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Resolution Improvement of Ultrasonic Signals Using Sparse Deconvolution and Variational Mode Decomposition algorithms

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RUSSIAN JOURNAL OF NONDESTRUCTIVE TESTING 2020年第6期56卷 479-489页

作者： Abdessalem, Benammar Farid, Chibane Res Ctr Ind Technol CRTI POB 64 Algiers 16014 Algeria Univ Boumerdes Electrificat Ind Enterprises Lab Boumerdes Algeria

Over the past few years, the use of ultrasonic arrays for nondestructive testing (NDT) applications has grown rapidly and led to use new algorithms of signal processing. The present paper's main objective is to improve the resolution of defect detection and make the detection process as fast and accurate as possible. This paper introduces a novel method to improve the resolution of ultrasonic phased array. The proposed method is based on the variational decomposition of signal and on a deconvolution method. To reduce the level of signal's noise, a method based on the variational mode decomposition (VMD) is used and to improve the resolution, a sparse deconvolution algorithm optimized using the majorization-minimization (mm) method is used. A simulation study has been carried out simulating a block of stainless steel containing several defects in different positions. Experimental tests were performed on a sample of stainless steel containing several defects. The obtained results show that the proposed method can improve the quality of ultrasonic data which enhances the localization of defects.

关键词： ultrasonic phased array empirical mode decomposition variational mode decomposition sparse deconvolution mm algorithm

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A Legacy of EM algorithms

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INTERNATIONAL STATISTICAL REVIEW 2022年第Sup1期90卷 S52-S66页

作者： Lange, Kenneth Zhou, Hua Univ Calif Los Angeles Dept Computat Med Los Angeles CA 90095 USA Univ Calif Los Angeles Dept Human Genet Los Angeles CA 90095 USA Univ Calif Los Angeles Dept Stat Los Angeles CA 90095 USA Univ Calif Los Angeles Dept Biostat Los Angeles CA 90095 USA

Nan Laird has an enormous and growing impact on computational statistics. Her paper with Dempster and Rubin on the expectation-maximisation (EM) algorithm is the second most cited paper in statistics. Her papers and book on longitudinal modelling are nearly as impressive. In this brief survey, we revisit the derivation of some of her most useful algorithms from the perspective of the minorisation-maximisation (mm) principle. The mm principle generalises the EM principle and frees it from the shackles of missing data and conditional expectations. Instead, the focus shifts to the construction of surrogate functions via standard mathematical inequalities. The mm principle can deliver a classical EM algorithm with less fuss or an entirely new algorithm with a faster rate of convergence. In any case, the mm principle enriches our understanding of the EM principle and suggests new algorithms of considerable potential in high-dimensional settings where standard algorithms such as Newton's method and Fisher scoring falter.

关键词： EM algorithm mm algorithm variance component model longitudinal data analysis

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A coordinate descent mm algorithm for fast computation of sparse logistic PCA

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2013年 62卷 26-38页

作者： Lee, Seokho Huang, Jianhua Z. Hankuk Univ Foreign Studies Dept Stat Seoul South Korea Texas A&M Univ Dept Stat College Stn TX 77843 USA

Sparse logistic principal component analysis was proposed in Lee et al. (2010) for exploratory analysis of binary data. Relying on the joint estimation of multiple principal components, the algorithm therein is computationally too demanding to be useful when the data dimension is high. We develop a computationally fast algorithm using a combination of coordinate descent and majorization-minimization (mm) auxiliary optimization. Our new algorithm decouples the joint estimation of multiple components into separate estimations and consists of closed-form elementwise updating formulas for each sparse principal component. The performance of the proposed algorithm is tested using simulation and high-dimensional real-world datasets. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Binary data Coordinate descent algorithm mm algorithm Penalized maximum likelihood Principal component analysis

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Generalized Minimal Distortion Principle for Blind Source Separation 21

Generalized Minimal Distortion Principle for Blind Source Se...

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Interspeech Conference

作者： Scheibler, Robin LINE Corp Tokyo Japan

ISBN: (纸本)9781713820697

We revisit the source image estimation problem from blind source separation (BSS). We generalize the traditional minimum distortion principle to maximum likelihood estimation with a model for the residual spectrograms. Because residual spectrograms typically contain other sources, we propose to use a mixed-norm model that lets us finely tune sparsity in time and frequency. We propose to carry out the minimization of the mixed-norm via majorization-minimization optimization, leading to an iteratively reweighted least-squares algorithm. The algorithm balances well efficiency and ease of implementation. We assess the performance of the proposed method as applied to two well-known determined BSS and one joint BSS-dereverberation algorithms. We find out that it is possible to tune the parameters to improve separation by up to 2 dB, with no increase in distortion, and at little computational cost. The method thus provides a cheap and easy way to boost the performance of blind source separation.

