Variation Regularization Research Articles

Observational Verification of High‐Order Solar Tidal Harmonics in the Earth's Atmosphere

AbstractThis study combines 8 years of middle atmospheric wind data observed at 52°N latitude from two radars in different longitudinal sectors to investigate solar tides. The power spectral density of horizontal winds exhibits a −3 power law within the frequency range 2.0 < f < 7.0 cpd (equivalent to periods 3.6 − 12.0 hr). Particularly noteworthy are the 4.8‐ and 4‐hr tides, exhibiting signal‐to‐noise ratios ranging between 13 and 16 dB, surpassing the 0.01 significance level. This challenges their previous oversight in literature, possibly due to inadequacies in prevailing noise models. Cross‐spectra between longitudinal sectors emphasize the dominance of sun‐synchronous components in the six lowest‐frequency tides. Composite spectra indicate that tidal enhancements during SSWs resemble regular seasonal variations. Intriguingly, year‐to‐year spectral variations suggest that these enhancements are more influenced by seasonal dynamics than by SSW, contrasting with established literature. These findings underscore the need to reevaluate tidal harmonics and consider appropriate noise models in future studies.

Adaptive weighted total variation expansion and Gaussian curvature guided low-dose CT image denoising network

The denoising task of low-dose CT images is a highly complex and uncertain inverse problem. Previous studies have primarily relied on convolutional neural network to reduce noise by learning the mapping from LDCT images to normal dose CT images. However, simply increasing the network depth alone is not an optimal choice due to the limited performance improvement and significant computational cost. In contrast, integrating prior knowledge of images with a model to assist in image reconstruction is a more efficient approach. This study proposes a new framework for denoising LDCT images, named Noise-Optimized Edge Feature Guided Network (NEFGN). The task of NEFGN is to integrate the noise optimization model of adaptive weighted total variation expansion, the edge detection model guided by Gaussian curvature, and image reconstruction into an end-to-end CNN framework. In order to achieve this goal, the noise optimization model is first constructed by learning the parameters in the adaptive weighted total variation regularization model to approximate the noise level in the NDCT image. The edge detection network is constructed using Gaussian curvature, predicting clear edges directly from the noise image. Finally, under the guidance of the noise optimization model and the edge detail model, NEFGN is more capable of suppressing artifact noise, demonstrating good accuracy and robustness, and can restore finer details. Numerous experimental studies demonstrate that the NEFGN denoising framework effectively restores the structure of LDCT images with limited image details and outperforms other methods in terms of performance.

Impulse Noise Image Restoration Using Nonconvex Variational Model and Difference of Convex Functions Algorithm.

In this article, the problem of impulse noise image restoration is investigated. A typical way to eliminate impulse noise is to use an L1 norm data fitting term and a total variation (TV) regularization. However, a convex optimization method designed in this way always yields staircase artifacts. In addition, the L1 norm fitting term tends to penalize corrupted and noise-free data equally, and is not robust to impulse noise. In order to seek a solution of high recovery quality, we propose a new variational model that integrates the nonconvex data fitting term and the nonconvex TV regularization. The usage of the nonconvex TV regularizer helps to eliminate the staircase artifacts. Moreover, the nonconvex fidelity term can detect impulse noise effectively in the way that it is enforced when the observed data is slightly corrupted, while is less enforced for the severely corrupted pixels. A novel difference of convex functions algorithm is also developed to solve the variational model. Using the variational method, we prove that the sequence generated by the proposed algorithm converges to a stationary point of the nonconvex objective function. Experimental results show that our proposed algorithm is efficient and compares favorably with state-of-the-art methods.

