-blurred picture has a significant improvement both in terms of intuition and evaluation indicators of face detection., Comment: 10 pages, 4 figures, appear in International Conference on Digital Signal Processing (ICDSP) 2021

Blur and noise corrupting Computed Tomography (CT) images can hide or distort small but important details, negatively affecting the diagnosis. In this paper, we present a novel gradient-based Plug-and-Play algorithm, constructed on the Half-Quadratic Splitting scheme, and we apply it to restore CT images. In particular, we consider different schemes encompassing external and internal denoisers as priors, defined on the image gradient domain. The internal prior is based on the Total Variation functional. The external denoiser is implemented by a deep Convolutional Neural Network (CNN) trained on the gradient domain (and not on the image one, as in state-of-the-art works). We also prove a general fixed-point convergence theorem under weak assumptions on both internal and external denoisers. The experiments confirm the effectiveness of the proposed framework in restoring blurred noisy CT images, both in simulated and real medical settings. The achieved enhancements in the restored images are really remarkable, if compared to the results of many state-of-the-art methods., Comment: Submitted to journal

In this paper we provide a generalization of the Douglas-Rachford splitting (DRS) and the primal-dual algorithm (Vu 2013, Condat 2013) for solving monotone inclusions in a real Hilbert space involving a general linear operator. The proposed method allows for primal and dual non-standard metrics and activates the linear operator separately from the monotone operators appearing in the inclusion. In the simplest case when the linear operator has full range, it reduces to classical DRS. Moreover, the weak convergence of primal-dual sequences to a Kuhn-Tucker point is guaranteed, generalizing the main result in Svaiter (2011). Inspired by Gabay (1983), we also derive a new Split-ADMM (SADMM) by applying our method to the dual of a convex optimization problem involving a linear operator which can be expressed as the composition of two linear operators. The proposed SADMM activates one linear operator implicitly and the other one explicitly, and we recover ADMM when the latter is set as the identity. Connections and comparisons of our theoretical results with respect to the literature are provided for the main algorithm and SADMM. The flexibility and efficiency of both methods is illustrated via a numerical simulations in total variation image restoration and a sparse minimization problem., Comment: 26 pages

Images acquired with a telescope are blurred and corrupted by noise. The blurring is usually modeled by a convolution with the Point Spread Function and the noise by Additive Gaussian Noise. Recovering the observed image is an ill-posed inverse problem. Sparse deconvolution is well known to be an efficient deconvolution technique, leading to optimized pixel Mean Square Errors, but without any guarantee that the shapes of objects (e.g. galaxy images) contained in the data will be preserved. In this paper, we introduce a new shape constraint and exhibit its properties. By combining it with a standard sparse regularization in the wavelet domain, we introduce the Shape COnstraint REstoration algorithm (SCORE), which performs a standard sparse deconvolution, while preserving galaxy shapes. We show through numerical experiments that this new approach leads to a reduction of galaxy ellipticity measurement errors by at least 44%., Comment: 22 pages, 6 figures, 1 table, accepted in Journal of Fourier Analysis and Applications

This paper provides a theoretical and numerical comparison of classical first-order splitting methods for solving smooth convex optimization problems and cocoercive equations. From a theoretical point of view, we compare convergence rates of gradient descent, forward-backward, Peaceman-Rachford, and Douglas-Rachford algorithms for minimizing the sum of two smooth convex functions when one of them is strongly convex. A similar comparison is given in the more general cocoercive setting under the presence of strong monotonicity and we observe that the convergence rates in optimization are strictly better than the corresponding rates for cocoercive equations for some algorithms. We obtain improved rates with respect to the literature in several instances by exploiting the structure of our problems. Moreover, we indicate which algorithm has the lowest convergence rate depending on strong convexity and cocoercive parameters. From a numerical point of view, we verify our theoretical results by implementing and comparing previous algorithms in well-established signal and image inverse problems involving sparsity. We replace the widely used $\ell_1$ norm with the Huber loss and we observe that fully proximal-based strategies have numerical and theoretical advantages with respect to methods using gradient steps., Comment: 20 pages, 18 figures

A compressive sensing based circular polarization snapshot spectral imaging system is proposed in this paper to acquire two-dimensional spatial, one-dimensional circular polarization (the right and left circular polarization), and one-dimensional spectral information, simultaneously. Using snapshot can collect the entire four-dimensional datacube in a single integration period. The dispersion prism in the coded aperture snapshot spectral imager is replaced by the combination of an Amici prism and a Wollaston prism to implement the spectral shifting along two orthogonal directions, which greatly improves the spectral resolution of the image. The right and left circular polarization components of objects are extracted by the assemble with an achromatic quarter wave-plate and a Wollaston prism. The encoding and reconstruction are illustrated comprehensively. The feasibility is verified by the simulation. It provides us an alternative approach for circular polarization spectral imaging such as defogging, underwater imaging, and so on., Comment: 20 pages, 11 figures, 1 table