关键词： blind source separation scale ambiguity minimal distortion sparsity inducing norms mm algorithm

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SPATIALLY GUIDED INDEPENDENT VECTOR ANALYSIS

SPATIALLY GUIDED INDEPENDENT VECTOR ANALYSIS

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IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Brendel, Andreas Haubner, Thomas Kellermann, Walter Friedrich Alexander Univ Erlangen Nurnberg Multimedia Commun & Signal Proc Cauerstr 7 D-91058 Erlangen Germany

ISBN: (纸本)9781509066315

We present a Maximum A Posteriori (MAP) derivation of the Independent Vector Analysis (IVA) algorithm for blind source separation incorporating an additional spatial prior over the demixing matrices. In this way, the outer permutation ambiguity of IVA is avoided and the algorithm can be guided towards a desired solution in adverse acoustic conditions. The resulting MAP optimization problem is solved by deriving majorize-minimize update rules to achieve convergence speed comparable to the well-known auxiliary function IVA algorithm, i.e., the convergence is not impaired by the additional constraint. The proposed algorithm exhibits superior performance at lower computational cost than a state-of-the-art spatially constrained IVA algorithm in a setup defined by real-world Room Impulse Responses (RIRs).

关键词： Independent Vector Analysis mm algorithm Directional Constraint

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Damped Anderson Acceleration With Restarts and Monotonicity Control for Accelerating EM and EM-like algorithms (10.1080/10618600.2019.1594835, 2019)

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2019年第4期28卷 I-I页

作者： Henderson, Nicholas C. Varadhan, Ravi Sidney Kimmel Comprehensive Cancer Center Johns Hopkins University Baltimore MD Sidney Kimmel Comprehensive Cancer Center Johns Hopkins University Baltimore MD Department of Biostatistics Bloomberg School of Public Health Johns Hopkins University Baltimore MD

The expectation-maximization (EM) algorithm is a well-known iterative method for computing maximum likelihood estimates in a variety of statistical problems. Despite its numerous advantages, a main drawback of the EM algorithm is its frequently observed slow convergence which often hinders the application of EM algorithms in high-dimensional problems or in other complex settings. To address the need for more rapidly convergent EM algorithms, we describe a new class of acceleration schemes that build on the Anderson acceleration technique for speeding fixed-point iterations. Our approach is effective at greatly accelerating the convergence of EM algorithms and is automatically scalable to high-dimensional settings. Through the introduction of periodic algorithm restarts and a damping factor, our acceleration scheme provides faster and more robust convergence when compared to un-modified Anderson acceleration, while also improving global convergence. Crucially, our method works as an “off-the-shelf” method in that it may be directly used to accelerate any EM algorithm without relying on the use of any model-specific features or insights. Through a series of simulation studies involving five representative problems, we show that our algorithm is substantially faster than the existing state-of-art acceleration schemes. The acceleration schemes described in this paper are implemented in the R package daarem which is available from the comprehensive R archive network (https://***). Supplementary materials for this article are available online.

关键词： algorithm restarts Convergence acceleration mm algorithm Quasi-Newton SQUAREM

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A Mixture of Coalesced Generalized Hyperbolic Distributions

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JOURNAL OF CLASSIFICATION 2019年第1期36卷 26-57页

作者： Tortora, Cristina Franczak, Brian C. Browne, Ryan P. McNicholas, Paul D. San Jose State Univ Dept Math & Stat San Jose CA 95192 USA MacEwan Univ Dept Math & Stat Edmonton AB Canada Univ Waterloo Dept Stat & Actuarial Sci Waterloo ON Canada McMaster Univ Dept Math & Stat Hamilton ON Canada

A mixture of multiple scaled generalized hyperbolic distributions (mmSGHDs) is introduced. Then, a coalesced generalized hyperbolic distribution (CGHD) is developed by joining a generalized hyperbolic distribution with a multiple scaled generalized hyperbolic distribution. After detailing the development of the mmSGHDs, which arises via implementation of a multi-dimensional weight function, the density of the mixture of CGHDs is developed. A parameter estimation scheme is developed using the ever-expanding class of mm algorithms and the Bayesian information criterion is used for model selection. The issue of cluster convexity is examined and a special case of the mmSGHDs is developed that is guaranteed to have convex clusters. These approaches are illustrated and compared using simulated and real data. The identifiability of the mmSGHDs and the mixture of CGHDs are discussed in an appendix.

