Iterative Reweighting Research Articles

Pig-DTpV: A prior information guided directional TpV algorithm for orthogonal translation computed laminography

The local scanning orthogonal translation computed laminography (OTCL) has great potential for tiny fault detection of laminated structure thin-plate parts. However, it generates limited-angle and truncated projection data, which result in aliasing and truncation artifacts in the reconstructed images. The directional total variation (DTV) algorithm has been demonstrated to achieve highly accurate reconstructed images in limited-angle computed tomography (CT). However, its application in local scanning OTCL has not been explored. Based on this algorithm, we introduce the lp norm to better suppress artifacts, and prior information to further constrain the reconstructed image. Thus, we propose a prior information guided directional total p-variation (DTpV) algorithm (Pig-DTpV). The Pig-DTpV model is a constrained non-convex optimization model. The constraint term are the six DTpV terms, whereas the objective term is the data fidelity term. Then, we use the iterative reweighting strategy and the Chambolle–Pock (CP) algorithm to solve the model. The Pig-DTpV reconstruction algorithm’s performance is compared with other algorithms such as simultaneous algebraic reconstruction technique (SART), TV, reweighted anisotropic-TV (RwATV), and DTV in simulation and real data experiments. The experiment results demonstrate that the Pig-DTpV algorithm can reduce truncation and aliasing artifacts and enhance the quality of reconstructed images.

Iterative embedding and reweighting of complex networks reveals community structure

Graph embeddings learn the structure of networks and represent it in low-dimensional vector spaces. Community structure is one of the features that are recognized and reproduced by embeddings. We show that an iterative procedure, in which a graph is repeatedly embedded and its links are reweighted based on the geometric proximity between the nodes, reinforces intra-community links and weakens inter-community links, making the clusters of the initial network more visible and more easily detectable. The geometric separation between the communities can become so strong that even a very simple parsing of the links may recover the communities as isolated components with surprisingly high precision. Furthermore, when used as a pre-processing step, our embedding and reweighting procedure can improve the performance of traditional community detection algorithms.

Locally sparse and robust partial least squares in scalar-on-function regression

We present a novel approach for estimating a scalar-on-function regression model, leveraging a functional partial least squares methodology. Our proposed method involves computing the functional partial least squares components through sparse partial robust M regression, facilitating robust and locally sparse estimations of the regression coefficient function. This strategy delivers a robust decomposition for the functional predictor and regression coefficient functions. After the decomposition, model parameters are estimated using a weighted loss function, incorporating robustness through iterative reweighting of the partial least squares components. The robust decomposition feature of our proposed method enables the robust estimation of model parameters in the scalar-on-function regression model, ensuring reliable predictions in the presence of outliers and leverage points. Moreover, it accurately identifies zero and nonzero sub-regions where the slope function is estimated, even in the presence of outliers and leverage points. We assess our proposed method’s estimation and predictive performance through a series of Monte Carlo experiments and an empirical dataset—that is, data collected in relation to oriented strand board. Compared to existing methods our proposed method performs favorably. Notably, our robust procedure exhibits superior performance in the presence of outliers while maintaining competitiveness in their absence. Our method has been implemented in the robsfplsr package in .

An adaptive iterative reweighted filtering methodology for urban MLS dataset

ABSTRACT This study presents a novel filtering methodology for Mobile Laser Scanning (MLS) data using robust iterative reweighting. Initially, 3D point clouds are projected onto a 2D grid to create surfaces from the lowest points. Weights are assigned based on the Height Above Ground (HAG) of these points. Ground points are distinguished by applying a surface function to the dataset via iterative reweighting. Among the tested four robust weight functions, the Denmark and Beaton-Tukey functions outperformed others, achieving total error values of 2.30 and 2.32 across three test areas, respectively. This method efficiently filters MLS data, irrespective of ground point proportions.