Rapid and Noise‐Resilient Mapping of Photogenerated Carrier Lifetime in Halide Perovskite Thin Films

AbstractHalide perovskite materials offer significant promise for solar energy and optoelectronics yet understanding and enhancing their efficiency and stability require addressing lateral inhomogeneity challenges. While photoluminescence imaging techniques are employed for the measurement of their opto‐electronic and transport properties, going further in terms of precision requires longer acquisition times. Prolonged exposure of perovskites to light, given their high reactivity, can substantially alter these layers, rendering the acquired data less meaningful for analysis. In this paper, a method to extract high‐quality lifetime images from rapidly acquired, noisy time‐resolved photoluminescence images is proposed. This method leverages concepts of the field of constrained reconstruction and includes the Huber loss function and a specific form of total variation regularization. Through both simulations and experiments, it is demonstrated that the approach outperforms conventional pointwise methods. Optimal acceleration and optimization parameters tailored for decay time imaging of perovskite materials, offering new perspectives for accelerated experiments crucial in degradation process characterization are identified. Importantly, this methodology holds the potential for broader applications: it can be extended to explore additional beam‐sensitive materials, and other imaging characterization techniques and employed with more complex physical models to treat time‐resolved decays.

Buzz Characteristics Under Fluid–Structure Interaction of Variable-Geometry Lip for Hypersonic Inlet

Variable-geometry lip structures can effectively broaden the operating range and improve the performance of hypersonic inlets. However, the presence of connection devices leads to a significant reduction in structural stiffness, which can easily trigger fluid–structure interaction (FSI) issues of the lip. In this study, an in-house FSI program is employed to investigate the buzz characteristics under FSI of the lip for a hypersonic inlet. The results indicate that FSI induces instability in the downstream shock train, resulting in the premature occurrence of inlet buzz. The buzz mode induced by FSI significantly differs from the rigid inlet buzz. During the buzz induced by FSI, both violent and mild buzz modes coexist, with these two modes irregularly alternating. During the violent buzz, the inlet achieves a brief start, leading to a fundamentally different evolution of the flowfield structure compared to the rigid model. During the mild buzz, the inlet remains unstart, so the evolution of the flowfield structure is similar to that of the rigid model. In comparison to the rigid inlet buzz, the amplitudes of pressure fluctuations significantly increase, and the dominant frequency decreases for the buzz induced by FSI. Simultaneously, different evolution characteristics of flow frequencies within various inlet regions are observed. Additionally, performance parameters no longer exhibit regular cyclic variations, with significant amplifications in their amplitudes. This study deepens the understanding of the buzz characteristics under FSI of lips for hypersonic inlets and provides a novel perspective on the mechanisms underlying buzz occurrence.

An Iterative Method for the Inverse Eddy Current Problem with Total Variation Regularization

An Iterative Method for the Inverse Eddy Current Problem with Total Variation Regularization

Convergence of non-linear diagonal frame filtering for regularizing inverse problems

Inverse problems are key issues in several scientific areas, including signal processing and medical imaging. Since inverse problems typically suffer from instability with respect to data perturbations, a variety of regularization techniques have been proposed. In particular, the use of filtered diagonal frame decompositions (DFDs) has proven to be effective and computationally efficient. However, existing convergence analysis applies only to linear filters and a few non-linear filters such as soft thresholding. In this paper, we analyze filtered DFDs with general non-linear filters. In particular, our results generalize singular value decomposition-based spectral filtering from linear to non-linear filters as a special case. As a first approach, we establish a connection between non-linear diagonal frame filtering and variational regularization, allowing us to use results from variational regularization to derive the convergence of non-linear spectral filtering. In the second approach, as our main theoretical results, we relax the assumptions involved in the variational case while still deriving convergence. Furthermore, we discuss connections between non-linear filtering and plug-and-play regularization and explore potential benefits of this relationship.

Q-compensated image-domain least-squares reverse time migration through preconditioned point-spread functions

Image-domain least-squares reverse time migration (IDLSRTM) through point-spread functions (PSFs) has been proven to be a feasible approach to improve the spatial resolution and amplitude fidelity of reflection images recovered by reverse time migration (RTM). However, it usually ignores the earth’s Q-effects, which may lead to an unfocused reflection image with an undesired spatial resolution. In this paper, we develop a Q-compensated IDLSRTM approach (denoted as Q-IDLSRTM) through PSFs, in which we use the viscoacoustic wave equation based on the generalized standard linear solid model to simulate inherent subsurface attenuation and the linear inversion to compensate for the amplitude attenuation. The PSFs are estimated by a round of modeling-migration computation and spatial interpolation on the fly. There are two key points in the developed Q-IDLSRTM approach. The first is that we must apply the deblurring filter as a preconditioner to compensate for the attenuation of image amplitude of PSFs and RTM in a viscoacoustic medium, before the iterative solution. The preconditioned PSFs and RTM images can help us to construct a less ill-posed image-domain inverse problem that can produce an improved image quality and a faster convergence rate, compared with the conventional Q-IDLSRTM approach without the deblurring filter. The second key point is that we can impose the L1-norm constraint and total variation regularization on the reflection image to stabilize the solution of the ill-posed inverse problem. Several 2D and 3D experiments verify that the developed approach can achieve better imaging quality in terms of amplitude fidelity and spatial resolution relative to the conventional Q-IDLSRTM and acoustic IDLSRTM approaches.