关键词： Clustering Coalesced distributions Convexity Finite mixture models Generalized hyperbolic distribution Mixture of mixtures mm algorithm Multiple scaled distributions

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Some new statistical methods for a class of zero-truncated discrete distributions with applications

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COMPUTATIONAL STATISTICS 2019年第3期34卷 1393-1426页

作者： Tian, Guo-Liang Ding, Xiqian Liu, Yin Tang, Man-Lai Southern Univ Sci & Technol Dept Math Shenzhen 518055 Guangdong Peoples R China Univ Hong Kong Dept Stat & Actuarial Sci Lung Fu Shan Pokfulam Rd Hong Kong Peoples R China Zhongnan Univ Econ & Law Sch Math & Stat Wuhan 430073 Hubei Peoples R China Hang Seng Univ Hong Kong Sch Decis Sci Dept Math & Stat ShatinSiu Lek Yuen Hong Kong Peoples R China

Counting data without zero category often occurs in various fields. A class of zero-truncated discrete distributions such as the zero-truncated Poisson, zero-truncated binomial and zero-truncated negative-binomial distributions are proposed in literature to model such count data. In this paper, three main contributions have been made for better studying the zero-truncated discrete distributions: First, a novel unified expectation-maximization (EM) algorithm is developed for calculating the maximum likelihood estimates (MLEs) of parameters in general zero-truncated discrete distributions and an important feature of the proposed EM algorithm is that the latent variables and the observed variables are independent, which is unusual in general EM-type algorithms;Second, for those who do not understand the principle of latent variables, a unified minorization-maximization algorithm, as an alternative to the EM algorithm, for obtaining the MLEs of parameters in a class of zero-truncated discrete distributions is discussed;Third, a unified method is proposed to derive the distribution of the sum of ***-truncated discrete random variables, which has important applications in the construction of the shortest Clopper-Pearson confidence intervals of parameters of interest and in the calculation of the exact p value of a two-sided test for small sample sizes in one sample problem.

关键词： EM algorithm mm algorithm Shortest confidence intervals Stochastic representation Zero-truncated discrete models

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An Adapted Loss Function for Censored Quantile Regression

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2019年第527期114卷 1126-1137页

作者： De Backer, Mickael Ghouch, Anouar El Van Keilegom, Ingrid Catholic Univ Louvain Inst Stat Biostat & Sci Actuarielles Voie Roman Pays 20 B-1348 Louvain La Neuve Belgium Katholieke Univ Leuven Res Ctr Operat Res & Business Stat Leuven Belgium

In this article, we study a novel approach for the estimation of quantiles when facing potential right censoring of the responses. Contrary to the existing literature on the subject, the adopted strategy of this article is to tackle censoring at the very level of the loss function usually employed for the computation of quantiles, the so-called "check" function. For interpretation purposes, a simple comparison with the latter reveals how censoring is accounted for in the newly proposed loss function. Subsequently, when considering the inclusion of covariates for conditional quantile estimation, by defining a new general loss function the proposed methodology opens the gate to numerous parametric, semiparametric, and nonparametric modeling techniques. To illustrate this statement, we consider the well-studied linear regression under the usual assumption of conditional independence between the true response and the censoring variable. For practical minimization of the studied loss function, we also provide a simple algorithmic procedure shown to yield satisfactory results for the proposed estimator with respect to the existing literature in an extensive simulation study. From a more theoretical prospect, consistency and asymptotic normality of the estimator for linear regression are obtained using several recent results on nonsmooth semiparametric estimation equations with an infinite-dimensional nuisance parameter, while numerical examples illustrate the adequateness of a simple bootstrap procedure for inferential purposes. Lastly, an application to a real dataset is used to further illustrate the validity and finite sample performance of the proposed estimator. Supplementary materials for this article are available online.

关键词： Beran estimator Bootstrap Check function Linear regression mm algorithm

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Worst-case weighted sum-rate maximization in multicell massive MIMO downlink system for 5G communications

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PHYSICAL COmmUNICATION 2018年 27卷 116-124页

作者： Chinnadurai, Sunil Selvaprabhu, Poongundran Jiang, Xueqin Hai, Han Lee, Moon Ho Chonbuk Natl Univ Inst Informat & Commun 664-14 Deokjin Dong Jeonju 561756 South Korea Donghua Univ Sch Informat Sci & Technol Shanghai Peoples R China

In this paper, we present a robust beamforming design to examine the weighted sum-rate maximization (WSRM) problem in a multicell massive MIMO downlink system for 5G communications. This work assume imperfect channel state information (CSI) by adding uncertainties to channel matrices with worst-case models i.e. singular value uncertainty model (SVUM) and ellipsoidal uncertainty model (EUM). In SVUM, WSRM problem is formulated subject to the transmit power constraints. While, the problem is devised in EUM by alternatively considering its dual power minimization problem subject to the worst-case signal-to-interference-plus-noise ratio (SINR) constraints for all mobile stations. The designed problem for both SVUM and EUM are known as non-deterministic polynomial (NP) problem which is difficult to solve. We propose an iterative algorithm established on majorization minimization (mm) technique that solves and achieves convergence to stationary point of these two problems. In EUM, the convergence point is obtained after converting the infinite number of SINR constraints into linear matrix inequalities (LMI) by employing S-Procedure. Extensive numerical results are provided to show that the proposed iterative algorithm significantly increases performance in terms of sum-rate and also attains faster convergence as compared with the conventional polynomial time algorithm. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Massive MIMO 5G Convergence Optimization mm algorithm Beamforming Worst-case weighted sum-rate Singular value uncertainty Ellipsoidal uncertainty

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