From Rank Estimation to Rank Approximation: Rank Residual Constraint for Image Restoration

Unsupervised Degradation Representation Learning for Unpaired Restoration of Images and Point Clouds

Restoration tasks in low-level vision aim to restore high-quality (HQ) data from their low-quality (LQ) observations. To circumvents the difficulty of acquiring paired data in real scenarios, unpaired approaches that aim to restore HQ data solely on unpaired data are drawing increasing interest. Since restoration tasks are tightly coupled with the degradation model, unknown and highly diverse degradations in real scenarios make learning from unpaired data quite challenging. In this paper, we propose a degradation representation learning scheme to address this challenge. By learning to distinguish various degradations in the representation space, our degradation representations can extract implicit degradation information in an unsupervised manner. Moreover, to handle diverse degradations, we develop degradation-aware (DA) convolutions with flexible adaption to various degradations to fully exploit the degrdation information in the learned representations. Based on our degradation representations and DA convolutions, we introduce a generic framework for unpaired restoration tasks. Based on our framework, we propose UnIRnet and UnPRnet for unpaired image and point cloud restoration tasks, respectively. It is demonstrated that our degradation representation learning scheme can extract discriminative representations to obtain accurate degradation information. Experiments on unpaired image and point cloud restoration tasks show that our UnIRnet and UnPRnet achieve state-of-the-art performance.

The Impact of Noise and Brightness on Object Detection Methods

The application of deep learning to image and video processing has become increasingly popular nowadays. Employing well-known pre-trained neural networks for detecting and classifying objects in images is beneficial in a wide range of application fields. However, diverse impediments may degrade the performance achieved by those neural networks. Particularly, Gaussian noise and brightness, among others, may be presented on images as sensor noise due to the limitations of image acquisition devices. In this work, we study the effect of the most representative noise types and brightness alterations on images in the performance of several state-of-the-art object detectors, such as YOLO or Faster-RCNN. Different experiments have been carried out and the results demonstrate how these adversities deteriorate their performance. Moreover, it is found that the size of objects to be detected is a factor that, together with noise and brightness factors, has a considerable impact on their performance.

Natural image restoration based on multi-scale group sparsity residual constraints

The Group Sparse Representation (GSR) model shows excellent potential in various image restoration tasks. In this study, we propose a novel Multi-Scale Group Sparse Residual Constraint Model (MS-GSRC) which can be applied to various inverse problems, including denoising, inpainting, and compressed sensing (CS). Our new method involves the following three steps: (1) finding similar patches with an overlapping scheme for the input degraded image using a multi-scale strategy, (2) performing a group sparse coding on these patches with low-rank constraints to get an initial representation vector, and (3) under the Bayesian maximum a posteriori (MAP) restoration framework, we adopt an alternating minimization scheme to solve the corresponding equation and reconstruct the target image finally. Simulation experiments demonstrate that our proposed model outperforms in terms of both objective image quality and subjective visual quality compared to several state-of-the-art methods.

Low-Rankness Guided Group Sparse Representation for Image Restoration

As a spotlighted nonlocal image representation model, group sparse representation (GSR) has demonstrated a great potential in diverse image restoration tasks. Most of the existing GSR-based image restoration approaches exploit the nonlocal self-similarity (NSS) prior by clustering similar patches into groups and imposing sparsity to each group coefficient, which can effectively preserve image texture information. However, these methods have imposed only plain sparsity over each individual patch of the group, while neglecting other beneficial image properties, e.g., low-rankness (LR), leads to degraded image restoration results. In this article, we propose a novel low-rankness guided group sparse representation (LGSR) model for highly effective image restoration applications. The proposed LGSR jointly utilizes the sparsity and LR priors of each group of similar patches under a unified framework. The two priors serve as the complementary priors in LGSR for effectively preserving the texture and structure information of natural images. Moreover, we apply an alternating minimization algorithm with an adaptively adjusted parameter scheme to solve the proposed LGSR-based image restoration problem. Extensive experiments are conducted to demonstrate that the proposed LGSR achieves superior results compared with many popular or state-of-the-art algorithms in various image restoration tasks, including denoising, inpainting, and compressive sensing (CS).