Automatic and accurate compensation for phase aberrations in digital holographic microscopy based on iteratively reweighted least squares fitting

Phase aberrations must be precisely compensated for phase-contrast imaging in digital holographic microscopy. In this paper, an automatic and accurate phase aberration compensation method is proposed based on iteratively reweighted least squares fitting. Instead of selecting the known-to-be-flat region with manual operation or image segmentation, this method starts from conventional least squares fitting in the whole image and attributes lower weights to the pixels with higher fitting residuals in an iterative reweighting procedure, during which the influence of specimen and noise is automatically reduced. Both phase curvature and high-order aberrations could be corrected without extra operation. Numerical simulation demonstrates that the proposed method is more accurate than the state-of-the-art numerical methods. Experimental result proves that this method is robust and fast enough for dynamic imaging of living cells.

Robust Target Localization in Distributed MIMO Radar With Nonconvex ℓp Minimization and Iterative Reweighting

Robust Target Localization in Distributed MIMO Radar With Nonconvex <i>ℓ_p </i> Minimization and Iterative Reweighting

Joint antenna selection and beamforming for frequency diverse multiple‐input multiple‐output radar in mainlobe spectrum interferences and signal‐dependent interferences coexistence scenarios

AbstractDue to the controllable degrees of freedom of frequency diverse array in the distance dimension, the frequency diverse multiple‐input multiple‐output (FDA‐MIMO) radar can easily deal with mainlobe interference, which is often difficult to solve in traditional phased arrays. Nevertheless, the performance of FDA‐MIMO radar will suffer from degradation in the scenario where spectrum interferences and signal‐dependent interferences coexist. In order to solve this problem, a novel FDA‐MIMO radar framework via antenna switching is proposed. Based on this framework, an effective method for jointly optimising antenna selection and beamforming against spectrum interferences and signal‐dependent interferences is developed. The resulting optimization problem is nonconvex and NP‐hard owing to the integer constraints caused by antenna selection. By relaxing the integer constraints, the original problem can be transformed into a convex optimization form and an iterative reweighting strategy is used to force the obtained solution to satisfy the integer constraints. Simulation examples show that the proposed algorithm has better performance in output signal‐to‐interference‐plus‐noise ratio (SINR) and beampattern radiation performance than the existing competitive methods.

All-in-one robust estimator of the Gaussian mean

The goal of this paper is to show that a single robust estimator of the mean of a multivariate Gaussian distribution can enjoy five desirable properties. First, it is computationally tractable in the sense that it can be computed in a time which is at most polynomial in dimension, sample size and the logarithm of the inverse of the contamination rate. Second, it is equivariant by translations, uniform scaling and orthogonal transformations. Third, it has a high breakdown point equal to $0.5$, and a nearly-minimax-rate-breakdown point approximately equal to $0.28$. Fourth, it is minimax rate optimal, up to a logarithmic factor, when data consists of independent observations corrupted by adversarially chosen outliers. Fifth, it is asymptotically efficient when the rate of contamination tends to zero. The estimator is obtained by an iterative reweighting approach. Each sample point is assigned a weight that is iteratively updated by solving a convex optimization problem. We also establish a dimension-free non-asymptotic risk bound for the expected error of the proposed estimator. It is the first result of this kind in the literature and involves only the effective rank of the covariance matrix. Finally, we show that the obtained results can be extended to sub-Gaussian distributions, as well as to the cases of unknown rate of contamination or unknown covariance matrix.

Joint Optimization of Sparse FDAs for Time Invariant Transmit Beampattern Synthesis

Beampattern synthesis of frequency diverse arrays (FDAs) has recently raised increased attention attributed to their range-dependent beampattern. The transmit beampattern of uniform FDA appears <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$S$</tex-math></inline-formula> -shaped, which implies coupling in the range-angle domain and thus causing unwanted energy leakage into the area of non-interest. In this work, we propose a joint optimization of sparse FDAs to synthesize a decoupled transmit beampattern from the perspective of spatial-frequency virtual array. Specifically, both spatial and spectral configuration of FDAs are optimized via joint antenna-frequency selection. In order to solve the resultant NP-hard combinatorial optimization problem, we propose an iterative reweighting strategy to transform the original problem into a convex optimization. Further, we proceed to synthesize a time-invariant decoupled beampattern by designing a time-varying unit frequency step. Comparative simulations are provided to manifest the superior performance of the proposed FDA in the metric of normalized peak sidelobe level (NPSLL) of transmit beampatterns.