Boosting MR Image Impulse Noise Removal With Overlapping Group Sparse Fractional-Order Total Variation and Minimax Concave Penalty

The acquisition and transmission of magnetic resonance images are susceptible to noise, particularly impulse noise. Although the method based on the ℓ0-norm and overlapping group sparse total variation (ℓ0-OGSTV) is effective for impulse noise image restoration, it can only mitigate the staircase artifacts to a certain extent. To boost the impulse noise removal performance of ℓ0-OGSTV, we propose a new restoration model that consists of two terms. Specifically, in the first term, we keep using the ℓ0-norm as the data fidelity term to eliminate impulse noise. In the second term, we first introduce an overlapping group sparsity fractional-order total variation regularizer to eliminate staircase artifacts while preserving structural information. Then, we adopt the minimax-concave penalty to further accurately estimate the image edges. Finally, we employ an alternate direction method of multipliers to solve the proposed optimization model. Clinical experiments demonstrate its effectiveness in denoising medical images.

Trust your source: quantifying source condition elements for variational regularisation methods

Abstract Source conditions are a key tool in regularisation theory that are needed to derive error estimates and convergence rates for ill-posed inverse problems. In this paper, we provide a recipe to practically compute source condition elements as the solution of convex minimisation problems that can be solved with first-order algorithms. We demonstrate the validity of our approach by testing it on two inverse problem case studies in machine learning and image processing: sparse coefficient estimation of a polynomial via LASSO regression and recovering an image from a subset of the coefficients of its discrete Fourier transform. We further demonstrate that the proposed approach can easily be modified to solve the machine learning task of identifying the optimal sampling pattern in the Fourier domain for a given image and variational regularisation method, which has applications in the context of sparsity promoting reconstruction from magnetic resonance imaging data.

Improvements in the estimation of the Weibull tail coefficient: A comparative study

The Weibull tail‐coefficient (WTC) plays a crucial role in extreme value statistics when dealing with Weibull‐type tails. Several distributions, such as normal, Gamma, Weibull, and logistic distributions, exhibit this type of tail behavior. The WTC, denoted by , is a parameter in a right‐tail function of the form , where represents a regularly varying cumulative hazard function with an index of regular variation equal to 1/ . The commonly used WTC‐estimators in literature are often defined as functions of the log‐excesses, making them closely related to estimators of the extreme value index (EVI) for Pareto‐type tails. For a positive EVI, the classical estimator is the Hill estimator. Generalized means have been successfully employed in estimating the EVI, leading to reduction of bias and of root mean square error for appropriate threshold values. In this study, we propose and investigate new classes of WTC‐estimators based on power of the log‐excesses within a second‐order framework. The performance of these new estimators is evaluated through a large‐scale Monte Carlo simulation study, comparing them with existing WTC‐estimators available in the literature.

Image restoration based on transformed total variation and deep image prior

Most supervised learning methods require observation data and ground truth pairs as data sets to train the network. However, it is difficult and time-consuming to obtain a large number of high quality data sets, because ground truth is not available in some practical settings, such as medical imaging, dynamic scenes. Deep image prior (DIP) only uses one degraded image for image recovery tasks, which gets rid of the limitation of constructing a large number of training sets but requires an early stop mechanism. In order to further improve the image restoration ability of the DIP model, we combine it with the transformed total variation (TTV) regularization, which is a generalization of the classical total variation (TV) regularization and can achieve better performance for image restoration problems. The proposed method not only uses the deep neural network to capture image prior, but also exploits inherent sparse prior in image gradient domain. In addition, we provide an adaptive weight selection strategy for TTV regularization. The ADMM scheme is employed to solve the proposed models. Numerical results of image restoration illustrate that the proposed methods perform better than the compared methods.

