Solving inverse problems with piecewise linear estimators: from Gaussian mixture models to structured sparsity

Physically interpretable performance metrics for clustering

Clustering is a type of machine learning technique, which is used to group huge amounts of data based on their similarity into separate groups or clusters. Clustering is a very important task that is nowadays used to analyze the huge and diverse amount of data coming out of molecular dynamics (MD) simulations. Typically, the data from the MD simulations in terms of their various frames in the trajectory are clustered into different groups and a representative element from each group is studied separately. Now, a very important question coming in this process is: what is the quality of the clusters that are obtained? There are several performance metrics that are available in the literature such as the silhouette index and the Davies-Bouldin Index that are often used to analyze the quality of clustering. However, most of these metrics focus on the overlap or the similarity of the clusters in the reduced dimension that is used for clustering and do not focus on the physically important properties or the parameters of the system. To address this issue, we have developed two physically interpretable scoring metrics that focus on the physical parameters of the system that we are analyzing. We have used and tested our algorithm on three different systems: (1) Ising model, (2) peptide folding and unfolding of WT HP35, (3) a protein-ligand trajectory of an enzyme and substrate, and (4) a protein-ligand dissociated trajectory. We show that the scoring metrics provide us clusters that match with our physical intuition about the systems.

Past rewinding of fluid dynamics from noisy observation via physics-informed neural computing

Reconstructing the past of observed fluids has been known as an ill-posed problem due to both numerical and physical challenges, especially when observations are distorted by inevitable noise, resolution limits, or unknown factors. When employing traditional differencing schemes to reconstruct the past, the computation often becomes highly unstable or diverges within a few backward time steps from the distorted and noisy observation. Although several techniques have been recently developed for inverse problems, such as adjoint solvers and supervised learning, they are also unrobust against errors in observation when there is time-reversed simulation. Here we present that by using physics-informed neural computing, robust time-reversed fluid simulation is possible. By seeking a solution that closely satisfies the given physics and observations while allowing for errors, it reconstructs the most probable past from noisy observations. Our work showcases time rewinding in extreme fluid scenarios such as shock, instability, blast, and magnetohydrodynamic vortex. Potentially, this can be applied to trace back the interstellar evolution and determining the origin of fusion plasma instabilities.

Convolutional Sparse Support Estimator Network (CSEN): From Energy-Efficient Support Estimation to Learning-Aided Compressive Sensing

Support estimation (SE) of a sparse signal refers to finding the location indices of the nonzero elements in a sparse representation. Most of the traditional approaches dealing with SE problems are iterative algorithms based on greedy methods or optimization techniques. Indeed, a vast majority of them use sparse signal recovery (SR) techniques to obtain support sets instead of directly mapping the nonzero locations from denser measurements (e.g., compressively sensed measurements). This study proposes a novel approach for learning such a mapping from a training set. To accomplish this objective, the convolutional sparse support estimator networks (CSENs), each with a compact configuration, are designed. The proposed CSEN can be a crucial tool for the following scenarios: 1) real-time and low-cost SE can be applied in any mobile and low-power edge device for anomaly localization, simultaneous face recognition, and so on and 2) CSEN's output can directly be used as "prior information," which improves the performance of sparse SR algorithms. The results over the benchmark datasets show that state-of-the-art performance levels can be achieved by the proposed approach with a significantly reduced computational complexity.

Hierarchical Materials from High Information Content Macromolecular Building Blocks: Construction, Dynamic Interventions, and Prediction

Hierarchical materials that exhibit order over multiple length scales are ubiquitous in nature. Because hierarchy gives rise to unique properties and functions, many have sought inspiration from nature when designing and fabricating hierarchical matter. More and more, however, nature's own high-information content building blocks, proteins, peptides, and peptidomimetics, are being coopted to build hierarchy because the information that determines structure, function, and interfacial interactions can be readily encoded in these versatile macromolecules. Here, we take stock of recent progress in the rational design and characterization of hierarchical materials produced from high-information content blocks with a focus on stimuli-responsive and "smart" architectures. We also review advances in the use of computational simulations and data-driven predictions to shed light on how the side chain chemistry and conformational flexibility of macromolecular blocks drive the emergence of order and the acquisition of hierarchy and also on how ionic, solvent, and surface effects influence the outcomes of assembly. Continued progress in the above areas will ultimately usher in an era where an understanding of designed interactions, surface effects, and solution conditions can be harnessed to achieve predictive materials synthesis across scale and drive emergent phenomena in the self-assembly and reconfiguration of high-information content building blocks.

