Article
Mathematics, Applied
Baasansuren Jadamba, Akhtar A. Khan, Fabio Raciti, Miguel Sama
Summary: This paper develops a stochastic approximation approach for estimating the flexural rigidity within the framework of variational inequalities. The nonlinear inverse problem is analyzed as a stochastic optimization problem using an energy least-squares formulation. A stochastic variational inequality is solved by a stochastic auxiliary problem principle-based iterative scheme, which satisfies the necessary and sufficient optimality condition for the optimization problem. The convergence analysis for the proposed iterative scheme is given under general conditions on the random noise. Detailed computational results demonstrate the feasibility and efficacy of the proposed methodology.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Engineering, Marine
Pablo Barreno, Juan Parras, Santiago Zazo
Summary: In this work, an optimal control method based on the receding horizon approach is proposed for Autonomous Underwater Vehicles (AUVs) to cope with hazardous underwater medium. The proposed model estimates the kinematics of the medium and its disturbances using efficient tools based on linear algebra and first-order optimization methods. Extensive simulations demonstrate the competitive cost and computational efficiency of the proposed ideas in cases of total and partial observability.
JOURNAL OF MARINE SCIENCE AND ENGINEERING
(2023)
Article
Optics
Vedat Suat Erturk, Asghar Ahmadkhanlu, Pushpendra Kumar, V. Govindaraj
Summary: This article investigates a fractional boundary value problem for modeling human corneal shape dynamics, proposing novel simulations to prove the existence of a unique solution and deriving the numerical solution using a polynomial least squares method.
Article
Biophysics
Allison L. Clouthier, Jessica Wenghofer, Eugene K. Wai, Ryan B. Graham
Summary: The goal of this study was to develop and share morphable models of the lumbar spine that allow the geometry to be varied according to pathology, demographics, or anatomical measurements. This method can be used to analyze the relationship among shape, pathology, demographics, and function through computational simulations.
JOURNAL OF BIOMECHANICS
(2023)
Article
Automation & Control Systems
Stefanie J. M. Fonken, Karthik Raghavan Ramaswamy, Paul M. J. Van den Hof
Summary: This research proposes an identification method for dynamic networks, where the estimation of disturbance topology precedes the identification of the full dynamic network. By extending existing methods to handle reduced rank noise, a multi-step least squares algorithm is provided with parallel computation capabilities and relies only on explicit analytical solutions, consistently estimating the structure of dynamic networks.
Article
Computer Science, Interdisciplinary Applications
D. J. J. Farnell, S. Richmond, J. Galloway, A. I. Zhurov, P. Pirttiniemi, T. Heikkinen, V. Harila, H. Matthews, P. Claes
Summary: This study investigated facial shape changes with age during adolescence using multilevel statistical models, specifically multilevel partial-least squares regression (mPLSR). Results showed reduction in buccal fat and enlargement of features like nose, brow, and chin with increasing age. The model accurately predicted plausible simulated faces for different ages, sexes, and ethnicities.
COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE
(2021)
Article
Automation & Control Systems
Zhiwen Liu, Tianji Cheng, Chongyang Han, Enhai Liu, Ranjun Wang
Summary: In this article, the parameter identification problem of the output error model in a two-degree-of-freedom servo turntable system is investigated, and two algorithms, MI-RLS and MR-MILS, are proposed to improve the identification accuracy and convergence speed. The MI-RLS algorithm introduces a momentum factor into the recursive least squares algorithm to eliminate the influence of colored noise, while the MR-MILS algorithm incorporates a reframed multi-innovation strategy to accelerate convergence without significantly increasing complexity. The effectiveness of these algorithms is demonstrated through simulation results.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2023)
Article
Mathematics
Zaineb Yakoub, Omar Naifar, Dmitriy Ivanov
Summary: This paper presents a method to identify continuous-time fractional order systems with unknown time-delay using the bias compensated least squares algorithm. The suggested approach makes a significant contribution by estimating the system coefficients, orders, and time-delay iteratively through a nonlinear optimization algorithm. The method provides a simple and powerful algorithm with good accuracy.
Article
Mathematics, Applied
Dinh Nho Hao, Akhtar A. Khan, Simeon Reich
Summary: This study focuses on establishing new convergence rates for nonlinear inverse problems, applicable to a wide array of practical models without the need for any smallness condition.
JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS
(2023)
Article
Computer Science, Artificial Intelligence
Shuping Zhao, Bob Zhang
Summary: This study proposes to learn complete and discriminative direction patterns for palmprint recognition. It extracts complete and salient local direction patterns, learns sparse and discriminative directions from them, and concatenates the projected features to form a complete and discriminative direction feature. Experimental results demonstrate the effectiveness of the proposed method on seven palmprint databases and three noisy datasets.
IEEE TRANSACTIONS ON IMAGE PROCESSING
(2021)
Article
Mathematics, Interdisciplinary Applications
Yaqi Zhang, Lei Guo
Summary: This paper investigates self-tuning regulators for linear stochastic systems with unknown parameters and conditional heteroscedastic noises. By designing an adaptive controller based on the weighted least-squares algorithm and the certainty equivalence principle, the authors demonstrate that the closed-loop adaptive control system can achieve global stability and asymptotically optimal tracking error under certain conditions with unbounded conditional variances of the noises.
JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
(2021)
Article
Engineering, Electrical & Electronic
Ye Tian, Yunbai Qin, Zhiyan Dong, He Xu
Summary: This paper proposes a DOA estimation algorithm for massive MIMO systems considering unknown mutual coupling, using an enhanced SCM and STLS technique to achieve DOA and angular spread estimation, while solving the mutual coupling coefficients. The proposed algorithm not only improves DOA estimation performance, but also overcomes deficiencies in a more efficient way, as validated by theoretical analysis and numerical examples.
DIGITAL SIGNAL PROCESSING
(2021)
Article
Economics
Seojeong Lee, Youngki Shin
Summary: The study introduces a CSA-2SLS estimator method that minimizes mean squared error by selecting the most appropriate subset size k from available instruments, showing better performance in cases of high correlation.
ECONOMETRICS JOURNAL
(2021)
Article
Operations Research & Management Science
E. G. Birgin, J. M. Martinez
Summary: This paper proposes a general framework for solving nonlinear least squares problems without the use of derivatives, and introduces two dimension-reduction procedures. The practical motivation of this work is to estimate parameters in hydraulic models for dam breaking problems.
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
(2022)
Article
Multidisciplinary Sciences
Qinqing Xiong, Wenju Wang, Mingya Wang, Chunhui Zhang, Xuechun Zhang, Chun Chen, Mingshi Wang
Summary: This study proposes a hybrid neural network model SOM-NARX based on the correlation of predictors for ozone prediction. The model filters predictors using MIC, transforms them into feature sequences using SOM, and makes predictions using NARX networks. The results show that the correlation of predictors, classification numbers of SOM, neuron numbers, and delay steps can affect prediction accuracy. Model comparison shows that the SOM-NARX model outperforms other models in terms of RMSE, MAE, and MAEP.
Article
Mathematics, Applied
Henrik Garde, Nuutti Hyvonen
Summary: This paper introduces a constructive method for approximating relative continuum measurements in two-dimensional electrical impedance tomography based on data originating from either the point electrode model or the complete electrode model. The upper bounds for the corresponding approximation errors explicitly depend on the number (and size) of the employed electrodes as well as on the regularity of the continuum current that is mimicked. In particular, if the input current and the object boundary are infinitely smooth, the discrepancy associated with the point electrode model converges to zero faster than any negative power of the number of electrodes.
NUMERISCHE MATHEMATIK
(2021)
Article
Mathematics, Applied
M. Burger, A. Hauptmann, T. Helin, N. Hyvonen, J. P. Puska
Summary: This work applies Bayesian experimental design to select optimal projection geometries in (discretized) parallel beam x-ray tomography with Gaussian prior and additive noise. The introduced greedy exhaustive optimization algorithm proceeds sequentially, allowing redefining the region of interest after each projection and considering both A and D-optimality. Two-dimensional numerical experiments demonstrate the functionality of the approach.
Article
Automation & Control Systems
Jeremi Darde, Sylvain Ervedoza, Roberto Morales
Summary: This article studies the null-controllability of a heat equation in a domain consisting of two media with different constant conductivities. The behavior of the system when the conductivity of the non-actuated medium approaches infinity is of particular interest, leading to a uniform null-controllability result under suitable geometric conditions. The strategy is based on analyzing the controllability of wave operators and using the transmutation technique to explain the geometric conditions.