ADCoC: Adaptive Distribution Modeling Based Collaborative Clustering for Disentangling Disease Heterogeneity from Neuroimaging Data

Conventional clustering techniques for neuroimaging applications usually focus on capturing differences between given subjects, while neglecting arising differences between features and the potential bias caused by degraded data quality. In practice, collected neuroimaging data are often inevitably contaminated by noise, which may lead to errors in clustering and clinical interpretation. Additionally, most methods ignore the importance of feature grouping towards optimal clustering. In this paper, we exploit the underlying heterogeneous clusters of features to serve as weak supervision for improved clustering of subjects, which is achieved by simultaneously clustering subjects and features via nonnegative matrix tri-factorization. In order to suppress noise, we further introduce adaptive regularization based on coefficient distribution modeling. Particularly, unlike conventional sparsity regularization techniques that assume zero mean of the coefficients, we form the distributions using the data of interest so that they could better fit the non-negative coefficients. In this manner, the proposed approach is expected to be more effective and robust against noise. We compared the proposed method with standard techniques and recently published methods demonstrating superior clustering performance on synthetic data with known ground truth labels. Furthermore, when applying our proposed technique to magnetic resonance imaging (MRI) data from a cohort of patients with Parkinson's disease, we identified two stable and highly reproducible patient clusters characterized by frontal and posterior cortical/medial temporal atrophy patterns, respectively, which also showed corresponding differences in cognitive characteristics.

Sparse Representation-Based Multi-Focus Image Fusion Method via Local Energy in Shearlet Domain

Multi-focus image fusion plays an important role in the application of computer vision. In the process of image fusion, there may be blurring and information loss, so it is our goal to obtain high-definition and information-rich fusion images. In this paper, a novel multi-focus image fusion method via local energy and sparse representation in the shearlet domain is proposed. The source images are decomposed into low- and high-frequency sub-bands according to the shearlet transform. The low-frequency sub-bands are fused by sparse representation, and the high-frequency sub-bands are fused by local energy. The inverse shearlet transform is used to reconstruct the fused image. The Lytro dataset with 20 pairs of images is used to verify the proposed method, and 8 state-of-the-art fusion methods and 8 metrics are used for comparison. According to the experimental results, our method can generate good performance for multi-focus image fusion.

Nonconvex Structural Sparsity Residual Constraint for Image Restoration

This article proposes a novel nonconvex structural sparsity residual constraint (NSSRC) model for image restoration, which integrates structural sparse representation (SSR) with nonconvex sparsity residual constraint (NC-SRC). Although SSR itself is powerful for image restoration by combining the local sparsity and nonlocal self-similarity in natural images, in this work, we explicitly incorporate the novel NC-SRC prior into SSR. Our proposed approach provides more effective sparse modeling for natural images by applying a more flexible sparse representation scheme, leading to high-quality restored images. Moreover, an alternating minimizing framework is developed to solve the proposed NSSRC-based image restoration problems. Extensive experimental results on image denoising and image deblocking validate that the proposed NSSRC achieves better results than many popular or state-of-the-art methods over several publicly available datasets.

A Hybrid Structural Sparsification Error Model for Image Restoration

Recent works on structural sparse representation (SSR), which exploit image nonlocal self-similarity (NSS) prior by grouping similar patches for processing, have demonstrated promising performance in various image restoration applications. However, conventional SSR-based image restoration methods directly fit the dictionaries or transforms to the internal (corrupted) image data. The trained internal models inevitably suffer from overfitting to data corruption, thus generating the degraded restoration results. In this article, we propose a novel hybrid structural sparsification error (HSSE) model for image restoration, which jointly exploits image NSS prior using both the internal and external image data that provide complementary information. Furthermore, we propose a general image restoration scheme based on the HSSE model, and an alternating minimization algorithm for a range of image restoration applications, including image inpainting, image compressive sensing and image deblocking. Extensive experiments are conducted to demonstrate that the proposed HSSE-based scheme outperforms many popular or state-of-the-art image restoration methods in terms of both objective metrics and visual perception.