Biological experiments based on organ-on-chips (OOCs) exploit light Time-Lapse Microscopy (TLM) for a direct observation of cell movement that is an observable signature of underlying biological processes. A high spatial resolution is essential to capture cell dynamics and interactions from recorded experiments by TLM. Unfortunately, due to physical and cost limitations, acquiring high resolution videos is not always possible. To overcome the problem, we present here a new deep learning-based algorithm that extends the well known Deep Image Prior (DIP) to TLM Video Super Resolution (SR) without requiring any training. The proposed Recursive Deep Prior Video (RDPV) method introduces some novelties. The weights of the DIP network architecture are initialized for each of the frames according to a new recursive updating rule combined with an efficient early stopping criterion. Moreover, the DIP loss function is penalized by two different Total Variation (TV) based terms. The method has been validated on synthetic, i.e., artificially generated, as well as real videos from OOC experiments related to tumor-immune interaction. Achieved results are compared with several state-of-the-art trained deep learning SR algorithms showing outstanding performances., Comment: Paper submitted to a peer-reviewed journal

Recently, deep Convolutional Neural Networks (CNNs) have revolutionized image super-resolution (SR), dramatically outperforming past methods for enhancing image resolution. They could be a boon for the many scientific fields that involve image or gridded datasets: satellite remote sensing, radar meteorology, medical imaging, numerical modeling etc. Unfortunately, while SR-CNNs produce visually compelling outputs, they may break physical conservation laws when applied to scientific datasets. Here, a method for ``Downsampling Enforcement" in SR-CNNs is proposed. A differentiable operator is derived that, when applied as the final transfer function of a CNN, ensures the high resolution outputs exactly reproduce the low resolution inputs under 2D-average downsampling while improving performance of the SR schemes. The method is demonstrated across seven modern CNN-based SR schemes on several benchmark image datasets, and applications to weather radar, satellite imager, and climate model data are also shown. The approach improves training time and performance while ensuring physical consistency between the super-resolved and low resolution data., Comment: 16 pages, 7 figures

Face restoration is an inherently ill-posed problem, where additional prior constraints are typically considered crucial for mitigating such pathology. However, real-world image prior are often hard to simulate with precise mathematical models, which inevitably limits the performance and generalization ability of existing prior-regularized restoration methods. In this paper, we study the problem of face restoration under a more practical ``dual blind'' setting, i.e., without prior assumptions or hand-crafted regularization terms on the degradation profile or image contents. To this end, a novel implicit subspace prior learning (ISPL) framework is proposed as a generic solution to dual-blind face restoration, with two key elements: 1) an implicit formulation to circumvent the ill-defined restoration mapping and 2) a subspace prior decomposition and fusion mechanism to dynamically handle inputs at varying degradation levels with consistent high-quality restoration results. Experimental results demonstrate significant perception-distortion improvement of ISPL against existing state-of-the-art methods for a variety of restoration subtasks, including a 3.69db PSNR and 45.8% FID gain against ESRGAN, the 2018 NTIRE SR challenge winner. Overall, we prove that it is possible to capture and utilize prior knowledge without explicitly formulating it, which will help inspire new research paradigms towards low-level vision tasks., Comment: TPAMI submission

In the last decades, unsupervised deep learning based methods have caught researchers attention, since in many real applications, such as medical imaging, collecting a great amount of training examples is not always feasible. Moreover, the construction of a good training set is time consuming and hard because the selected data have to be enough representative for the task. In this paper, we focus on the Deep Image Prior (DIP) framework and we propose to combine it with a space-variant Total Variation regularizer with an automatic estimation of the local regularization parameters. Differently from other existing approaches, we solve the arising minimization problem via the flexible Alternating Direction Method of Multipliers (ADMM). Furthermore, we provide a specific implementation also for the standard isotropic Total Variation. The promising performances of the proposed approach, in terms of PSNR and SSIM values, are addressed through several experiments on simulated as well as real natural and medical corrupted images., Comment: conference paper

This study proposes a convolutional nonlinear dictionary (CNLD) for image restoration using cascaded filter banks. Generally, convolutional neural networks (CNN) demonstrate their practicality in image restoration applications; however, existing CNNs are constructed without considering the relationship among atomic images (convolution kernels). As a result, there remains room for discussing the role of design spaces. To provide a framework for constructing an effective and structured convolutional network, this study proposes the CNLD. The backpropagation learning procedure is derived from certain image restoration experiments, and thereby the significance of CNLD is verified. It is demonstrated that the number of parameters is reduced while preserving the restoration performance., Comment: 4 pages, 5 figures

Blind image restoration (IR) is a common yet challenging problem in computer vision. Classical model-based methods and recent deep learning (DL)-based methods represent two different methodologies for this problem, each with their own merits and drawbacks. In this paper, we propose a novel blind image restoration method, aiming to integrate both the advantages of them. Specifically, we construct a general Bayesian generative model for the blind IR, which explicitly depicts the degradation process. In this proposed model, a pixel-wise non-i.i.d. Gaussian distribution is employed to fit the image noise. It is with more flexibility than the simple i.i.d. Gaussian or Laplacian distributions as adopted in most of conventional methods, so as to handle more complicated noise types contained in the image degradation. To solve the model, we design a variational inference algorithm where all the expected posteriori distributions are parameterized as deep neural networks to increase their model capability. Notably, such an inference algorithm induces a unified framework to jointly deal with the tasks of degradation estimation and image restoration. Further, the degradation information estimated in the former task is utilized to guide the latter IR process. Experiments on two typical blind IR tasks, namely image denoising and super-resolution, demonstrate that the proposed method achieves superior performance over current state-of-the-arts., Comment: Accepted by TPAMI@2024. Code: https://github.com/zsyOAOA/VIRNet

