Multilayer Sparsity-Based Tensor Decomposition for Low-Rank Tensor Completion

Semi-supervised non-negative matrix factorization with structure preserving for image clustering

Semi-supervised learning methods have wide applications thanks to the reasonable utilization for a part of label information of data. In recent years, non-negative matrix factorization (NMF) has received considerable attention because of its interpretability and practicality. Based on the advantages of semi-supervised learning and NMF, many semi-supervised NMF methods have been presented. However, these existing semi-supervised NMF methods construct a label matrix only containing elements 1 and 0 to represent the labeled data and further construct a label regularization, which neglects an intrinsic structure of NMF. To address the deficiency, in this paper, we propose a novel semi-supervised NMF method with structure preserving. Specifically, we first construct a new label matrix with weights and further construct a label constraint regularizer to both utilize the label information and maintain the intrinsic structure of NMF. Then, based on the label constraint regularizer, the basis images of labeled data are extracted for monitoring and modifying the basis images learning of all data by establishing a basis regularizer. Finally, incorporating the label constraint regularizer and the basis regularizer into NMF, we propose a new semi-supervised NMF method. To solve the optimization problem, a multiplicative updating algorithm is developed. The proposed method is applied to image clustering to test its performance. Experimental results on eight data sets demonstrate the effectiveness of the proposed method in contrast with state-of-the-art unsupervised and semi-supervised algorithms.

Balanced Unfolding Induced Tensor Nuclear Norms for High-Order Tensor Completion

The recently proposed tensor tubal rank has been witnessed to obtain extraordinary success in real-world tensor data completion. However, existing works usually fix the transform orientation along the third mode and may fail to turn multidimensional low-tubal-rank structure into account. To alleviate these bottlenecks, we introduce two unfolding induced tensor nuclear norms (TNNs) for the tensor completion (TC) problem, which naturally extends tensor tubal rank to high-order data. Specifically, we show how multidimensional low-tubal-rank structure can be captured by utilizing a novel balanced unfolding strategy, upon which two TNNs, namely, overlapped TNN (OTNN) and latent TNN (LTNN), are developed. We also show the immediate relationship between the tubal rank of unfolding tensor and the existing tensor network (TN) rank, e.g., CANDECOMP/PARAFAC (CP) rank, Tucker rank, and tensor ring (TR) rank, to demonstrate its efficiency and practicality. Two efficient TC models are then proposed with theoretical guarantees by analyzing a unified nonasymptotic upper bound. To solve optimization problems, we develop two alternating direction methods of multipliers (ADMM) based algorithms. The proposed models have been demonstrated to exhibit superior performance based on experimental findings involving synthetic and real-world tensors, including facial images, light field images, and video sequences.

Hyperspectral image restoration using noise gradient and dual priors under mixed noise conditions

Images obtained from hyperspectral sensors provide information about the target area that extends beyond the visible portions of the electromagnetic spectrum. However, due to sensor limitations and imperfections during the image acquisition and transmission phases, noise is introduced into the acquired image, which can have a negative impact on downstream analyses such as classification, target tracking, and spectral unmixing. Noise in hyperspectral images (HSI) is modelled as a combination from several sources, including Gaussian/impulse noise, stripes, and deadlines. An HSI restoration method for such a mixed noise model is proposed. First, a joint optimisation framework is proposed for recovering hyperspectral data corrupted by mixed Gaussian‐impulse noise by estimating both the clean data as well as the sparse/impulse noise levels. Second, a hyper‐Laplacian prior is used along both the spatial and spectral dimensions to express sparsity in clean image gradients. Third, to model the sparse nature of impulse noise, an ℓ1 − norm over the impulse noise gradient is used. Because the proposed methodology employs two distinct priors, the authors refer to it as the hyperspectral dual prior (HySpDualP) denoiser. To the best of authors' knowledge, this joint optimisation framework is the first attempt in this direction. To handle the non‐smooth and non‐convex nature of the general ℓp − norm‐based regularisation term, a generalised shrinkage/thresholding (GST) solver is employed. Finally, an efficient split‐Bregman approach is used to solve the resulting optimisation problem. Experimental results on synthetic data and real HSI datacube obtained from hyperspectral sensors demonstrate that the authors’ proposed model outperforms state‐of‐the‐art methods, both visually and in terms of various image quality assessment metrics.