Hilbert transform using a robust geostatistical method

In this paper, we introduced an efficient inversion method for Hilbert transform calculation which can be able to eliminate the outlier noise. The Most Frequent Value method (MFV) developed by Steiner merged with an inversion-based Fourier transform to introduce a powerful Fourier transform. The Fourier transform process (IRLS-FT) ability to noise overthrow efficiency and refusal to outliers make it an applicable method in the field of seismic data processing. In the first part of the study, we introduced the Hilbert transform stand on a efficient inversion, after that as an example we obtain the absolute value of the analytical signal which can be used as an attribute gauge. The method depends on a dual inversion, first we obtain the Fourier spectrum of the time signal via inversion, after that, the spectrum calculated via transformation of Hilbert transforms into time range using a efficient inversion. Steiner Weights is used later and calculated using the Iterative Reweighting Least Squares (IRLS) method (efficient inverse Fourier transform). Hermite functions in a series expansion are used to discretize the spectrum of the signal in time. These expansion coefficients are the unknowns in this case. The test procedure was made on a Ricker wavelet signal loaded with Cauchy distribution noise to test the new Hilbert transform. The method shows very good resistance to outlier noises better than the conventional (DFT) method.

Robustness by Reweighting for Kernel Estimators: An Overview

Using least squares techniques, there is an awareness of the dangers posed by the occurrence of outliers present in the data. In general, outliers may totally spoil an ordinary least squares analysis. To cope with this problem, statistical techniques have been developed that are not so easily affected by outliers. These methods are called robust or resistant. In this overview paper, we illustrate that robust solutions can be acquired by solving a reweighted least squares problem even though the initial solution is not robust. This overview paper relates classical results from robustness to the most recent advances of robustness in least squares kernel based regression, with an emphasis on theoretical results as well as practical examples. Software for iterative reweighting is also made freely available to the user.

Simultaneous sparse learning algorithm of structured approximation with transformation analysis embedded in Bayesian framework

Sparse approximation is critical to the applications of signal or image processing, and it is conducive to estimate the sparse signals with the joint efforts of transformation analysis. A simultaneous Bayesian framework is extended for sparse approximation by structured shared support, and a simultaneous sparse learning algorithm of structured approximation is proposed with transformation analysis, which leads to the feasible solutions more sensibly. Then the improvements of sparse Bayesian learning and iterative reweighting are embedded into the framework to achieve rapid convergence and high efficiency with robustness. Furthermore, the iterative optimization and transformation analysis are embedded in the overall learning process to obtain the relative optima for sparse approximation. Finally, compared with conventional reweighting algorithms for simultaneous sparse models with l1 and l2, simulation results present the preponderance of the proposed approach to solve the sparse structure and iterative redundancy in processing sparse signals. The fact indicates that the proposed method will be effective to sparsely approximate the various signals and images, which does accurately analyze the target in optimal transformation. It is envisaged that the proposed model could be suitable for a wide range of data in sparse separation and signal denoising.

(Invited) Approaches to Understanding and Predicting the Stability of Liquid Electrolytes and the Early Formation of the Solid-Liquid Electrolyte Interphase

Electrolytes with improved stability have the potential to transform the current state-of-the-art Li-ion architectures and enable future technologies such as multivalent systems (e.g., Mg2+, Ca2+ and Zn2+), as well as Li-S and Li-O2 conversion systems. A remaining challenge in the pursuit of rational design of novel and optimized electrolytes is understanding and ultimately predicting the reaction cascade responsible for the creation of a functional liquid-anode solid-electrolyte interface (SEI). We here present an overview of the challenge, coupled with several examples of systems where minority as well as majority speciation of the electrolyte is imperative to understand the origin of the electrochemical window. Furthermore, to address the complexity of the resulting reaction cascade once these species start to decompose, we advocate the need for data-driven approach coupled with a high-throughput quantum chemistry computational infrastructure. To this end, we have constructed a chemical reaction network with tens of thousands of elementary reactions which allow for bond breaking/formation as well as oxidation/reduction reactions. The reaction energetics are obtained from our computational framework which automate geometry optimization and vibrational frequency calculations for molecules, including radical, charged, metal-coordinated, and solvated species. To analyze possible reaction pathways, we apply a graph representation to our network, leveraging an iterative reweighting strategy that solves for all prerequisite branching such that traditional pathfinding algorithms correctly capture coordinated pathways. Machine-learning algorithms operating on bond-formation and breaking energetics aid in rapid evaluation of highly reactive processes. We show that without any apriori chemical intuition, our automated framework can recover favorable reaction paths to form key SEI components, which have been carefully identified over the past two decades. This data-driven approach and infrastructure show promise to accelerate the understanding of chemical reactivity in complex environments, in the aid of novel electrolyte design.