Iterative deep neural networks based on proximal gradient descent for image restoration

The algorithm unfolding networks with explainability of algorithms and higher efficiency of Deep Neural Networks (DNN) have received considerable attention in solving ill-posed inverse problems. Under the algorithm unfolding network framework, we propose a novel end-to-end iterative deep neural network and its fast network for image restoration. The first one is designed making use of proximal gradient descent algorithm of variational models, which consists of denoiser and reconstruction sub-networks. The second one is its accelerated version with momentum factors. For sub-network of denoiser, we embed the Convolutional Block Attention Module (CBAM) in previous U-Net for adaptive feature refinement. Experiments on image denoising and deblurring demonstrate that competitive performances in quality and efficiency are gained by compared with several state-of-the-art networks for image restoration. Proposed unfolding DNN can be easily extended to solve other similar image restoration tasks, such as image super-resolution, image demosaicking, etc.

A Hybrid Sparse Representation Model for Image Restoration

Group-based sparse representation (GSR) uses image nonlocal self-similarity (NSS) prior to grouping similar image patches, and then performs sparse representation. However, the traditional GSR model restores the image by training degraded images, which leads to the inevitable over-fitting of the data in the training model, resulting in poor image restoration results. In this paper, we propose a new hybrid sparse representation model (HSR) for image restoration. The proposed HSR model is improved in two aspects. On the one hand, the proposed HSR model exploits the NSS priors of both degraded images and external image datasets, making the model complementary in feature space and the plane. On the other hand, we introduce a joint sparse representation model to make better use of local sparsity and NSS characteristics of the images. This joint model integrates the patch-based sparse representation (PSR) model and GSR model, while retaining the advantages of the GSR model and the PSR model, so that the sparse representation model is unified. Extensive experimental results show that the proposed hybrid model outperforms several existing image recovery algorithms in both objective and subjective evaluations.

Modeling viral dynamics in SARS-CoV-2 infection based on differential equations and numerical analysis

Computational modeling and simulation of viral dynamics would explain the pathogenesis for any virus. Such computational attempts have been successfully made to predict and control HIV-1 or hepatitis B virus. However, the dynamics for SARS-CoV-2 has not been adequately investigated. The purpose of this research is to propose different SARS-CoV-2 dynamics models based on differential equations and numerical analysis towards distilling the models to explain the mechanism of SARS-CoV-2 pathogenesis. The proposed four models formalize the dynamical system of SARS-CoV-2 infection, which consists of host cells and viral particles. These models undergo numerical analysis, including sensitivity analysis and stability analysis. Based on the sensitivity indices of the four models' parameters, the four models are simplified into two models. In advance of the following calibration experiments, the eigenvalues of the Jacobian matrices of these two models are calculated, thereby guaranteeing that any solutions are stable. Then, the calibration experiments fit the simulated data sequences of the two models to two observed data sequences, SARS-CoV-2 viral load in mild cases and that in severe cases. Comparing the estimated parameters in mild cases and severe cases indicates that cell-to-cell transmission would significantly correlate to the COVID-19 severity. These experiments for modeling and simulation provide plausible computational models for the SARS-CoV-2 dynamics, leading to further investigation for identifying the essential factors in severe cases.

Comparative Molecular Dynamics Investigation of the Electromotile Hearing Protein Prestin

The mammalian protein prestin is expressed in the lateral membrane wall of the cochlear hair outer cells and is responsible for the electromotile response of the basolateral membrane, following hyperpolarisation or depolarisation of the cells. Its impairment marks the onset of severe diseases, like non-syndromic deafness. Several studies have pointed out possible key roles of residues located in the Transmembrane Domain (TMD) that differentiate mammalian prestins as incomplete transporters from the other proteins belonging to the same solute-carrier (SLC) superfamily, which are classified as complete transporters. Here, we exploit the homology of a prototypical incomplete transporter (rat prestin, rPres) and a complete transporter (zebrafish prestin, zPres) with target structures in the outward open and inward open conformations. The resulting models are then embedded in a model membrane and investigated via a rigorous molecular dynamics simulation protocol. The resulting trajectories are analyzed to obtain quantitative descriptors of the equilibration phase and to assess a structural comparison between proteins in different states, and between different proteins in the same state. Our study clearly identifies a network of key residues at the interface between the gate and the core domains of prestin that might be responsible for the conformational change observed in complete transporters and hindered in incomplete transporters. In addition, we study the pathway of Cl− ions in the presence of an applied electric field towards their putative binding site in the gate domain. Based on our simulations, we propose a tilt and shift mechanism of the helices surrounding the ion binding cavity as the working principle of the reported conformational changes in complete transporters.

Determining the sex-specific distributions of average daily alcohol consumption using cluster analysis: is there a separate distribution for people with alcohol dependence?

BACKGROUND

It remains unclear whether alcohol use disorders (AUDs) can be characterized by specific levels of average daily alcohol consumption. The aim of the current study was to model the distributions of average daily alcohol consumption among those who consume alcohol and those with alcohol dependence, the most severe AUD, using various clustering techniques.