Using a deep learning prior for accelerating hyperpolarized 13C MRSI on synthetic cancer datasets.

We aimed to incorporate a deep learning prior with k-space data fidelity for accelerating hyperpolarized carbon-13 MRSI, demonstrated on synthetic cancer datasets. A two-site exchange model, derived from the Bloch equation of MR signal evolution, was firstly used in simulating training and testing data, that is, synthetic phantom datasets. Five singular maps generated from each simulated dataset were used to train a deep learning prior, which was then employed with the fidelity term to reconstruct the undersampled MRI k-space data. The proposed method was assessed on synthetic human brain tumor images (N = 33), prostate cancer images (N = 72), and mouse tumor images (N = 58) for three undersampling factors and 2.5% additive Gaussian noise. Furthermore, varied levels of Gaussian noise with SDs of 2.5%, 5%, and 10% were added on synthetic prostate cancer data, and corresponding reconstruction results were evaluated. For quantitative evaluation, peak SNRs were approximately 32 dB, and the accuracy was generally improved for 5 to 8 dB compared with those from compressed sensing with L1-norm regularization or total variation regularization. Reasonable normalized RMS error were obtained. Our method also worked robustly against noise, even on a data with noise SD of 10%. The proposed singular value decomposition + iterative deep learning model could be considered as a general framework that extended the application of deep learning MRI reconstruction to metabolic imaging. The morphology of tumors and metabolic images could be measured robustly in six times acceleration using our method.

Tensor completion via multi-directional partial tensor nuclear norm with total variation regularization

Tensor completion via multi-directional partial tensor nuclear norm with total variation regularization

On heavy-tailed risks under Gaussian copula: The effects of marginal transformation

In this paper, we compute multivariate tail risk probabilities where the marginal risks are heavy-tailed and the dependence structure is a Gaussian copula. The marginal heavy-tailed risks are modeled using regular variation which leads to a few interesting consequences. First, as the threshold increases, we note that the rate of decay of probabilities of tail sets varies depending on the type of tail sets considered and the Gaussian correlation matrix. Second, we discover that although any multivariate model with a Gaussian copula admits the so-called asymptotic tail independence property, the joint tail behavior under heavier tailed marginal variables is structurally distinct from that under Gaussian marginal variables. The results obtained are illustrated using examples and simulations.

The Sun’s Large-Scale Flows I: Measurements of Differential Rotation & Torsional Oscillation

We have developed a comprehensive catalog of the variable differential rotation measured near the solar photosphere. This catalog includes measurements of these flows obtained using several techniques: direct Doppler, granule tracking, magnetic pattern tracking, global helioseismology, as well as both time-distance and ring-diagram methods of local helioseismology. We highlight historical differential rotation measurements to provide context, and thereafter provide a detailed comparison of the MDI-HMI-GONG-Mt. Wilson overlap period (April 2010 – Jan 2011) and investigate the differences between velocities obtained from different techniques and attempt to explain discrepancies. A comparison of the rotation rate obtained by magnetic pattern tracking with the rotation rates obtained using local and global helioseismic techniques shows that magnetic pattern tracking measurements correspond to helioseismic flows located at a depth of 25 to 28 Mm. In addition, we show the torsional oscillation from Sunspot Cycles 23 and 24 and discuss properties that are consistent across measurement techniques. We find that acceleration derived from torsional oscillation is a better indicator of long-term trends in torsional oscillation compared to the residual velocity magnitude. Finally, this analysis will pave the way toward understanding systematic effects associated with various flow measurement techniques and enable more accurate determination of the global patterns of flows and their regular and irregular variations.