Proportionate Adaptive Filtering Algorithms Derived Using an Iterative Reweighting Framework.

In this paper, based on sparsity-promoting regularization techniques from the sparse signal recovery (SSR) area, least mean square (LMS)-type sparse adaptive filtering algorithms are derived. The approach mimics the iterative reweighted ℓ 2 and ℓ 1 SSR methods that majorize the regularized objective function during the optimization process. We show that introducing the majorizers leads to the same algorithm as simply using the gradient update of the regularized objective function, as is done in existing approaches. Different from the past works, the reweighting formulation naturally leads to an affine scaling transformation (AST) strategy, which effectively introduces a diagonal weighting on the gradient, giving rise to new algorithms that demonstrate improved convergence properties. Interestingly, setting the regularization coefficient to zero in the proposed AST-based framework leads to the Sparsity-promoting LMS (SLMS) and Sparsity-promoting Normalized LMS (SNLMS) algorithms, which exploit but do not strictly enforce the sparsity of the system response if it already exists. The SLMS and SNLMS realize proportionate adaptation for convergence speedup should sparsity be present in the underlying system response. In this manner, we develop a new way for rigorously deriving a large class of proportionate algorithms, and also explain why they are useful in applications where the underlying systems admit certain sparsity, e.g., in acoustic echo and feedback cancellation.

Sparse representations and compressive sampling approaches in engineering mechanics: A review of theoretical concepts and diverse applications

A review of theoretical concepts and diverse applications of sparse representations and compressive sampling (CS) approaches in engineering mechanics problems is provided from a broad perspective. First, following a presentation of well-established CS concepts and optimization algorithms, attention is directed to currently emerging tools and techniques for enhancing solution sparsity and for exploiting additional information in the data. These include alternative to ℓ1-norm minimization formulations and iterative re-weighting solution schemes, Bayesian approaches, as well as structured sparsity and dictionary learning strategies. Next, CS-based research work of relevance to engineering mechanics problems is categorized and discussed under three distinct application areas: a) inverse problems in structural health monitoring, b) uncertainty modeling and simulation, and c) computationally efficient uncertainty propagation. Notably, the vast majority of problems in all three areas share the challenge of “incomplete data”, addressed by the versatile CS framework. In this regard, incomplete data may manifest themselves in various different forms and can correspond to missing or compressed data, or even refer generally to insufficiently few function evaluations. The primary objective of this review paper relates to identifying and presenting significant contributions in each of the above three application areas in engineering mechanics, with the goal of expediting additional research and development efforts. To this aim, an extensive list of 248 references is provided, composed almost exclusively of books and archival papers, which can be readily available to a potential reader.

Statistical data assimilation for estimating electrophysiology simultaneously with connectivity within a biological neuronal network.

A method of data assimilation (DA) is employed to estimate electrophysiological parameters of neurons simultaneously with their synaptic connectivity in a small model biological network. The DA procedure is cast as an optimization, with a cost function consisting of both a measurement error and a model error term. An iterative reweighting of these terms permits a systematic method to identify the lowest minimum, within a local region of state space, on the surface of a nonconvex cost function. In the model, two sets of parameter values are associated with two particular functional modes of network activity: simultaneous firing of all neurons and a pattern-generating mode wherein the neurons burst in sequence. The DA procedure is able to recover these modes if: (i) the stimulating electrical currents have chaotic waveforms and (ii) the measurements consist of the membrane voltages of all neurons in the circuit. Further, this method is able to prune a model of unnecessarily high dimensionality to a representation that contains the maximum dimensionality required to reproduce the provided measurements. This paper offers a proof-of-concept that DA has the potential to inform laboratory designs for estimating properties in small and isolatable functional circuits.