Pathology is practiced by visual inspection of histochemically stained slides. Most commonly, the hematoxylin and eosin (H&E) stain is used in the diagnostic workflow and it is the gold standard for cancer diagnosis. However, in many cases, especially for non-neoplastic diseases, additional "special stains" are used to provide different levels of contrast and color to tissue components and allow pathologists to get a clearer diagnostic picture. In this study, we demonstrate the utility of supervised learning-based computational stain transformation from H&E to different special stains (Masson's Trichrome, periodic acid-Schiff and Jones silver stain) using tissue sections from kidney needle core biopsies. Based on evaluation by three renal pathologists, followed by adjudication by a fourth renal pathologist, we show that the generation of virtual special stains from existing H&E images improves the diagnosis in several non-neoplastic kidney diseases sampled from 58 unique subjects. A second study performed by three pathologists found that the quality of the special stains generated by the stain transformation network was statistically equivalent to those generated through standard histochemical staining. As the transformation of H&E images into special stains can be achieved within 1 min or less per patient core specimen slide, this stain-to-stain transformation framework can improve the quality of the preliminary diagnosis when additional special stains are needed, along with significant savings in time and cost, reducing the burden on healthcare system and patients., Comment: 27 Pages, 6 Figures

We consider a variational model for single-image super-resolution based on the assumption that the gradient of the target image is sparse. We enforce this assumption by considering both an isotropic and an anisotropic $\ell^0$ regularisation on the image gradient combined with a quadratic data fidelity, similarly as studied in [1] for general signal recovery problems. For the numerical realisation of the model, we propose a novel efficient ADMM splitting algorithm whose substeps solutions are computed efficiently by means of hard-thresholding and standard conjugate-gradient solvers. We test our model on highly-degraded synthetic and real-world data and quantitatively compare our results with several variational approaches as well as with state-of-the-art deep-learning techniques. Our experiments show that $\ell^0$ gradient-regularised super-resolved images can be effectively used to improve the accuracy of standard segmentation algorithms when applied to QR and cell detection, and landcover classification problems, in comparison to the results achieved by other approaches., Comment: 10 pages + appendices, 7 figures

Real-world image noise removal is a long-standing yet very challenging task in computer vision. The success of deep neural network in denoising stimulates the research of noise generation, aiming at synthesizing more clean-noisy image pairs to facilitate the training of deep denoisers. In this work, we propose a novel unified framework to simultaneously deal with the noise removal and noise generation tasks. Instead of only inferring the posteriori distribution of the latent clean image conditioned on the observed noisy image in traditional MAP framework, our proposed method learns the joint distribution of the clean-noisy image pairs. Specifically, we approximate the joint distribution with two different factorized forms, which can be formulated as a denoiser mapping the noisy image to the clean one and a generator mapping the clean image to the noisy one. The learned joint distribution implicitly contains all the information between the noisy and clean images, avoiding the necessity of manually designing the image priors and noise assumptions as traditional. Besides, the performance of our denoiser can be further improved by augmenting the original training dataset with the learned generator. Moreover, we propose two metrics to assess the quality of the generated noisy image, for which, to the best of our knowledge, such metrics are firstly proposed along this research line. Extensive experiments have been conducted to demonstrate the superiority of our method over the state-of-the-arts both in the real noise removal and generation tasks. The training and testing code is available at https://github.com/zsyOAOA/DANet., Comment: Accepted by ECCV 2020

Edge-enhancing diffusion (EED) can reconstruct a close approximation of an original image from a small subset of its pixels. This makes it an attractive foundation for PDE based image compression. In this work, we generalize second-order EED to a fourth-order counterpart. It involves a fourth-order diffusion tensor that is constructed from the regularized image gradient in a similar way as in traditional second-order EED, permitting diffusion along edges, while applying a non-linear diffusivity function across them. We show that our fourth-order diffusion tensor formalism provides a unifying framework for all previous anisotropic fourth-order diffusion based methods, and that it provides additional flexibility. We achieve an efficient implementation using a fast semi-iterative scheme. Experimental results on natural and medical images suggest that our novel fourth-order method produces more accurate reconstructions compared to the existing second-order EED., Comment: Accepted for publication in Springer book "Anisotropy Across Fields and Scales"

Existing face restoration researches typically relies on either the degradation prior or explicit guidance labels for training, which often results in limited generalization ability over real-world images with heterogeneous degradations and rich background contents. In this paper, we investigate the more challenging and practical "dual-blind" version of the problem by lifting the requirements on both types of prior, termed as "Face Renovation"(FR). Specifically, we formulated FR as a semantic-guided generation problem and tackle it with a collaborative suppression and replenishment (CSR) approach. This leads to HiFaceGAN, a multi-stage framework containing several nested CSR units that progressively replenish facial details based on the hierarchical semantic guidance extracted from the front-end content-adaptive suppression modules. Extensive experiments on both synthetic and real face images have verified the superior performance of HiFaceGAN over a wide range of challenging restoration subtasks, demonstrating its versatility, robustness and generalization ability towards real-world face processing applications., Comment: Published in ACM Multimedia 2020