Tensor Coupled Learning of Incomplete Longitudinal Features and Labels for Clinical Score Regression

Longitudinal data with incomplete entries pose a significant challenge for clinical score regression over multiple time points. Although many methods primarily estimate longitudinal scores with complete baseline features (i.e., features collected at the initial time point), such snapshot features may overlook beneficial latent longitudinal traits for generalization. Alternatively, certain completion approaches (e.g., tensor decomposition technology) have been proposed to impute incomplete longitudinal data before score estimation, most of which, however, are transductive and cannot utilize label semantics. This work presents a tensor coupled learning (TCL) paradigm of incomplete longitudinal features and labels for clinical score regression. The TCL enjoys three advantages: 1) It drives semantic-aware factor matrices and collaboratively deals with incomplete longitudinal entries (of features and labels), during which a dynamic regularizer is designed for adaptive attribute selection. 2) It establishes a closed loop connecting baseline features and the coupled factor matrices, which enables inductive inference of longitudinal scores relying on only baseline features. 3) It reinforces the information encoding of baseline data by preserving the local manifold of longitudinal feature space and detecting the temporal alteration across multiple time points. Extensive experiments demonstrate the remarkable performance improvement of our method on clinical score regression with incomplete longitudinal data.

SOUL-Net: A Sparse and Low-Rank Unrolling Network for Spectral CT Image Reconstruction

Spectral computed tomography (CT) is an emerging technology, that generates a multienergy attenuation map for the interior of an object and extends the traditional image volume into a 4-D form. Compared with traditional CT based on energy-integrating detectors, spectral CT can make full use of spectral information, resulting in high resolution and providing accurate material quantification. Numerous model-based iterative reconstruction methods have been proposed for spectral CT reconstruction. However, these methods usually suffer from difficulties such as laborious parameter selection and expensive computational costs. In addition, due to the image similarity of different energy bins, spectral CT usually implies a strong low-rank prior, which has been widely adopted in current iterative reconstruction models. Singular value thresholding (SVT) is an effective algorithm to solve the low-rank constrained model. However, the SVT method requires a manual selection of thresholds, which may lead to suboptimal results. To relieve these problems, in this article, we propose a sparse and low-rank unrolling network (SOUL-Net) for spectral CT image reconstruction, that learns the parameters and thresholds in a data-driven manner. Furthermore, a Taylor expansion-based neural network backpropagation method is introduced to improve the numerical stability. The qualitative and quantitative results demonstrate that the proposed method outperforms several representative state-of-the-art algorithms in terms of detail preservation and artifact reduction.

Multi-Dimensional Visual Data Restoration: Uncovering the Global Discrepancy in Transformed High-Order Tensor Singular Values

The recently proposed high-order tensor algebraic framework generalizes the tensor singular value decomposition (t-SVD) induced by the invertible linear transform from order-3 to order-d ( ). However, the derived order-d t-SVD rank essentially ignores the implicit global discrepancy in the quantity distribution of non-zero transformed high-order singular values across the higher modes of tensors. This oversight leads to suboptimal restoration in processing real-world multi-dimensional visual datasets. To address this challenge, in this study, we look in-depth at the intrinsic properties of practical visual data tensors, and put our efforts into faithfully measuring their high-order low-rank nature. Technically, we first present a novel order-d tensor rank definition. This rank function effectively captures the aforementioned discrepancy property observed in real visual data tensors and is thus called the discrepant t-SVD rank. Subsequently, we introduce a nonconvex regularizer to facilitate the construction of the corresponding discrepant t-SVD rank minimization regime. The results show that the investigated low-rank approximation has the closed-form solution and avoids dilemmas caused by the previous convex optimization approach. Based on this new regime, we meticulously develop two models for typical restoration tasks: high-order tensor completion and high-order tensor robust principal component analysis. Numerical examples on order-4 hyperspectral videos, order-4 color videos, and order-5 light field images substantiate that our methods outperform state-of-the-art tensor-represented competitors. Finally, taking a fundamental order-3 hyperspectral tensor restoration task as an example, we further demonstrate the effectiveness of our new rank minimization regime for more practical applications. The source codes of the proposed methods are available at https://github.com/CX-He/DTSVD.git.