Imaging brain extended sources from EEG/MEG based on variation sparsity using automatic relevance determination

Estimating the extents and localizations of extended sources from noninvasive EEG/MEG signals is challenging. In this paper, we have proposed a fully data driven source imaging method, namely Variation Sparse Source Imaging based on Automatic Relevance Determination (VSSI-ARD), to reconstruct extended cortical activities. VSSI-ARD explores the sparseness of current sources on the variation domain by employing ARD prior under empirical Bayesian framework. With convex analysis, the sources are efficiently obtained by solving a series of reweighting L21-norm regularization problems with ADMM. By virtue of the iterative reweighting process and sparse signal processing techniques, VSSI-ARD gets rid of the small amplitude dipoles that are more probably outside the extent of underlying sources. With the sparsity enforced on the edges using ARD prior, the estimations show clear boundaries between active and background regions without subjective thresholds. Validation with both simulated and human experimental data indicates that VSSI-ARD not only estimates the localizations of sources, but also provides relatively useful and accurate information about the extents of cortical activities.

Acousto-electric tomography with total variation regularization

We study the numerical reconstruction problem in acousto-electric tomography of recovering the conductivity distribution in a bounded domain from interior power density data. We propose a numerical method for recovering discontinuous conductivity distributions, by reformulating it as an optimization problem with L1 fitting and total variation penalty subject to PDE constraints. We establish continuity and differentiability results for the forward map, and the well-posedness of the optimization problem, and present an easy-to-implement and robust numerical method based on successive linearization, smoothing and iterative reweighting. Extensive numerical experiments are presented to illustrate the feasibility of the proposed approach.

Shearlet-based compressed sensing for fast 3D cardiac MR imaging using iterative reweighting

High-resolution three-dimensional (3D) cardiovascular magnetic resonance (CMR) is a valuable medical imaging technique, but its widespread application in clinical practice is hampered by long acquisition times. Here we present a novel compressed sensing (CS) reconstruction approach using shearlets as a sparsifying transform allowing for fast 3D CMR (3DShearCS) using 3D radial phase encoding (RPE). An iterative reweighting scheme was applied during image reconstruction to ensure fast convergence and high image quality. Shearlets are mathematically optimal for a simplified model of natural images and have been proven to be more efficient than classical systems such as wavelets. 3DShearCS was compared to three other commonly used reconstruction approaches. Image quality was assessed quantitatively using general image quality metrics and using clinical diagnostic scores from expert reviewers. The proposed technique had lower relative errors, higher structural similarity and higher diagnostic scores compared to the other reconstruction techniques especially for high undersampling factors, i.e. short scan times. 3DShearCS provided ensured accurate depiction of cardiac anatomy for fast imaging and could help to promote 3D high-resolution CMR in clinical practice.

Identification of linear parameter-varying systems: A reweightedℓ2,1-norm regularization approach

Abstract This paper presents a regularized nonlinear least-squares identification approach for linear parameter-varying (LPV) systems. The objective of the method is, on the one hand, to obtain an LPV model of which the response fits the system measurements as accurately as possible and, on the other hand, to favor models with an as simple as possible dependency on the scheduling parameter. This is accomplished by introducing l 2 , 1 -norm regularization into the nonlinear least-squares problem. The resulting nonsmooth optimization problem is reformulated into a nonlinear second-order cone program and solved using a sequential convex programming approach. Through an iterative reweighting of the regularization, the parameters that do not substantially contribute to the system response are penalized heavily, while the significant parameters remain unaffected or are penalized only slightly. Numerical and experimental validations of the proposed method show a substantial model simplification in comparison with the nonregularized solution, without significantly sacrificing model accuracy.