Although Neural Differential Equations have shown promise on toy problems such as MNIST, they have yet to be successfully applied to more challenging tasks. Inspired by variational methods for image restoration relying on partial differential equations, we choose to benchmark several forms of Neural DEs and backpropagation methods on single image super-resolution. The adjoint method previously proposed for gradient estimation has no theoretical stability guarantees; we find a practical case where this makes it unusable, and show that discrete sensitivity analysis has better stability. In our experiments, differential models match the performance of a state-of-the art super-resolution model., Comment: 7 pages, 5 figures, ICLR 2020 Workshop on Integration of Deep Neural Models and Differential Equations

In this paper, we explore the space-time video super-resolution task, which aims to generate a high-resolution (HR) slow-motion video from a low frame rate (LFR), low-resolution (LR) video. A simple solution is to split it into two sub-tasks: video frame interpolation (VFI) and video super-resolution (VSR). However, temporal interpolation and spatial super-resolution are intra-related in this task. Two-stage methods cannot fully take advantage of the natural property. In addition, state-of-the-art VFI or VSR networks require a large frame-synthesis or reconstruction module for predicting high-quality video frames, which makes the two-stage methods have large model sizes and thus be time-consuming. To overcome the problems, we propose a one-stage space-time video super-resolution framework, which directly synthesizes an HR slow-motion video from an LFR, LR video. Rather than synthesizing missing LR video frames as VFI networks do, we firstly temporally interpolate LR frame features in missing LR video frames capturing local temporal contexts by the proposed feature temporal interpolation network. Then, we propose a deformable ConvLSTM to align and aggregate temporal information simultaneously for better leveraging global temporal contexts. Finally, a deep reconstruction network is adopted to predict HR slow-motion video frames. Extensive experiments on benchmark datasets demonstrate that the proposed method not only achieves better quantitative and qualitative performance but also is more than three times faster than recent two-stage state-of-the-art methods, e.g., DAIN+EDVR and DAIN+RBPN., Comment: This work is accepted in CVPR 2020. The source code and pre-trained model are available on https://github.com/Mukosame/Zooming-Slow-Mo-CVPR-2020. 12 pages, 10 figures

Histological staining is a vital step used to diagnose various diseases and has been used for more than a century to provide contrast to tissue sections, rendering the tissue constituents visible for microscopic analysis by medical experts. However, this process is time-consuming, labor-intensive, expensive and destructive to the specimen. Recently, the ability to virtually-stain unlabeled tissue sections, entirely avoiding the histochemical staining step, has been demonstrated using tissue-stain specific deep neural networks. Here, we present a new deep learning-based framework which generates virtually-stained images using label-free tissue, where different stains are merged following a micro-structure map defined by the user. This approach uses a single deep neural network that receives two different sources of information at its input: (1) autofluorescence images of the label-free tissue sample, and (2) a digital staining matrix which represents the desired microscopic map of different stains to be virtually generated at the same tissue section. This digital staining matrix is also used to virtually blend existing stains, digitally synthesizing new histological stains. We trained and blindly tested this virtual-staining network using unlabeled kidney tissue sections to generate micro-structured combinations of Hematoxylin and Eosin (H&E), Jones silver stain, and Masson's Trichrome stain. Using a single network, this approach multiplexes virtual staining of label-free tissue with multiple types of stains and paves the way for synthesizing new digital histological stains that can be created on the same tissue cross-section, which is currently not feasible with standard histochemical staining methods., Comment: 19 pages, 5 figures, 2 tables

We propose a method to reduce non-uniform sample variance to a predetermined target level. The proposed space-variant filter can equalize variance of the non-stationary signal, or vary filtering strength based on image features, such as edges, etc., as shown by applications in this work. This approach computes variance reduction ratio at each point of the image, based on the given target variance. Then, a space-variant filter with matching variance reduction power is applied. A mathematical framework of atomic kernels is developed to facilitate stable and fast computation of the filter bank kernels. Recursive formulation allows using small kernel size, which makes the space-variant filter more suitable for fast parallel implementation. Despite the small kernel size, the recursive filter possesses strong variance reduction power. Filter accuracy is measured by the variance reduction against the target variance; testing demonstrated high accuracy of variance reduction of the recursive filter compared to the fixed-size filter. The proposed filter was applied to adaptive filtering in image reconstruction and edge-preserving denoising., Comment: 12 pages, 13 figures

We present a nonlocal variational image completion technique which admits simultaneous inpainting of multiple structures and textures in a unified framework. The recovery of geometric structures is achieved by using general convolution operators as a measure of behavior within an image. These are combined with a nonlocal exemplar-based approach to exploit the self-similarity of an image in the selected feature domains and to ensure the inpainting of textures. We also introduce an anisotropic patch distance metric to allow for better control of the feature selection within an image and present a nonlocal energy functional based on this metric. Finally, we derive an optimization algorithm for the proposed variational model and examine its validity experimentally with various test images.