METHODS

Data from Wave 1 and Wave 2 of the National Epidemiologic Survey on Alcohol and Related Conditions were used in the current analyses. Clustering algorithms were applied in order to group a set of data points that represent the average daily amount of alcohol consumed. Gaussian Mixture Models (GMMs) were then used to estimate the likelihood of a data point belonging to one of the mixture distributions. Individuals were assigned to the clusters which had the highest posterior probabilities from the GMMs, and their treatment utilization rate was examined for each of the clusters.

RESULTS

Modeling alcohol consumption via clustering techniques was feasible. The clusters identified did not point to alcohol dependence as a separate cluster characterized by a higher level of alcohol consumption. Among both females and males with alcohol dependence, daily alcohol consumption was relatively low.

CONCLUSIONS

Overall, we found little evidence for clusters of people with the same drinking distribution, which could be characterized as clinically relevant for people with alcohol use disorders as currently defined.

SSIM Compliant Modeling Framework With Denoising and Deblurring Applications

In image processing, it is well known that mean square error criteria is perceptually inadequate. Consequently, image quality assessment (IQA) has emerged as a new branch to overcome this issue, and this has led to the discovery of one of the most popular perceptual measures, namely, the structural similarity index (SSIM). This measure is mathematically simple, yet powerful enough to express the quality of an image. Therefore, it is natural to deploy SSIM in model based applications, such as denoising, restoration, classification, etc. However, the non-convex nature of this measure makes this task difficult. Our attempt in this work is to discuss problems associated with its convex program and take remedial action in the process of obtaining a generalized convex framework. The obtained framework has been seen as a component of an alternative learning scheme for the case of a regularized linear model. Subsequently, we develop a relevant dictionary learning module as a part of alternative learning. This alternative learning scheme with sparsity prior is finally used in denoising and deblurring applications. To further boost the performance, an iterative scheme is developed based on the statistical nature of added noise. Experiments on image denoising and deblurring validate the effectiveness of the proposed scheme. Furthermore, it has been shown that the proposed framework achieves highly competitive performance with respect to other schemes in literature and performs better in natural images in terms of SSIM and visual inspection.

Tracking atomic structure evolution during directed electron beam induced Si-atom motion in graphene via deep machine learning

Using electron beam manipulation, we enable deterministic motion of individual Si atoms in graphene along predefined trajectories. Structural evolution during the dopant motion was explored, providing information on changes of the Si atom neighborhood during atomic motion and providing statistical information of possible defect configurations. The combination of a Gaussian mixture model and principal component analysis applied to the deep learning-processed experimental data allowed disentangling of the atomic distortions for two different graphene sublattices. This approach demonstrates the potential of e-beam manipulation to create defect libraries of multiple realizations of the same defect and explore the potential of symmetry breaking physics. The rapid image analytics enabled via a deep learning network further empowers instrumentation for e-beam controlled atom-by-atom fabrication. The analysis described in the paper can be reproduced via an interactive Jupyter notebook at https://git.io/JJ3Bx.

Quantifying the Dynamics of Protein Self-Organization Using Deep Learning Analysis of Atomic Force Microscopy Data

The dynamics of protein self-assembly on the inorganic surface and the resultant geometric patterns are visualized using high-speed atomic force microscopy. The time dynamics of the classical macroscopic descriptors such as 2D fast Fourier transforms, correlation, and pair distribution functions are explored using the unsupervised linear unmixing, demonstrating the presence of static ordered and dynamic disordered phases and establishing their time dynamics. The deep learning (DL)-based workflow is developed to analyze detailed particle dynamics and explore the evolution of local geometries. Finally, we use a combination of DL feature extraction and mixture modeling to define particle neighborhoods free of physics constraints, allowing for a separation of possible classes of particle behavior and identification of the associated transitions. Overall, this work establishes the workflow for the analysis of the self-organization processes in complex systems from observational data and provides insight into the fundamental mechanisms.

Investigation of the Wastewater Treatment Plant Processes Efficiency Using Statistical Tools

The paper presents modelling of wastewater treatment plant (WWTP) operation work efficiency using a two-stage method based on selected probability distributions and the Monte Carlo method. Calculations were carried out in terms of sewage susceptibility to biodegradability. Pollutant indicators in raw sewage and in sewage after mechanical treatment and biological treatment were analysed: BOD5, COD, total suspended solids (TSS), total nitrogen (TN) and total phosphorus (TP). The compatibility of theoretical and empirical distributions was assessed using the Anderson–Darling test. The best-fitted statistical distributions were selected using Akaike criterion. Performed calculations made it possible to state that out of all proposed methods, the Gaussian mixture model (GMM) for distribution proved to be the best-fitted. Obtained simulation results proved that the statistical tools used in this paper describe the changes of pollutant indicators correctly. The calculations allowed us to state that the proposed calculation method can be an effective tool for predicting the course of subsequent sewage treatment stages. Modelling results can be used to make a reliable assessment of sewage susceptibility to biodegradability expressed by the BOD5/COD, BOD5/TN and BOD5/TP ratios. New data generated this way can be helpful for the assessment of WWTP operation work and for preparing different possible scenarios for their operation.