SMDS-Net: Model Guided Spectral-Spatial Network for Hyperspectral Image Denoising

Deep learning (DL) based hyperspectral images (HSIs) denoising approaches directly learn the nonlinear mapping between noisy and clean HSI pairs. They usually do not consider the physical characteristics of HSIs. This drawback makes the models lack interpretability that is key to understanding their denoising mechanism and limits their denoising ability. In this paper, we introduce a novel model-guided interpretable network for HSI denoising to tackle this problem. Fully considering the spatial redundancy, spectral low-rankness, and spectral-spatial correlations of HSIs, we first establish a subspace-based multidimensional sparse (SMDS) model under the umbrella of tensor notation. After that, the model is unfolded into an end-to-end network named SMDS-Net, whose fundamental modules are seamlessly connected with the denoising procedure and optimization of the SMDS model. This makes SMDS-Net convey clear physical meanings, i.e., learning the low-rankness and sparsity of HSIs. Finally, all key variables are obtained by discriminative training. Extensive experiments and comprehensive analysis on synthetic and real-world HSIs confirm the strong denoising ability, strong learning capability, promising generalization ability, and high interpretability of SMDS-Net against the state-of-the-art HSI denoising methods. The source code and data of this article will be made publicly available at https://github.com/bearshng/smds-net for reproducible research.

Toward Efficient Direct Dynamics Studies of Chemical Reactions: A Novel Matrix Completion Algorithm

This paper describes the development and testing of a polynomial variety-based matrix completion (PVMC) algorithm. Our goal is to reduce computational effort associated with reaction rate coefficient calculations using variational transition state theory with multidimensional tunneling (VTST-MT). The algorithm recovers eigenvalues of quantum mechanical Hessians constituting the minimum energy path (MEP) of a reaction using only a small sample of the information, by leveraging underlying properties of these eigenvalues. In addition to the low-rank property that constitutes the basis for most matrix completion (MC) algorithms, this work introduces a polynomial constraint in the objective function. This enables us to sample matrix columns unlike most conventional MC methods that can only sample elements, which makes PVMC readily compatible with quantum chemistry calculations as sampling a single column requires one Hessian calculation. For various types of reactions─S_N2, hydrogen atom transfer, metal-ligand cooperative catalysis, and enzyme chemistry─we demonstrate that PVMC on average requires only six to seven Hessian calculations to accurately predict both quantum and variational effects.

Self-Supervised Nonlinear Transform-Based Tensor Nuclear Norm for Multi-Dimensional Image Recovery

Recently, transform-based tensor nuclear norm (TNN) minimization methods have received increasing attention for recovering third-order tensors in multi-dimensional imaging problems. The main idea of these methods is to perform the linear transform along the third mode of third-order tensors and then minimize the nuclear norm of frontal slices of the transformed tensor. The main aim of this paper is to propose a nonlinear multilayer neural network to learn a nonlinear transform by solely using the observed tensor in a self-supervised manner. The proposed network makes use of the low-rank representation of the transformed tensor and data-fitting between the observed tensor and the reconstructed tensor to learn the nonlinear transform. Extensive experimental results on different data and different tasks including tensor completion, background subtraction, robust tensor completion, and snapshot compressive imaging demonstrate the superior performance of the proposed method over state-of-the-art methods.

BPGAN: Brain PET synthesis from MRI using generative adversarial network for multi-modal Alzheimer's disease diagnosis

BACKGROUND AND OBJECTIVE

Multi-modal medical images, such as magnetic resonance imaging (MRI) and positron emission tomography (PET), have been widely used for the diagnosis of brain disorder diseases like Alzheimer's disease (AD) since they can provide various information. PET scans can detect cellular changes in organs and tissues earlier than MRI. Unlike MRI, PET data is difficult to acquire due to cost, radiation, or other limitations. Moreover, PET data is missing for many subjects in the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset. To solve this problem, a 3D end-to-end generative adversarial network (named BPGAN) is proposed to synthesize brain PET from MRI scans, which can be used as a potential data completion scheme for multi-modal medical image research.