A new and an enriched JPEG algorithm is provided for identifying redundancies in a sequence of irregular noisy data points which also accommodates a reference-free criterion function. Our main contribution is by formulating analytically (instead of approximating) the inverse of the transpose of JPEGwavelet transform without involving matrices which are computationally cumbersome. The algorithm is suitable for the widely-spread situations where the original data distribution is unobservable such as in cases where there is deficient representation of the entire population in the training data (in machine learning) and thus the covariate shift assumption is violated. The proposed estimator corrects for both biases, the one generated by endogenous truncation and the one generated by endogenous covariates. Results from utilizing 2,000,000 different distribution functions verify the applicability and high accuracy of our procedure to cases in which the disturbances are neither jointly nor marginally normally distributed., Comment: 18 pages

Blind and universal image denoising consists of using a unique model that denoises images with any level of noise. It is especially practical as noise levels do not need to be known when the model is developed or at test time. We propose a theoretically-grounded blind and universal deep learning image denoiser for additive Gaussian noise removal. Our network is based on an optimal denoising solution, which we call fusion denoising. It is derived theoretically with a Gaussian image prior assumption. Synthetic experiments show our network's generalization strength to unseen additive noise levels. We also adapt the fusion denoising network architecture for image denoising on real images. Our approach improves real-world grayscale additive image denoising PSNR results for training noise levels and further on noise levels not seen during training. It also improves state-of-the-art color image denoising performance on every single noise level, by an average of 0.1dB, whether trained on or not., Comment: Final uncompressed TIP version available online in open access (DOI attached)

A blurring algorithm with linear time complexity can reduce the small-scale content of data observed at scattered locations in a spatially extended domain of arbitrary dimension. The method works by forming a Gaussian interpolant of the input data, and then convolving the interpolant with a multiresolution Gaussian approximation of the Green's function to a differential operator whose spectrum can be tuned for problem-specific considerations. Like conventional blurring algorithms, which the new algorithm generalizes to data measured at locations other than a uniform grid, applications include deblurring and separation of spatial scales. An example illustrates a possible application toward enabling importance sampling approaches to data assimilation of geophysical observations, which are often scattered over a spatial domain, since blurring observations can make particle filters more effective at state estimation of large scales. Another example, motivated by data analysis of dynamics like ocean eddies that have strong separation of spatial scales, uses the algorithm to decompose scattered oceanographic float measurements into large-scale and small-scale components., Comment: 19 pages, 5 figures

Convolutional neural networks have been the focus of research aiming to solve image denoising problems, but their performance remains unsatisfactory for most applications. These networks are trained with synthetic noise distributions that do not accurately reflect the noise captured by image sensors. Some datasets of clean-noisy image pairs have been introduced but they are usually meant for benchmarking or specific applications. We introduce the Natural Image Noise Dataset (NIND), a dataset of DSLR-like images with varying levels of ISO noise which is large enough to train models for blind denoising over a wide range of noise. We demonstrate a denoising model trained with the NIND and show that it significantly outperforms BM3D on ISO noise from unseen images, even when generalizing to images from a different type of camera. The Natural Image Noise Dataset is published on Wikimedia Commons such that it remains open for curation and contributions. We expect that this dataset will prove useful for future image denoising applications., Comment: NTIRE at CVPR 2019

Haze degrades content and obscures information of images, which can negatively impact vision-based decision-making in real-time systems. In this paper, we propose an efficient fully convolutional neural network (CNN) image dehazing method designed to run on edge graphical processing units (GPUs). We utilize three variants of our architecture to explore the dependency of dehazed image quality on parameter count and model design. The first two variants presented, a small and big version, make use of a single efficient encoder-decoder convolutional feature extractor. The final variant utilizes a pair of encoder-decoders for atmospheric light and transmission map estimation. Each variant ends with an image refinement pyramid pooling network to form the final dehazed image. For the big variant of the single-encoder network, we demonstrate state-of-the-art performance on the NYU Depth dataset. For the small variant, we maintain competitive performance on the super-resolution O/I-HAZE datasets without the need for image cropping. Finally, we examine some challenges presented by the Dense-Haze dataset when leveraging CNN architectures for dehazing of dense haze imagery and examine the impact of loss function selection on image quality. Benchmarks are included to show the feasibility of introducing this approach into real-time systems., Comment: Accepted to the NTIRE 2019 CVPR Workshop. Paper number 77. 8 Pages

We propose a simple yet effective model for Single Image Super-Resolution (SISR), by combining the merits of Residual Learning and Convolutional Sparse Coding (RL-CSC). Our model is inspired by the Learned Iterative Shrinkage-Threshold Algorithm (LISTA). We extend LISTA to its convolutional version and build the main part of our model by strictly following the convolutional form, which improves the network's interpretability. Specifically, the convolutional sparse codings of input feature maps are learned in a recursive manner, and high-frequency information can be recovered from these CSCs. More importantly, residual learning is applied to alleviate the training difficulty when the network goes deeper. Extensive experiments on benchmark datasets demonstrate the effectiveness of our method. RL-CSC (30 layers) outperforms several recent state-of-the-arts, e.g., DRRN (52 layers) and MemNet (80 layers) in both accuracy and visual qualities. Codes and more results are available at https://github.com/axzml/RL-CSC., Comment: 10 pages, 8 figures, 4 tables