Tensor Completion Using Bilayer Multimode Low-Rank Prior and Total Variation

In this article, we propose a novel bilayer low-rankness measure and two models based on it to recover a low-rank (LR) tensor. The global low rankness of underlying tensor is first encoded by LR matrix factorizations (MFs) to the all-mode matricizations, which can exploit multiorientational spectral low rankness. Presumably, the factor matrices of all-mode decomposition are LR, since local low-rankness property exists in within-mode correlation. In the decomposed subspace, to describe the refined local LR structures of factor/subspace, a new low-rankness insight of subspace: a double nuclear norm scheme is designed to explore the so-called second-layer low rankness. By simultaneously representing the bilayer low rankness of the all modes of the underlying tensor, the proposed methods aim to model multiorientational correlations for arbitrary N -way ( N ≥ 3 ) tensors. A block successive upper-bound minimization (BSUM) algorithm is designed to solve the optimization problem. Subsequence convergence of our algorithms can be established, and the iterates generated by our algorithms converge to the coordinatewise minimizers in some mild conditions. Experiments on several types of public datasets show that our algorithm can recover a variety of LR tensors from significantly fewer samples than its counterparts.

Hyperspectral Tensor Completion Using Low-Rank Modeling and Convex Functional Analysis

Hyperspectral tensor completion (HTC) for remote sensing, critical for advancing space exploration and other satellite imaging technologies, has drawn considerable attention from recent machine learning community. Hyperspectral image (HSI) contains a wide range of narrowly spaced spectral bands hence forming unique electrical magnetic signatures for distinct materials, and thus plays an irreplaceable role in remote material identification. Nevertheless, remotely acquired HSIs are of low data purity and quite often incompletely observed or corrupted during transmission. Therefore, completing the 3-D hyperspectral tensor, involving two spatial dimensions and one spectral dimension, is a crucial signal processing task for facilitating the subsequent applications. Benchmark HTC methods rely on either supervised learning or nonconvex optimization. As reported in recent machine learning literature, John ellipsoid (JE) in functional analysis is a fundamental topology for effective hyperspectral analysis. We therefore attempt to adopt this key topology in this work, but this induces a dilemma that the computation of JE requires the complete information of the entire HSI tensor that is, however, unavailable under the HTC problem setting. We resolve the dilemma, decouple HTC into convex subproblems ensuring computational efficiency, and show state-of-the-art HTC performances of our algorithm. We also demonstrate that our method has improved the subsequent land cover classification accuracy on the recovered hyperspectral tensor.

Robust Tensor Completion via Capped Frobenius Norm

Tensor completion (TC) refers to restoring the missing entries in a given tensor by making use of the low-rank structure. Most existing algorithms have excellent performance in Gaussian noise or impulsive noise scenarios. Generally speaking, the Frobenius-norm-based methods achieve excellent performance in additive Gaussian noise, while their recovery severely degrades in impulsive noise. Although the algorithms using the lp -norm ( ) or its variants can attain high restoration accuracy in the presence of gross errors, they are inferior to the Frobenius-norm-based methods when the noise is Gaussian-distributed. Therefore, an approach that is able to perform well in both Gaussian noise and impulsive noise is desired. In this work, we use a capped Frobenius norm to restrain outliers, which corresponds to a form of the truncated least-squares loss function. The upper bound of our capped Frobenius norm is automatically updated using normalized median absolute deviation during iterations. Therefore, it achieves better performance than the lp -norm with outlier-contaminated observations and attains comparable accuracy to the Frobenius norm without tuning parameter in Gaussian noise. We then adopt the half-quadratic theory to convert the nonconvex problem into a tractable multivariable problem, that is, convex optimization with respect to (w.r.t.) each individual variable. To address the resultant task, we exploit the proximal block coordinate descent (PBCD) method and then establish the convergence of the suggested algorithm. Specifically, the objective function value is guaranteed to be convergent while the variable sequence has a subsequence converging to a critical point. Experimental results based on real-world images and videos exhibit the superiority of the devised approach over several state-of-the-art algorithms in terms of recovery performance. MATLAB code is available at https://github.com/Li-X-P/Code-of-Robust-Tensor-Completion.