Image Restoration via Simultaneous Nonlocal Self-Similarity Priors

Through exploiting the image nonlocal self-similarity (NSS) prior by clustering similar patches to construct patch groups, recent studies have revealed that structural sparse representation (SSR) models can achieve promising performance in various image restoration tasks. However, most existing SSR methods only exploit the NSS prior from the input degraded (internal) image, and few methods utilize the NSS prior from external clean image corpus; how to jointly exploit the NSS priors of internal image and external clean image corpus is still an open problem. In this paper, we propose a novel approach for image restoration by simultaneously considering internal and external nonlocal self-similarity (SNSS) priors that offer mutually complementary information. Specifically, we first group nonlocal similar patches from images of a training corpus. Then a group-based Gaussian mixture model (GMM) learning algorithm is applied to learn an external NSS prior. We exploit the SSR model by integrating the NSS priors of both internal and external image data. An alternating minimization with an adaptive parameter adjusting strategy is developed to solve the proposed SNSS-based image restoration problems, which makes the entire algorithm more stable and practical. Experimental results on three image restoration applications, namely image denoising, deblocking and deblurring, demonstrate that the proposed SNSS produces superior results compared to many popular or state-of-the-art methods in both objective and perceptual quality measurements.

Super-Resolution of Optical Coherence Tomography Images by Scale Mixture Models

In this paper, a new statistical model is proposed for the single image super-resolution of retinal Optical Coherence Tomography (OCT) images. OCT imaging relies on interfero-metry, which explains why OCT images suffer from a high level of noise. Moreover, data subsampling is carried out during the acquisition of OCT A-scans and B-scans. So, it is necessary to utilize effective super-resolution algorithms to reconstruct high-resolution clean OCT images. In this paper, a nonlocal sparse model-based Bayesian framework is proposed for OCT restoration. For this reason, by characterizing nonlocal patches with similar structures, known as a group, the sparse coefficients of each group of OCT images are modeled by the scale mixture models. In this base, the coefficient vector is decomposed into the point-wise product of a random vector and a positive scaling variable. Estimation of the sparse coefficients depends on the proposed distribution for the random vector and scaling variable where the Laplacian random vector and Generalized Extreme-Value (GEV) scale parameter (Laplacian+GEV model) show the best goodness of fit for each group of OCT images. Finally, a new OCT super-resolution method based on this new scale mixture model is introduced, where the maximum a posterior estimation of both sparse coefficients and scaling variables are calculated efficiently by applying an alternating minimization method. Our experimental results prove that the proposed OCT super-resolution method based on the Laplacian+GEV model outperforms other competing methods in terms of both subjective and objective visual qualities.

Local conformational dynamics regulating transport properties of a Cl- /H+ antiporter

ClC-ec1 is a Cl- /H+ antiporter that exchanges Cl- and H+ ions across the membrane. Experiments have demonstrated that several mutations, including I109F, decrease the Cl- and H+ transport rates by an order of magnitude. Using reactive molecular dynamics simulations of explicit proton transport across the central region in the I109F mutant, a two-dimensional free energy profile has been constructed that is consistent with the experimental transport rates. The importance of a phenylalanine gate formed by F109 and F357 and its influence on hydration connectivity through the central proton transport pathway is revealed. This work demonstrates how seemingly subtle changes in local conformational dynamics can dictate hydration changes and thus transport properties. © 2019 Wiley Periodicals, Inc.

Efficient inexact proximal gradient algorithms for structured sparsity-inducing norm

Structured-sparsity regularization is popular for sparse learning because of its flexibility of encoding the feature structures. This paper considers a generalized version of structured-sparsity regularization (especially for l₁∕l_∞ norm) with arbitrary group overlap. Due to the group overlap, it is time-consuming to solve the associated proximal operator. Although Mairal et al. have proposed a network-flow algorithm to solve the proximal operator, it is still time-consuming, especially in the high-dimensional setting. To address this challenge, in this paper, we have developed a more efficient solution for l₁∕l_∞ group lasso with arbitrary group overlap using inexact proximal gradient method. In each iteration, our algorithm only requires to calculate an inexact solution to the proximal sub-problem, which can be done efficiently. On the theoretic side, the proposed algorithm enjoys the same global convergence rate as the exact proximal methods. Experiments demonstrate that our algorithm is much more efficient than the network-flow algorithm while retaining similar generalization performance.