We further develop a new framework, called PDE Acceleration, by applying it to calculus of variations problems defined for general functions on $\mathbb{R}^n$, obtaining efficient numerical algorithms to solve the resulting class of optimization problems based on simple discretizations of their corresponding accelerated PDE's. While the resulting family of PDE's and numerical schemes are quite general, we give special attention to their application for regularized inversion problems, with particular illustrative examples on some popular image processing applications. The method is a generalization of momentum, or accelerated, gradient descent to the PDE setting. For elliptic problems, the descent equations are a nonlinear damped wave equation, instead of a diffusion equation, and the acceleration is realized as an improvement in the CFL condition from $\Delta t\sim \Delta x^{2}$ (for diffusion) to $\Delta t\sim \Delta x$ (for wave equations). We work out several explicit as well as a semi-implicit numerical schemes, together with their necessary stability constraints, and include recursive update formulations which allow minimal-effort adaptation of existing gradient descent PDE codes into the accelerated PDE framework. We explore these schemes more carefully for a broad class of regularized inversion applications, with special attention to quadratic, Beltrami, and Total Variation regularization, where the accelerated PDE takes the form of a nonlinear wave equation. Experimental examples demonstrate the application of these schemes for image denoising, deblurring, and inpainting, including comparisons against Primal Dual, Split Bregman, and ADMM algorithms.

This paper proposes a novel algorithm to reassemble an arbitrarily shredded image to its original status. Existing reassembly pipelines commonly consist of a local matching stage and a global compositions stage. In the local stage, a key challenge in fragment reassembly is to reliably compute and identify correct pairwise matching, for which most existing algorithms use handcrafted features, and hence, cannot reliably handle complicated puzzles. We build a deep convolutional neural network to detect the compatibility of a pairwise stitching, and use it to prune computed pairwise matches. To improve the network efficiency and accuracy, we transfer the calculation of CNN to the stitching region and apply a boost training strategy. In the global composition stage, we modify the commonly adopted greedy edge selection strategies to two new loop closure based searching algorithms. Extensive experiments show that our algorithm significantly outperforms existing methods on solving various puzzles, especially those challenging ones with many fragment pieces.

Using a deep neural network, we demonstrate a digital staining technique, which we term PhaseStain, to transform quantitative phase images (QPI) of labelfree tissue sections into images that are equivalent to brightfield microscopy images of the same samples that are histochemically stained. Through pairs of image data (QPI and the corresponding brightfield images, acquired after staining) we train a generative adversarial network (GAN) and demonstrate the effectiveness of this virtual staining approach using sections of human skin, kidney and liver tissue, matching the brightfield microscopy images of the same samples stained with Hematoxylin and Eosin, Jones' stain, and Masson's trichrome stain, respectively. This digital staining framework might further strengthen various uses of labelfree QPI techniques in pathology applications and biomedical research in general, by eliminating the need for chemical staining, reducing sample preparation related costs and saving time. Our results provide a powerful example of some of the unique opportunities created by data driven image transformations enabled by deep learning.

We discuss recently emerging applications of the state-of-art deep learning methods on optical microscopy and microscopic image reconstruction, which enable new transformations among different modes and modalities of microscopic imaging, driven entirely by image data. We believe that deep learning will fundamentally change both the hardware and image reconstruction methods used in optical microscopy in a holistic manner.

Histological analysis of tissue samples is one of the most widely used methods for disease diagnosis. After taking a sample from a patient, it goes through a lengthy and laborious preparation, which stains the tissue to visualize different histological features under a microscope. Here, we demonstrate a label-free approach to create a virtually-stained microscopic image using a single wide-field auto-fluorescence image of an unlabeled tissue sample, bypassing the standard histochemical staining process, saving time and cost. This method is based on deep learning, and uses a convolutional neural network trained using a generative adversarial network model to transform an auto-fluorescence image of an unlabeled tissue section into an image that is equivalent to the bright-field image of the stained-version of the same sample. We validated this method by successfully creating virtually-stained microscopic images of human tissue samples, including sections of salivary gland, thyroid, kidney, liver and lung tissue, also covering three different stains. This label-free virtual-staining method eliminates cumbersome and costly histochemical staining procedures, and would significantly simplify tissue preparation in pathology and histology fields.

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 PnP approach where a scene-adapted prior (i.e., where the denoiser is targeted to the specific scene being imaged) is plugged into ADMM (alternating direction method of multipliers), and prove convergence of the resulting algorithm. Finally, we apply the proposed framework in two different imaging inverse problems: hyperspectral sharpening/fusion and image deblurring from blurred/noisy image pairs., Comment: Submitted

Mobile-phones have facilitated the creation of field-portable, cost-effective imaging and sensing technologies that approach laboratory-grade instrument performance. However, the optical imaging interfaces of mobile-phones are not designed for microscopy and produce spatial and spectral distortions in imaging microscopic specimens. Here, we report on the use of deep learning to correct such distortions introduced by mobile-phone-based microscopes, facilitating the production of high-resolution, denoised and colour-corrected images, matching the performance of benchtop microscopes with high-end objective lenses, also extending their limited depth-of-field. After training a convolutional neural network, we successfully imaged various samples, including blood smears, histopathology tissue sections, and parasites, where the recorded images were highly compressed to ease storage and transmission for telemedicine applications. This method is applicable to other low-cost, aberrated imaging systems, and could offer alternatives for costly and bulky microscopes, while also providing a framework for standardization of optical images for clinical and biomedical applications.