Hyperspectral Anomaly Detection Based on Adaptive Low-Rank Transformed Tensor

Hyperspectral anomaly detection, which is aimed at distinguishing anomaly pixels from the surroundings in spatial features and spectral characteristics, has attracted considerable attention due to its various applications. In this article, we propose a novel hyperspectral anomaly detection algorithm based on adaptive low-rank transform, in which the input hyperspectral image (HSI) is divided into a background tensor, an anomaly tensor, and a noise tensor. To take full advantage of the spatial-spectral information, the background tensor is represented as the product of a transformed tensor and a low-rank matrix. The low-rank constraint is imposed on frontal slices of the transformed tensor to depict the spatial-spectral correlation of the HSI background. Besides, we initialize a matrix with predefined size and then minimize its l2.1 -norm to adaptively derive an appropriate low-rank matrix. The anomaly tensor is constrained with the l2.1.1 -norm to depict the group sparsity of anomalous pixels. We integrate all regularization terms and a fidelity term into a non-convex problem and develop a proximal alternating minimization (PAM) algorithm to solve it. Interestingly, the sequence generated by the PAM algorithm is proven to converge to a critical point. Experimental results conducted on four widely used datasets demonstrate the superiority of the proposed anomaly detector over several state-of-the-art methods.

Fourier Domain Robust Denoising Decomposition and Adaptive Patch MRI Reconstruction

The sparsity of the Fourier transform domain has been applied to magnetic resonance imaging (MRI) reconstruction in k -space. Although unsupervised adaptive patch optimization methods have shown promise compared to data-driven-based supervised methods, the following challenges exist in MRI reconstruction: 1) in previous k -space MRI reconstruction tasks, MRI with noise interference in the acquisition process is rarely considered. 2) Differences in transform domains should be resolved to achieve the high-quality reconstruction of low undersampled MRI data. 3) Robust patch dictionary learning problems are usually nonconvex and NP-hard, and alternate minimization methods are often computationally expensive. In this article, we propose a method for Fourier domain robust denoising decomposition and adaptive patch MRI reconstruction (DDAPR). DDAPR is a two-step optimization method for MRI reconstruction in the presence of noise and low undersampled data. It includes the low-rank and sparse denoising reconstruction model (LSDRM) and the robust dictionary learning reconstruction model (RDLRM). In the first step, we propose LSDRM for different domains. For the optimization solution, the proximal gradient method is used to optimize LSDRM by singular value decomposition and soft threshold algorithms. In the second step, we propose RDLRM, which is an effective adaptive patch method by introducing a low-rank and sparse penalty adaptive patch dictionary and using a sparse rank-one matrix to approximate the undersampled data. Then, the block coordinate descent (BCD) method is used to optimize the variables. The BCD optimization process involves valid closed-form solutions. Extensive numerical experiments show that the proposed method has a better performance than previous methods in image reconstruction based on compressed sensing or deep learning.

T2LR-Net: An unrolling network learning transformed tensor low-rank prior for dynamic MR image reconstruction