METHODS

We propose BPGAN, which learns an end-to-end mapping function to transform the input MRI scans to their underlying PET scans. First, we design a 3D multiple convolution U-Net (MCU) generator architecture to improve the visual quality of synthetic results while preserving the diverse brain structures of different subjects. By further employing a 3D gradient profile (GP) loss and structural similarity index measure (SSIM) loss, the synthetic PET scans have higher-similarity to the ground truth. In this study, we explore alternative data partitioning ways to study their impact on the performance of the proposed method in different medical scenarios.

RESULTS

We conduct experiments on a publicly available ADNI database. The proposed BPGAN is evaluated by mean absolute error (MAE), peak-signal-to-noise-ratio (PSNR) and SSIM, superior to other compared models in these quantitative evaluation metrics. Qualitative evaluations also validate the effectiveness of our approach. Additionally, combined with MRI and our synthetic PET scans, the accuracies of multi-class AD diagnosis on dataset-A and dataset-B are 85.00% and 56.47%, which have been improved by about 1% and 1%, respectively, compared to the stand-alone MRI.

CONCLUSIONS

The experimental results of quantitative measures, qualitative displays, and classification evaluation demonstrate that the synthetic PET images by BPGAN are reasonable and high-quality, which provide complementary information to improve the performance of AD diagnosis. This work provides a valuable reference for multi-modal medical image analysis.

Motion Blur Kernel Rendering Using an Inertial Sensor: Interpreting the Mechanism of a Thermal Detector

Various types of motion blur are frequently observed in the images captured by sensors based on thermal and photon detectors. The difference in mechanisms between thermal and photon detectors directly results in different patterns of motion blur. Motivated by this observation, we propose a novel method to synthesize blurry images from sharp images by analyzing the mechanisms of the thermal detector. Further, we propose a novel blur kernel rendering method, which combines our proposed motion blur model with the inertial sensor in the thermal image domain. The accuracy of the blur kernel rendering method is evaluated by the task of thermal image deblurring. We construct a synthetic blurry image dataset based on acquired thermal images using an infrared camera for evaluation. This dataset is the first blurry thermal image dataset with ground-truth images in the thermal image domain. Qualitative and quantitative experiments are extensively carried out on our dataset, which show that our proposed method outperforms state-of-the-art methods.

Image Stripe Noise Removal Based on Compressed Sensing

The sensors or electronic components are vulnerable to interference in the camera’s imaging process, usually leading to random directional stripes. Therefore, a method of stripe noise removal based on compressed sensing is proposed. First, the measurement matrix of the image with stripe noise is established, which makes the stripe images equivalent to the observation of the original image. Second, the relationships between the corresponding coefficients of adjacent scales are defined. On this basis, the bivariate threshold function is set in the curvelet sparse domain to represent the features of images. Finally, the Landweber iteration algorithm of alternating convex projection and filtering operation is achieved. Furthermore, to accelerate the noise removal at the initial stage of iteration and preserve the image details later, the exponential threshold function is utilized. This method does not need many samples, which is different from the current deep learning method. The experimental results show that the proposed algorithm represents excellent performance in removing the stripes and preserving the texture details. In addition, the PSNR of the denoised image has been dramatically improved compared with similar algorithms.