We study the Pareto frontier for two competing norms $\|\cdot\|_X$ and $\|\cdot\|_Y$ on a vector space. For a given vector $c$, the pareto frontier describes the possible values of $(\|a\|_X,\|b\|_Y)$ for a decomposition $c=a+b$. The singular value decomposition of a matrix is closely related to the Pareto frontier for the spectral and nuclear norm. We will develop a general theory that extends the notion of singular values of a matrix to arbitrary finite dimensional euclidean vector spaces equipped with dual norms. This also generalizes the diagonal singular value decompositions for tensors introduced by the author in previous work. We can apply the results to denoising, where $c$ is a noisy signal, $a$ is a sparse signal and $b$ is noise. Applications include 1D total variation denoising, 2D total variation Rudin-Osher-Fatemi image denoising, LASSO, basis pursuit denoising and tensor decompositions., Comment: 59 pages, 27 figures

We demonstrate that a deep neural network can significantly improve optical microscopy, enhancing its spatial resolution over a large field-of-view and depth-of-field. After its training, the only input to this network is an image acquired using a regular optical microscope, without any changes to its design. We blindly tested this deep learning approach using various tissue samples that are imaged with low-resolution and wide-field systems, where the network rapidly outputs an image with remarkably better resolution, matching the performance of higher numerical aperture lenses, also significantly surpassing their limited field-of-view and depth-of-field. These results are transformative for various fields that use microscopy tools, including e.g., life sciences, where optical microscopy is considered as one of the most widely used and deployed techniques. Beyond such applications, our presented approach is broadly applicable to other imaging modalities, also spanning different parts of the electromagnetic spectrum, and can be used to design computational imagers that get better and better as they continue to image specimen and establish new transformations among different modes of imaging.

The human eye appears to be using a low number of sensors for image capturing. Furthermore, regarding the physical dimensions of cones-photoreceptors responsible for the sharp central vision-, we may realize that these sensors are of a relatively small size and area. Nonetheless, the eye is capable to obtain high resolution images due to visual hyperacuity and presents an impressive sensitivity and dynamic range when set against conventional digital cameras of similar characteristics. This article is based on the hypothesis that the human eye may be benefiting from diffraction to improve both image resolution and acquisition process. The developed method intends to explain and simulate using MATLAB software the visual hyperacuity: the introduction of a controlled diffraction pattern at an initial stage, enables the use of a reduced number of sensors for capturing the image and makes possible a subsequent processing to improve the final image resolution. The results have been compared with the outcome of an equivalent system but in absence of diffraction, achieving promising results. The main conclusion of this work is that diffraction could be helpful for capturing images or signals when a small number of sensors available, which is far from being a resolution-limiting factor., Comment: 8 pages,9 figures

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 method of multipliers and prove the algorithm is guaranteed to converge. Moreover, we build upon the concept of scene-adapted priors where we learn a model targeted to a specific scene being imaged, and apply the proposed method to address the hyperspectral sharpening problem.

Functions of brain areas in complex animals are believed to rely on the dynamics of networks of neurons rather than on single neurons. On the other hand, the network dynamics reflect and arise from the integration and coordination of the activity of populations of single neurons. Understanding how single-neurons and neural-circuits dynamics complement each other to produce brain functions is thus of paramount importance. LFPs and EEGs are good indicators of the dynamics of mesoscopic and macroscopic populations of neurons, while microscopic-level activities can be documented by measuring the membrane potential, the synaptic currents or the spiking activity of individual neurons. In this thesis we develop mathematical modelling and mathematical analysis tools that can help the interpretation of joint measures of neural activity at microscopic and mesoscopic or macroscopic scales. In particular, we develop network models of recurrent cortical circuits that can clarify the impact of several aspects of single-neuron (i.e., microscopic-level) dynamics on the activity of the whole neural population (as measured by LFP). We then develop statistical tools to characterize the relationship between the action potential firing of single neurons and mass signals. We apply these latter analysis techniques to joint recordings of the firing activity of individual cell-type identified neurons and mesoscopic (i.e., LFP) and macroscopic (i.e., EEG) signals in the mouse neocortex. We identified several general aspects of the relationship between cell-specific neural firing and mass circuit activity, providing for example general and robust mathematical rules which infer single-neuron firing activity from mass measures such as the LFP and the EEG., Comment: PhD thesis (integrate-and-fire neurons, recurrent neural networks, current based neurons, conductance based neurons, LFP, EEG, information encoding, GLM, Wiener filtering, PV-pos interneuron) 170 pages, 57 figures, 8 tables