The tensor low-rank prior has attracted considerable attention in dynamic MR reconstruction. Tensor low-rank methods preserve the inherent high-dimensional structure of data, allowing for improved extraction and utilization of intrinsic low-rank characteristics. However, most current methods are still confined to utilizing low-rank structures either in the image domain or predefined transformed domains. Designing an optimal transformation adaptable to dynamic MRI reconstruction through manual efforts is inherently challenging. In this paper, we propose a deep unrolling network that utilizes the convolutional neural network (CNN) to adaptively learn the transformed domain for leveraging tensor low-rank priors. Under the supervised mechanism, the learning of the tensor low-rank domain is directly guided by the reconstruction accuracy. Specifically, we generalize the traditional t-SVD to a transformed version based on arbitrary high-dimensional unitary transformations and introduce a novel unitary transformed tensor nuclear norm (UTNN). Subsequently, we present a dynamic MRI reconstruction model based on UTNN and devise an efficient iterative optimization algorithm using ADMM, which is finally unfolded into the proposed T2LR-Net. Experiments on two dynamic cardiac MRI datasets demonstrate that T2LR-Net outperforms the state-of-the-art optimization-based and unrolling network-based methods.

Unsupervised Spectral Demosaicing With Lightweight Spectral Attention Networks

This paper presents a deep learning-based spectral demosaicing technique trained in an unsupervised manner. Many existing deep learning-based techniques relying on supervised learning with synthetic images, often underperform on real-world images, especially as the number of spectral bands increases. This paper presents a comprehensive unsupervised spectral demosaicing (USD) framework based on the characteristics of spectral mosaic images. This framework encompasses a training method, model structure, transformation strategy, and a well-fitted model selection strategy. To enable the network to dynamically model spectral correlation while maintaining a compact parameter space, we reduce the complexity and parameters of the spectral attention module. This is achieved by dividing the spectral attention tensor into spectral attention matrices in the spatial dimension and spectral attention vector in the channel dimension. This paper also presents Mosaic 25 , a real 25-band hyperspectral mosaic image dataset featuring various objects, illuminations, and materials for benchmarking purposes. Extensive experiments on both synthetic and real-world datasets demonstrate that the proposed method outperforms conventional unsupervised methods in terms of spatial distortion suppression, spectral fidelity, robustness, and computational cost. Our code and dataset are publicly available at https://github.com/polwork/Unsupervised-Spectral-Demosaicing.

A Novel Tensor Ring Sparsity Measurement for Image Completion

As a promising data analysis technique, sparse modeling has gained widespread traction in the field of image processing, particularly for image recovery. The matrix rank, served as a measure of data sparsity, quantifies the sparsity within the Kronecker basis representation of a given piece of data in the matrix format. Nevertheless, in practical scenarios, much of the data are intrinsically multi-dimensional, and thus, using a matrix format for data representation will inevitably yield sub-optimal outcomes. Tensor decomposition (TD), as a high-order generalization of matrix decomposition, has been widely used to analyze multi-dimensional data. In a direct generalization to the matrix rank, low-rank tensor modeling has been developed for multi-dimensional data analysis and achieved great success. Despite its efficacy, the connection between TD rank and the sparsity of the tensor data is not direct. In this work, we introduce a novel tensor ring sparsity measurement (TRSM) for measuring the sparsity of the tensor. This metric relies on the tensor ring (TR) Kronecker basis representation of the tensor, providing a unified interpretation akin to matrix sparsity measurements, wherein the Kronecker basis serves as the foundational representation component. Moreover, TRSM can be efficiently computed by the product of the ranks of the mode-2 unfolded TR-cores. To enhance the practical performance of TRSM, the folded-concave penalty of the minimax concave penalty is introduced as a nonconvex relaxation. Lastly, we extend the TRSM to the tensor completion problem and use the alternating direction method of the multipliers scheme to solve it. Experiments on image and video data completion demonstrate the effectiveness of the proposed method.

Unsupervised band selection of medical hyperspectral images guided by data gravitation and weak correlation

BACKGROUND AND OBJECTIVE

Medical hyperspectral images (MHSIs) are used for a contact-free examination of patients without harmful radiation. However, high-dimensionality images contain large amounts of data that are sparsely distributed in a high-dimensional space, which leads to the "curse of dimensionality" (called Hughes' phenomenon) and increases the complexity and cost of data processing and storage. Hence, there is a need for spectral dimensionality reduction before the clinical application of MHSIs. Some dimensionality-reducing strategies have been proposed; however, they distort the data within MHSIs.