Simultaneous Patch-Group Sparse Coding with Dual-Weighted ℓp Minimization for Image Restoration

Sparse coding (SC) models have been proven as powerful tools applied in image restoration tasks, such as patch sparse coding (PSC) and group sparse coding (GSC). However, these two kinds of SC models have their respective drawbacks. PSC tends to generate visually annoying blocking artifacts, while GSC models usually produce over-smooth effects. Moreover, conventional ℓ1 minimization-based convex regularization was usually employed as a standard scheme for estimating sparse signals, but it cannot achieve an accurate sparse solution under many realistic situations. In this paper, we propose a novel approach for image restoration via simultaneous patch-group sparse coding (SPG-SC) with dual-weighted ℓp minimization. Specifically, in contrast to existing SC-based methods, the proposed SPG-SC conducts the local sparsity and nonlocal sparse representation simultaneously. A dual-weighted ℓp minimization-based non-convex regularization is proposed to improve the sparse representation capability of the proposed SPG-SC. To make the optimization tractable, a non-convex generalized iteration shrinkage algorithm based on the alternating direction method of multipliers (ADMM) framework is developed to solve the proposed SPG-SC model. Extensive experimental results on two image restoration tasks, including image inpainting and image deblurring, demonstrate that the proposed SPG-SC outperforms many state-of-the-art algorithms in terms of both objective and perceptual quality.

Triply Complementary Priors for Image Restoration

Recent works that utilized deep models have achieved superior results in various image restoration (IR) applications. Such approach is typically supervised, which requires a corpus of training images with distributions similar to the images to be recovered. On the other hand, the shallow methods, which are usually unsupervised remain promising performance in many inverse problems, e.g., image deblurring and image compressive sensing (CS), as they can effectively leverage nonlocal self-similarity priors of natural images. However, most of such methods are patch-based leading to the restored images with various artifacts due to naive patch aggregation in addition to the slow speed. Using either approach alone usually limits performance and generalizability in IR tasks. In this paper, we propose a joint low-rank and deep (LRD) image model, which contains a pair of triply complementary priors, namely, internal and external, shallow and deep, and non-local and local priors. We then propose a novel hybrid plug-and-play (H-PnP) framework based on the LRD model for IR. Following this, a simple yet effective algorithm is developed to solve the proposed H-PnP based IR problems. Extensive experimental results on several representative IR tasks, including image deblurring, image CS and image deblocking, demonstrate that the proposed H-PnP algorithm achieves favorable performance compared to many popular or state-of-the-art IR methods in terms of both objective and visual perception.

Image Restoration via Reconciliation of Group Sparsity and Low-Rank Models

Image nonlocal self-similarity (NSS) property has been widely exploited via various sparsity models such as joint sparsity (JS) and group sparse coding (GSC). However, the existing NSS-based sparsity models are either too restrictive, e.g., JS enforces the sparse codes to share the same support, or too general, e.g., GSC imposes only plain sparsity on the group coefficients, which limit their effectiveness for modeling real images. In this paper, we propose a novel NSS-based sparsity model, namely, low-rank regularized group sparse coding (LR-GSC), to bridge the gap between the popular GSC and JS. The proposed LR-GSC model simultaneously exploits the sparsity and low-rankness of the dictionary-domain coefficients for each group of similar patches. An alternating minimization with an adaptive adjusted parameter strategy is developed to solve the proposed optimization problem for different image restoration tasks, including image denoising, image deblocking, image inpainting, and image compressive sensing. Extensive experimental results demonstrate that the proposed LR-GSC algorithm outperforms many popular or state-of-the-art methods in terms of objective and perceptual metrics.

Weighted Schatten p-Norm Low Rank Error Constraint for Image Denoising

Traditional image denoising algorithms obtain prior information from noisy images that are directly based on low rank matrix restoration, which pays little attention to the nonlocal self-similarity errors between clear images and noisy images. This paper proposes a new image denoising algorithm based on low rank matrix restoration in order to solve this problem. The proposed algorithm introduces the non-local self-similarity error between the clear image and noisy image into the weighted Schatten p-norm minimization model using the non-local self-similarity of the image. In addition, the low rank error is constrained by using Schatten p-norm to obtain a better low rank matrix in order to improve the performance of the image denoising algorithm. The results demonstrate that, on the classic data set, when comparing with block matching 3D filtering (BM3D), weighted nuclear norm minimization (WNNM), weighted Schatten p-norm minimization (WSNM), and FFDNet, the proposed algorithm achieves a higher peak signal-to-noise ratio, better denoising effect, and visual effects with improved robustness and generalization.

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.