Denoising Prior Driven Deep Neural Network for Image Restoration

Deep neural networks (DNNs) have shown very promising results for various image restoration (IR) tasks. However, the design of network architectures remains a major challenging for achieving further improvements. While most existing DNN-based methods solve the IR problems by directly mapping low quality images to desirable high-quality images, the observation models characterizing the image degradation processes have been largely ignored. In this paper, we first propose a denoising-based IR algorithm, whose iterative steps can be computed efficiently. Then, the iterative process is unfolded into a deep neural network, which is composed of multiple denoisers modules interleaved with back-projection (BP) modules that ensure the observation consistencies. A convolutional neural network (CNN) based denoiser that can exploit the multi-scale redundancies of natural images is proposed. As such, the proposed network not only exploits the powerful denoising ability of DNNs, but also leverages the prior of the observation model. Through end-to-end training, both the denoisers and the BP modules can be jointly optimized. Experimental results on several IR tasks, e.g., image denoisig, super-resolution and deblurring show that the proposed method can lead to very competitive and often state-of-the-art results on several IR tasks, including image denoising, deblurring, and super-resolution.

Survey of Deep-Learning Approaches for Remote Sensing Observation Enhancement

Deep Learning, and Deep Neural Networks in particular, have established themselves as the new norm in signal and data processing, achieving state-of-the-art performance in image, audio, and natural language understanding. In remote sensing, a large body of research has been devoted to the application of deep learning for typical supervised learning tasks such as classification. Less yet equally important effort has also been allocated to addressing the challenges associated with the enhancement of low-quality observations from remote sensing platforms. Addressing such channels is of paramount importance, both in itself, since high-altitude imaging, environmental conditions, and imaging systems trade-offs lead to low-quality observation, as well as to facilitate subsequent analysis, such as classification and detection. In this paper, we provide a comprehensive review of deep-learning methods for the enhancement of remote sensing observations, focusing on critical tasks including single and multi-band super-resolution, denoising, restoration, pan-sharpening, and fusion, among others. In addition to the detailed analysis and comparison of recently presented approaches, different research avenues which could be explored in the future are also discussed.

A Feasibility Study of Extracting Tissue Textures From a Previous Full-Dose CT Database as Prior Knowledge for Bayesian Reconstruction of Current Low-Dose CT Images

Markov random field (MRF) has been widely used to incorporate a priori knowledge as penalty or regularizer to preserve edge sharpness while smoothing the region enclosed by the edge for pieces-wise smooth image reconstruction. In our earlier study, we proposed a type of MRF reconstruction method for low-dose CT (LdCT) scans using tissue-specific textures extracted from the same patient's previous full-dose CT (FdCT) scans as prior knowledge. It showed advantages in clinical applications. This paper aims to remove the constraint of using previous data of the same patient. We investigated the feasibility of extracting the tissue-specific MRF textures from an FdCT database to reconstruct a LdCT image of another patient. This feasibility study was carried out by experiments designed as follows. We constructed a tissue-specific MRF-texture database from 3990 FdCT scan slices of 133 patients who were scheduled for lung nodule biopsy. Each patient had one FdCT scan (120 kVp/100 mAs) and one LdCT scan (120 kVp/20 mAs) prior to biopsy procedure. When reconstructing the LdCT image of one patient among the 133 patients, we ranked the closeness of the MRF-textures from the other 132 patients saved in the database and used them as the a prior knowledge. Then, we evaluated the reconstructed image quality using Haralick texture measures. For any patient within our database, we found more than eighteen patients' FdCT MRF texures can be used without noticeably changing the Haralick texture measures on the lung nodules (to be biopsied). These experimental outcomes indicate it is promising that a sizable FdCT texture database could be used to enhance Bayesian reconstructions of any incoming LdCT scans.

Super-resolution reconstruction of neonatal brain magnetic resonance images via residual structured sparse representation

Magnetic resonance images of neonates, compared with toddlers, exhibit lower signal-to-noise ratio and spatial resolution. In this paper, we propose a novel method for super-resolution reconstruction of neonate images with the help of toddler images, using residual-structured sparse representation with convex regularization. Specifically, we introduce a two-layer image representation, consisting of a base layer and a detail layer, to cater to signal variation across scanners and sites. The base layer consists of the smoothed version of the image obtained via Gaussian filtering. The detail layer is the difference between the original image and the base layer. High-frequency details in the detail layer are borrowed across subjects for super-resolution reconstruction. Experimental results on T1 and T2 images demonstrate that the proposed algorithm can recover fine anatomical structures, and generally outperform the state-of-the-art methods both qualitatively and quantitatively.