We investigate the inverse scale space flow as a decomposition method for decomposing data into generalised singular vectors. We show that the inverse scale space flow, based on convex and absolutely one-homogeneous regularisation functionals, can decompose data represented by the application of a forward operator to a linear combination of generalised singular vectors into its individual singular vectors. We verify that for this decomposition to hold true, two additional conditions on the singular vectors are sufficient: orthogonality in the data space and inclusion of partial sums of the subgradients of the singular vectors in the subdifferential of the regularisation functional at zero. We also address the converse question of when the inverse scale space flow returns a generalised singular vector given that the initial data is arbitrary (and therefore not necessarily in the range of the forward operator). We prove that the inverse scale space flow is guaranteed to return a singular vector if the data satisfies a novel dual singular vector condition. We conclude the paper with numerical results that validate the theoretical results and that demonstrate the importance of the additional conditions required to guarantee the decomposition result., Comment: 36 pages, 5 figures, submitted to Inverse Problems

The present document aims at providing a short, didactical introduction to three standard versions of the Kalman filter, namely its variants identified as Basic, Extended, and Unscented. The application of these algorithms in three representative problems is discussed., Comment: 28 pages, 12 figures

We propose an image representation scheme combining the local and nonlocal characterization of patches in an image. Our representation scheme can be shown to be equivalent to a tight frame constructed from convolving local bases (e.g. wavelet frames, discrete cosine transforms, etc.) with nonlocal bases (e.g. spectral basis induced by nonlinear dimension reduction on patches), and we call the resulting frame elements {\it convolution framelets}. Insight gained from analyzing the proposed representation leads to a novel interpretation of a recent high-performance patch-based image inpainting algorithm using Point Integral Method (PIM) and Low Dimension Manifold Model (LDMM) [Osher, Shi and Zhu, 2016]. In particular, we show that LDMM is a weighted $\ell_2$-regularization on the coefficients obtained by decomposing images into linear combinations of convolution framelets; based on this understanding, we extend the original LDMM to a reweighted version that yields further improved inpainting results. In addition, we establish the energy concentration property of convolution framelet coefficients for the setting where the local basis is constructed from a given nonlocal basis via a linear reconstruction framework; a generalization of this framework to unions of local embeddings can provide a natural setting for interpreting BM3D, one of the state-of-the-art image denoising algorithms.

State-of-the-art algorithms for imaging inverse problems (namely deblurring and reconstruction) are typically iterative, involving a denoising operation as one of its steps. Using a state-of-the-art denoising method in this context is not trivial, and is the focus of current work. Recently, we have proposed to use a class-adapted denoiser (patch-based using Gaussian mixture models) in a so-called plug-and-play scheme, wherein a state-of-the-art denoiser is plugged into an iterative algorithm, leading to results that outperform the best general-purpose algorithms, when applied to an image of a known class (e.g. faces, text, brain MRI). In this paper, we extend that approach to handle situations where the image being processed is from one of a collection of possible classes or, more importantly, contains regions of different classes. More specifically, we propose a method to locally select one of a set of class-adapted Gaussian mixture patch priors, previously estimated from clean images of those classes. Our approach may be seen as simultaneously performing segmentation and restoration, thus contributing to bridging the gap between image restoration/reconstruction and analysis.

This paper proposes using a Gaussian mixture model as a prior, for solving two image inverse problems, namely image deblurring and compressive imaging. We capitalize on the fact that variable splitting algorithms, like ADMM, are able to decouple the handling of the observation operator from that of the regularizer, and plug a state-of-the-art algorithm into the pure denoising step. Furthermore, we show that, when applied to a specific type of image, a Gaussian mixture model trained from an database of images of the same type is able to outperform current state-of-the-art methods.

The wavelet frame systems have been widely investigated and applied for image restoration and many other image processing problems over the past decades, attributing to their good capability of sparsely approximating piece-wise smooth functions such as images. Most wavelet frame based models exploit the $l_1$ norm of frame coefficients for a sparsity constraint in the past. The authors in \cite{ZhangY2013, Dong2013} proposed an $l_0$ minimization model, where the $l_0$ norm of wavelet frame coefficients is penalized instead, and have demonstrated that significant improvements can be achieved compared to the commonly used $l_1$ minimization model. Very recently, the authors in \cite{Chen2015} proposed $l_0$-$l_2$ minimization model, where the nonlocal prior of frame coefficients is incorporated. This model proved to outperform the single $l_0$ minimization based model in terms of better recovered image quality. In this paper, we propose a truncated $l_0$-$l_2$ minimization model which combines sparsity, nonlocal and support prior of the frame coefficients. The extensive experiments have shown that the recovery results from the proposed regularization method performs better than existing state-of-the-art wavelet frame based methods, in terms of edge enhancement and texture preserving performance.

Iterative majorize-minimize (MM) (also called optimization transfer) algorithms solve challenging numerical optimization problems by solving a series of "easier" optimization problems that are constructed to guarantee monotonic descent of the cost function. Many MM algorithms replace a computationally expensive Hessian matrix with another more computationally convenient majorizing matrix. These majorizing matrices are often generated using various matrix inequalities, and consequently the set of available majorizers is limited to structures for which these matrix inequalities can be efficiently applied. In this paper, we present a technique to algorithmically design matrix majorizers with wide varieties of structures. We use a novel duality-based approach to avoid the high computational and memory costs of standard semidefinite programming techniques. We present some preliminary results for 2D X-ray CT reconstruction that indicate these more exotic regularizers may significantly accelerate MM algorithms., Comment: 10 pages, 4 figures