Hyperspectral sparse fusion using adaptive total variation regularization and superpixel-based weighted nuclear norm

Many recent studies have shown that the adaptive total variation regularization has the advantage of better preserving local features of images compared with the celebrated total variation regularization. On the other hand, the superpixel-based weighted nuclear norm can compensate for the shortcomings of the superpixel-based standard nuclear norm, assigning different weights to singular values and improving flexibility. Inspired by these two factors, we propose two new hyperspectral sparse fusion models related to the adaptive total variation regularization and superpixel-based weighted nuclear norm. Furthermore, we design the alternating direction method of multipliers (ADMM) to efficiently solve the proposed models, with complexity and convergence analyses. Experimental results demonstrate that the proposed methods outperform several state-of-the-art methods both numerically and visually.

Ferrocene-functionalized zirconium-oxo clusters for achieving high-performance thermocatalytic redox reactions

The Zr(IV) ions are easily hydrolyzed to form oxides, which severely limits the discovery of new structures and applications of Zr-based compounds. In this work, three ferrocene (Fc)-functionalized Zr-oxo clusters (ZrOCs), Zr9Fc6, Zr10Fc6 and Zr12Fc8 were synthesized through inhibiting the hydrolysis of Zr(IV) ions, which show increased nuclearity and regular structural variation. More importantly, these Fc-functionalized ZrOCs were used as heterogeneous catalysts for the transfer hydrogenation of levulinic acid (LA) and phenol oxidation reactions for the first time, and displayed outstanding catalytic activity. In particular, Zr12Fc8 with the largest number of Zr active sites and Fc groups can achieve > 95% yield for LA-to-γ-valerolactone within 4 h (130 °C) and > 98% yield for 2,3,6-trimethylphenol-to-2,3,5-trimethyl-p-benzoquinone within 30 min (80 °C), showing the best catalytic performance. Catalytic characterization combined with theory calculations reveal that in the Fc-functionalized ZrOCs, the Zr active sites could serve as substrate adsorption sites, while the Fc groups could act as hydrogen transfer reagent or Fenton reagent, and thus achieve effectively intramolecular metal–ligand synergistic catalysis. This work develops functionalized ZrOCs as catalysts for thermal-triggered redox reactions.

A color image fusion model by saturation-value total variation

In this paper, we propose and develop a novel color image fusion model by using saturation-value total variation. In the proposed model, we develop a variational approach containing an energy functional to determine the weighting mask functions and the fused image together. The objective fused image is modeled by using the saturation-value total variation regularization. The data-fitting term is formulated based on the weighting L2 norm of the objective fused image and the input observed images. The objective weighting mask functions are modeled by using total variation for the piecewise-smoothness purpose. Meanwhile, we add another fidelity term to capture more texture and color information from the input images by forcing the weighting local mean images to be close to the clear input image. The existence of a solution of the proposed minimizing model is shown. Numerically, we apply alternating direction method of multipliers (ADMM) to solve the proposed minimization problem, meanwhile, we give the convergence analysis of the proposed algorithm. Numerical examples are presented to demonstrate that the performance of the proposed color image fusion model is better than that of other testing methods in terms of visual quality and some criterias such as structure similarity (SSIM), average local contrast (ALC), discrete entropy (DE), natural image quality evaluator (NIQE) and perception-based image quality evaluator (PIQE).

Partial Tail-Correlation Coefficient Applied to Extremal-Network Learning

We propose a novel extremal dependence measure called the partial tail-correlation coefficient (PTCC), in analogy to the partial correlation coefficient in classical multivariate analysis. The construction of our new coefficient is based on the framework of multivariate regular variation and transformed-linear algebra operations. We show how this coefficient allows identifying pairs of variables that have partially uncorrelated tails given some other variables in a random vector. Unlike other recently introduced conditional independence frameworks for extremes, our approach requires minimal modeling assumptions and can thus be used in exploratory analyses to learn the structure of extremal graphical models. Similarly to traditional Gaussian graphical models where edges correspond to the nonzero entries of the precision matrix, we can exploit classical inference methods for high-dimensional data, such as the graphical Lasso with Laplacian spectral constraints, to efficiently learn the extremal network structure via the PTCC. We apply our new method to study extreme risk networks in two different datasets (extreme river discharges and historical global currency exchange data) and show that we can extract interesting extremal structures with meaningful domain-specific interpretations.