Application of the Mathematical Simulation Methods for the Assessment of the Wastewater Treatment Plant Operation Work Reliability

The aim of the present work was the modeling of the wastewater treatment plant operation work using Monte Carlo method and different random variables probability distributions modeling. The analysis includes the following pollutants indicators; BOD5 (Biochemical Oxygen Demand), CODCr (Chemical Oxygen Demand), Total Suspended Solids (SSt), Total Nitrogen (TN), and Total Phosphorus (TP). The Anderson–Darling (A–D) test was used for the assessment of theoretical and empirical distributions compatibility. The selection of the best-fitting statistical distributions was performed using peak-weighted root mean square (PWRMSE) parameter. Based on the performed calculations, it was stated that pollutants indicators in treated sewage were characterized by a significant variability. Obtained results indicate that the best-fitting pollutants indicators statistical distribution is Gauss Mixed Model (GMM) function. The results of the Monte Carlo simulation method confirmed that some problems related to the organic and biogenic pollutants reduction may be observed in the Wastewater Treatment Plant, in Jaworzno.

Longitudinally Guided Super-Resolution of Neonatal Brain Magnetic Resonance Images

Neonatal magnetic resonance (MR) images typically have low spatial resolution and insufficient tissue contrast. Interpolation methods are commonly used to upsample the images for the subsequent analysis. However, the resulting images are often blurry and susceptible to partial volume effects. In this paper, we propose a novel longitudinally guided super-resolution (SR) algorithm for neonatal images. This is motivated by the fact that anatomical structures evolve slowly and smoothly as the brain develops after birth. We propose a strategy involving longitudinal regularization, similar to bilateral filtering, in combination with low-rank and total variation constraints to solve the ill-posed inverse problem associated with image SR. Experimental results on neonatal MR images demonstrate that the proposed algorithm recovers clear structural details and outperforms state-of-the-art methods both qualitatively and quantitatively.

Accelerating GMM-Based Patch Priors for Image Restoration: Three Ingredients for a Speed-Up

Image restoration methods aim to recover the underlying clean image from corrupted observations. The expected patch log-likelihood (EPLL) algorithm is a powerful image restoration method that uses a Gaussian mixture model (GMM) prior on the patches of natural images. Although it is very effective for restoring images, its high runtime complexity makes the EPLL ill-suited for most practical applications. In this paper, we propose three approximations to the original EPLL algorithm. The resulting algorithm, which we call the fast-EPLL (FEPLL), attains a dramatic speed-up of two orders of magnitude over EPLL while incurring a negligible drop in the restored image quality (less than 0.5 dB). We demonstrate the efficacy and versatility of our algorithm on a number of inverse problems, such as denoising, deblurring, super-resolution, inpainting, and devignetting. To the best of our knowledge, the FEPLL is the first algorithm that can competitively restore a pixel image in under 0.5 s for all the degradations mentioned earlier without specialized code optimizations, such as CPU parallelization or GPU implementation.

Low-Dose Computed Tomography Image Super-Resolution Reconstruction via Random Forests

Aiming at reducing computed tomography (CT) scan radiation while ensuring CT image quality, a new low-dose CT super-resolution reconstruction method based on combining a random forest with coupled dictionary learning is proposed. The random forest classifier finds the optimal solution of the mapping relationship between low-dose CT (LDCT) images and high-dose CT (HDCT) images and then completes CT image reconstruction by coupled dictionary learning. An iterative method is developed to improve robustness, the important coefficients for the tree structure are discussed and the optimal solutions are reported. The proposed method is further compared with a traditional interpolation method. The results show that the proposed algorithm can obtain a higher peak signal-to-noise ratio (PSNR) and structural similarity index measurement (SSIM) and has better ability to reduce noise and artifacts. This method can be applied to many different medical imaging fields in the future and the addition of computer multithreaded computing can reduce time consumption.

Single Image Super-Resolution via Multiple Mixture Prior Models

Example learning-based single image super-resolution (SR) is a promising method for reconstructing a high-resolution (HR) image from a single-input low-resolution (LR) image. Lots of popular SR approaches are more likely either time-or space-intensive, which limit their practical applications. Hence, some research has focused on a subspace view and delivered state-of-the-art results. In this paper, we utilize an effective way with mixture prior models to transform the large nonlinear feature space of LR images into a group of linear subspaces in the training phase. In particular, we first partition image patches into several groups by a novel selective patch processing method based on difference curvature of LR patches, and then learning the mixture prior models in each group. Moreover, different prior distributions have various effectiveness in SR, and in this case, we find that student-t prior shows stronger performance than the well-known Gaussian prior. In the testing phase, we adopt the learned multiple mixture prior models to map the input LR features into the appropriate subspace, and finally reconstruct the corresponding HR image in a novel mixed matching way. Experimental results indicate that the proposed approach is both quantitatively and qualitatively superior to some state-of-the-art SR methods.