METHODS

To compress dimensionality without destroying the original data structure, we propose a method that involves data gravitation and weak correlation-based ranking (DGWCR) for removing bands of noise from MHSIs while clustering signal-containing bands. Band clustering is done by using the connection centre evolution (CCE) algorithm and selecting the most representative bands in each cluster based on the composite force. The bands within the clusters are ranked using the new entropy-containing matrix, and a global ranking of bands is obtained by applying an S-shaped strategy. The source code is available at https://www.github.com/zhangchenglong1116/DGWCR.

RESULTS

Upon feeding the reduced-dimensional images into various classifiers, the experimental results demonstrated that the small number of bands selected by the proposed DGWCR consistently achieved higher classification accuracy than the original data. Unlike other reference methods (e.g. the latest deep-learning-based strategies), DGWCR chooses the spectral bands with the least redundancy and greatest discrimination.

CONCLUSION

In this study, we present a method for efficient band selection for MHSIs that alleviates the "curse of dimensionality". Experiments were validated with three MHSIs in the human brain, and they outperformed several other band selection methods, demonstrating the clinical potential of DGWCR.

Incremental Learning for Online Data Using QR Factorization on Convolutional Neural Networks

Catastrophic forgetting, which means a rapid forgetting of learned representations while learning new data/samples, is one of the main problems of deep neural networks. In this paper, we propose a novel incremental learning framework that can address the forgetting problem by learning new incoming data in an online manner. We develop a new incremental learning framework that can learn extra data or new classes with less catastrophic forgetting. We adopt the hippocampal memory process to the deep neural networks by defining the effective maximum of neural activation and its boundary to represent a feature distribution. In addition, we incorporate incremental QR factorization into the deep neural networks to learn new data with both existing labels and new labels with less forgetting. The QR factorization can provide the accurate subspace prior, and incremental QR factorization can reasonably express the collaboration between new data with both existing classes and new class with less forgetting. In our framework, a set of appropriate features (i.e., nodes) provides improved representation for each class. We apply our method to the convolutional neural network (CNN) for learning Cifar-100 and Cifar-10 datasets. The experimental results show that the proposed method efficiently alleviates the stability and plasticity dilemma in the deep neural networks by providing the performance stability of a trained network while effectively learning unseen data and additional new classes.

Consensus Sparsity: Multi-Context Sparse Image Representation via L∞-Induced Matrix Variate

The sparsity is an attractive property that has been widely and intensively utilized in various image processing fields (e.g., robust image representation, image compression, image analysis, etc.). Its actual success owes to the exhaustive mining of the intrinsic (or homogenous) information from the whole data carrying redundant information. From the perspective of image representation, the sparsity can successfully find an underlying homogenous subspace from a collection of training data to represent a given test sample. The famous sparse representation (SR) and its variants embed the sparsity by representing the test sample using a linear combination of training samples with $L_{0}$ -norm regularization and $L_{1}$ -norm regularization. However, although these state-of-the-art methods achieve powerful and robust performances, the sparsity is not fully exploited on the image representation in the following three aspects: 1) the within-sample sparsity, 2) the between-sample sparsity, and 3) the image structural sparsity. In this paper, to make the above-mentioned multi-context sparsity properties agree and simultaneously learned in one model, we propose the concept of consensus sparsity (Con-sparsity) and correspondingly build a multi-context sparse image representation (MCSIR) framework to realize this. We theoretically prove that the consensus sparsity can be achieved by the $L_{\infty }$ -induced matrix variate based on the Bayesian inference. Extensive experiments and comparisons with the state-of-the-art methods (including deep learning) are performed to demonstrate the promising performance and property of the proposed consensus sparsity.