A Non-Local Dual-Domain Approach to Cartoon and Texture Decomposition

This paper addresses the problem of cartoon and texture decomposition. Microtextures being characterized by their power spectrum, we propose to extract cartoon and texture components from the information provided by the power spectrum of image patches. The contribution of texture to the spectrum of a patch is detected as statistically significant spectral components with respect to a null hypothesis modeling the power spectrum of a non-textured patch. The null-hypothesis model is built upon a coarse cartoon representation obtained by a basic yet fast filtering algorithm of the literature. Hence the term "dual domain": the coarse decomposition is obtained in the spatial domain and is an input of the proposed spectral approach. The statistical model is also built upon the power spectrum of patches with similar textures across the image. The proposed approach therefore falls within the family of non-local methods. Experimental results are shown in various application areas, including canvas pattern removal in fine arts painting, or periodic noise removal in remote sensing imaging.

Learning Converged Propagations with Deep Prior Ensemble for Image Enhancement

Enhancing visual qualities of images plays very important roles in various vision and learning applications. In the past few years, both knowledge-driven maximum a posterior (MAP) with prior modelings and fully data-dependent convolutional neural network (CNN) techniques have been investigated to address specific enhancement tasks. In this paper, by exploiting the advantages of these two types of mechanisms within a complementary propagation perspective, we propose a unified framework, named deep prior ensemble (DPE), for solving various image enhancement tasks. Specifically, we first establish the basic propagation scheme based on the fundamental image modeling cues and then introduce residual CNNs to help predicting the propagation direction at each stage. By designing prior projections to perform feedback control, we theoretically prove that even with experience-inspired CNNs, DPE is definitely converged and the output will always satisfy our fundamental task constraints. The main advantage against conventional optimization-based MAP approaches is that our descent directions are learned from collected training data, thus are much more robust to unwanted local minimums. While, compared with existing CNN type networks, which are often designed in heuristic manners without theoretical guarantees, DPE is able to gain advantages from rich task cues investigated on the bases of domain knowledges. Therefore, DPE actually provides a generic ensemble methodology to integrate both knowledge and data-based cues for different image enhancement tasks. More importantly, our theoretical investigations verify that the feedforward propagations of DPE are properly controlled toward our desired solution. Experimental results demonstrate that the proposed DPE outperforms state-of-the-arts on a variety of image enhancement tasks in terms of both quantitative measure and visual perception quality.

A Convergent Image Fusion Algorithm Using Scene-Adapted Gaussian-Mixture-Based Denoising

We propose a new approach to image fusion, inspired by the recent plug-and-play (PnP) framework. In PnP, a denoiser is treated as a black-box and plugged into an iterative algorithm, taking the place of the proximity operator of some convex regularizer, which is formally equivalent to a denoising operation. This approach offers flexibility and excellent performance, but convergence may be hard to analyze, as most state-of-the-art denoisers lack an explicit underlying objective function. Here, we propose using a scene-adapted denoiser (i.e., targeted to the specific scene being imaged) plugged into the iterations of the alternating direction method of multipliers (ADMM). This approach, which is a natural choice for image fusion problems, not only yields state-of-the-art results, but it also allows proving convergence of the resulting algorithm. The proposed method is tested on two different problems: hyperspectral fusion/sharpening and fusion of blurred-noisy image pairs.

Automatic computer aided analysis algorithms and system for adrenal tumors on CT images

BACKGROUND

The adrenal tumor will disturb the secreting function of adrenocortical cells, leading to many diseases. Different kinds of adrenal tumors require different therapeutic schedules.

OBJECTIVE

In the practical diagnosis, it highly relies on the doctor's experience to judge the tumor type by reading the hundreds of CT images.

METHODS

This paper proposed an automatic computer aided analysis method for adrenal tumors detection and classification. It consisted of the automatic segmentation algorithms, the feature extraction and the classification algorithms. These algorithms were then integrated into a system and conducted on the graphic interface by using MATLAB Graphic user interface (GUI).

RESULTS

The accuracy of the automatic computer aided segmentation and classification reached 90% on 436 CT images.

CONCLUSION

The experiments proved the stability and reliability of this automatic computer aided analytic system.

Quantum transport senses community structure in networks

Quantum time evolution exhibits rich physics, attributable to the interplay between the density and phase of a wave function. However, unlike classical heat diffusion, the wave nature of quantum mechanics has not yet been extensively explored in modern data analysis. We propose that the Laplace transform of quantum transport (QT) can be used to construct an ensemble of maps from a given complex network to a circle S^{1}, such that closely related nodes on the network are grouped into sharply concentrated clusters on S^{1}. The resulting QT clustering (QTC) algorithm is as powerful as the state-of-the-art spectral clustering in discerning complex geometric patterns and more robust when clusters show strong density variations or heterogeneity in size. The observed phenomenon of QTC can be interpreted as a collective behavior of the microscopic nodes that evolve as macroscopic cluster "orbitals" in an effective tight-binding model recapitulating the network. python source code implementing the algorithm and examples are available at https://github.com/jssong-lab/QTC.

Class-Aware Fully-Convolutional Gaussian and Poisson Denoising

We propose a fully-convolutional neural-network architecture for image denoising which is simple yet powerful. Its structure allows to exploit the gradual nature of the denoising process, in which shallow layers handle local noise statistics, while deeper layers recover edges and enhance textures. Our method advances the state-of-the-art when trained for different noise levels and distributions (both Gaussian and Poisson). In addition, we show that making the denoiser class-aware by exploiting semantic class information boosts performance, enhances textures and reduces artifacts.

Global Low-Rank Image Restoration With Gaussian Mixture Model

Low-rank restoration has recently attracted a lot of attention in the research of computer vision. Empirical studies show that exploring the low-rank property of the patch groups can lead to superior restoration performance, however, there is limited achievement on the global low-rank restoration because the rank minimization at image level is too strong for the natural images which seldom match the low-rank condition. In this paper, we describe a flexible global low-rank restoration model which introduces the local statistical properties into the rank minimization. The proposed model can effectively recover the latent global low-rank structure via nuclear norm, as well as the fine details via Gaussian mixture model. An alternating scheme is developed to estimate the Gaussian parameters and the restored image, and it shows excellent convergence and stability. Besides, experiments on image and video sequence datasets show the effectiveness of the proposed method in image inpainting problems.

Image Super-resolution with Parametric Sparse Model Learning

Recovering a high-resolution (HR) image from its low-resolution (LR) version is an ill-posed inverse problem. Learning accurate prior of HR images is of great importance to solve this inverse problem. Existing super-resolution (SR) methods either learn a non-parametric image prior from training data (a large set of LR/HR patch pairs) or estimate a parametric prior from the LR image analytically. Both methods have their limitations: the former lacks flexibility when dealing with different SR settings; while the latter often fails to adapt to spatially varying image structures. In this paper, we propose to take a hybrid approach toward image SR by combining those two lines of ideas - that is, a parametric sparse prior of HR images is learned from the training set as well as the input LR image. By exploiting the strengths of both worlds, we can more accurately recover the sparse codes and therefore HR image patches than conventional sparse coding approaches. Experimental results show that the proposed hybrid SR method significantly outperforms existing model-based SR methods and is highly competitive to current state-of-the-art learning-based SR methods in terms of both subjective and objective image qualities.

Training Very Deep CNNs for General Non-Blind Deconvolution

Non-blind image deconvolution is an ill-posed problem. The presence of noise and band-limited blur kernels makes the solution of this problem non-unique. Existing deconvolution techniques produce a residual between the sharp image and the estimation that is highly correlated with the sharp image, the kernel, and the noise. In most cases, different restoration models must be constructed for different blur kernels and different levels of noise, resulting in low computational efficiency or highly redundant model parameters. Here we aim to develop a single model that handles different types of kernels and different levels of noise: general non-blind deconvolution. Specifically, we propose a very deep convolutional neural network that predicts the residual between a pre-deconvolved image and the sharp image rather than the sharp image. The residual learning strategy makes it easier to train a single model for different kernels and different levels of noise, encouraging high effectiveness and efficiency. Quantitative evaluations demonstrate the practical applicability of the proposed model for different blur kernels. The model also shows state-of-the-art performance on synthesized blurry images.

Sparse and Low-Rank Decomposition of a Hankel Structured Matrix for Impulse Noise Removal

Recently, the annihilating filter-based low-rank Hankel matrix (ALOHA) approach was proposed as a powerful image inpainting method. Based on the observation that smoothness or textures within an image patch correspond to sparse spectral components in the frequency domain, ALOHA exploits the existence of annihilating filters and the associated rank-deficient Hankel matrices in an image domain to estimate any missing pixels. By extending this idea, we propose a novel impulse-noise removal algorithm that uses the sparse and low-rank decomposition of a Hankel structured matrix. This method, referred to as the robust ALOHA, is based on the observation that an image corrupted with the impulse noise has intact pixels; consequently, the impulse noise can be modeled as sparse components, whereas the underlying image can still be modeled using a low-rank Hankel structured matrix. To solve the sparse and low-rank matrix decomposition problem, we propose an alternating direction method of multiplier approach, with initial factorized matrices coming from a low-rank matrix-fitting algorithm. To adapt local image statistics that have distinct spectral distributions, the robust ALOHA is applied in a patch-by-patch manner. Experimental results from impulse noise for both single-channel and multichannel color images demonstrate that the robust ALOHA is superior to existing approaches, especially during the reconstruction of complex texture patterns.