Signal-to-Noise Ratio Enhancement of Single-Voxel In Vivo 31P and 1H Magnetic Resonance Spectroscopy in Mice Brain Data Using Low-Rank Denoising

Magnetic resonance spectroscopy (MRS) is a noninvasive technique for measuring metabolite concentration. It can be used for preclinical small animal brain studies using rodents to provide information about neurodegenerative diseases and metabolic disorders. However, data acquisition from small volumes in a limited scan time is technically challenging due to its inherently low sensitivity. To mitigate this problem, this study investigated the feasibility of a low-rank denoising method in enhancing the quality of single voxel multinuclei (³¹P and ¹H) MRS data at 9.4 T. Performance was evaluated using in vivo MRS data from a normal mouse brain (³¹P and ¹H) and stroke mouse model (¹H) by comparison with signal-to-noise ratios (SNRs), Cramer-Rao lower bounds (CRLBs), and metabolite concentrations of a linear combination of model analysis results. In ³¹P MRS data, low-rank denoising resulted in improved SNRs and reduced metabolite quantification uncertainty compared with the original data. In ¹H MRS data, the method also improved the SNRs, CRLBs, but it performed better for ³¹P MRS data with relatively simpler patterns compared to the ¹H MRS data. Therefore, we suggest that the low-rank denoising method can improve spectra SNR and metabolite quantification uncertainty in single-voxel in vivo ³¹P and ¹H MRS data, and it might be more effective for ³¹P MRS data. The main contribution of this study is that we demonstrated the effectiveness of the low-rank denoising method on small-volume single-voxel MRS data. We anticipate that our results will be useful for the precise quantification of low-concentration metabolites, further reducing data acquisition voxel size, and scan time in preclinical MRS studies.

WINNet: Wavelet-Inspired Invertible Network for Image Denoising

Image denoising aims to restore a clean image from an observed noisy one. Model-based image denoising approaches can achieve good generalization ability over different noise levels and are with high interpretability. Learning-based approaches are able to achieve better results, but usually with weaker generalization ability and interpretability. In this paper, we propose a wavelet-inspired invertible network (WINNet) to combine the merits of the wavelet-based approaches and learning-based approaches. The proposed WINNet consists of K -scale of lifting inspired invertible neural networks (LINNs) and sparsity-driven denoising networks together with a noise estimation network. The network architecture of LINNs is inspired by the lifting scheme in wavelets. LINNs are used to learn a non-linear redundant transform with perfect reconstruction property to facilitate noise removal. The denoising network implements a sparse coding process for denoising. The noise estimation network estimates the noise level from the input image which will be used to adaptively adjust the soft-thresholds in LINNs. The forward transform of LINNs produces a redundant multi-scale representation for denoising. The denoised image is reconstructed using the inverse transform of LINNs with the denoised detail channels and the original coarse channel. The simulation results show that the proposed WINNet method is highly interpretable and has strong generalization ability to unseen noise levels. It also achieves competitive results in the non-blind/blind image denoising and in image deblurring.

LR-Net: Low-Rank Spatial-Spectral Network for Hyperspectral Image Denoising

Due to the physical limitations of the imaging devices, hyperspectral images (HSIs) are commonly distorted by a mixture of Gaussian noise, impulse noise, stripes, and dead lines, leading to the decline in the performance of unmixing, classification, and other subsequent applications. In this paper, we propose a novel end-to-end low-rank spatial-spectral network (LR-Net) for the removal of the hybrid noise in HSIs. By integrating the low-rank physical property into a deep convolutional neural network (DCNN), the proposed LR-Net simultaneously enjoys the strong feature representation ability from DCNN and the implicit physical constraint of clean HSIs. Firstly, spatial-spectral atrous blocks (SSABs) are built to exploit spatial-spectral features of HSIs. Secondly, these spatial-spectral features are forwarded to a multi-atrous block (MAB) to aggregate the context in different receptive fields. Thirdly, the contextual features and spatial-spectral features from different levels are concatenated before being fed into a plug-and-play low-rank module (LRM) for feature reconstruction. With the help of the LRM, the workflow of low-rank matrix reconstruction can be streamlined in a differentiable manner. Finally, the low-rank features are utilized to capture the latent semantic relationships of the HSIs to recover clean HSIs. Extensive experiments on both simulated and real-world datasets were conducted. The experimental results show that the LR-Net outperforms other state-of-the-art denoising methods in terms of evaluation metrics and visual assessments. Particularly, through the collaborative integration of DCNNs and the low-rank property, the LR-Net shows strong stability and capacity for generalization.