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
(2021)
Article
Mathematics, Applied
V Candiani, N. Hyvonen, J. P. Kaipio, V Kolehmainen
Summary: This study focuses on electrical impedance tomography imaging of the human head for locating and classifying strokes in emergency care. By modeling natural variations in head geometry and skull, as well as the impact of misplaced electrodes, it enables reliable reconstruction of stroke-induced conductivity perturbations in an average head model. The functionality of a specific edge-preferring reconstruction algorithm for locating strokes is demonstrated through numerical experiments using simulated three-dimensional data.
Article
Mathematics, Applied
Jyrki Jauhiainen, Aku Seppanen, Tuomo Valkonen
Summary: Electrical impedance tomography (EIT) is a method that aims to determine the conductivity within a target body by measuring electrical signals on its surface. The inverse conductivity problem is challenging due to limited measurement data, hence requiring regularization. Traditional regularization methods focus on promoting smooth features, but for targets consisting of multiple distinct objects or materials, the Mumford-Shah (M-S) regularization familiar in image segmentation is more suitable. However, it poses numerical challenges. The study shows through theoretical analysis that a modification of the Ambrosio-Tortorelli approximation of the M-S regularizer is applicable to EIT, specifically in the complete electrode model of boundary measurements. Numerical and experimental studies confirm the practicality of this approach, producing higher quality results compared to typical regularizations employed in EIT when the conductivity of the target consists of distinct smoothly-varying regions.
Article
Mathematics, Applied
Henrik Garde, Nuutti Hyvonen
Summary: This work presents numerical methods for solving Calderon's problem using series reversions. By reversing the series of the forward map, a family of methods for solving the inverse problem is obtained, and the convergence of these methods is proven. The introduced numerical methods have the same computational complexity as solving the linearized inverse problem.
MATHEMATICS OF COMPUTATION
(2022)
Article
Mathematics, Applied
J. Darde, N. Hyvonen, T. Kuutela, T. Valkonens
Summary: This study proposes a new robust modeling method for contact electrodes in electrical impedance tomography. By assuming approximate knowledge about the electrodes' whereabouts and using a boundary admittivity function to determine their actual locations, the proposed method enables simultaneous reconstruction of the positions and strengths of the contacts.
SIAM JOURNAL ON APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Tapio Helin, Nuutti Hyvonen, Juha-Pekka Puska
Summary: This work focuses on sequential edge-promoting Bayesian experimental design for linear inverse problems, specifically X-ray tomography. It interprets the computation process of total variation-type absorption reconstruction inside the imaged body using lagged diffusivity iteration in the Bayesian framework. By assuming a Gaussian additive noise model, an approximate Gaussian posterior with a covariance structure containing information about the location of edges in the posterior mean is obtained. The next projection geometry is then determined using A- or D-optimal Bayesian design, which minimizes the trace or determinant of the updated posterior covariance matrix that accounts for the new projection. Two- and three-dimensional numerical examples based on simulated data demonstrate the effectiveness of this approach.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Laurent Bourgeois, Jeremi Darde
Summary: This paper focuses on the application of Morozov's principle to an abstract data assimilation framework and illustrates how to regularize ill-posed problems through three examples. It extends known results related to Morozov's choice of the regularization parameter to the case where the operator does not have a dense range, and computes the solution satisfying Morozov's principle using optimization duality.
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS
(2022)
Article
Mathematics, Applied
H. Garde, N. Hyvonen, T. Kuutela
Summary: This work extends the series reversion method for Calderon's problem to realistic electrode measurements, treating both the internal admittivity of the investigated body and the contact admittivity at the electrode-object interfaces as unknowns. A family of numerical methods for solving the inverse problem of electrical impedance tomography is obtained through Taylor series reversion, with different parametrizations for the unknown internal and boundary admittivities. The functionality and convergence of the methods are established under certain conditions, and the methods are heuristically extended to more general settings using regularization motivated by Bayesian inversion. The performance of the regularized approach is tested through three-dimensional numerical examples.
Article
Engineering, Biomedical
Pauliina Hirvi, Topi Kuutela, Qianqian Fang, Antti Hannukainen, Nuutti Hyvonen, Ilkka Nissila
Summary: This study investigates the approximation error when using an atlas instead of the neonate's own anatomical model in diffuse optical tomography (DOT). It is found that there is a considerable approximation error, but the method using atlas-based imaging can still detect small changes in brain absorption. Individual-level atlas models can be used in DOT difference imaging when an exactly age-appropriate atlas is not available.
PHYSICS IN MEDICINE AND BIOLOGY
(2023)
Article
Mathematics, Applied
Henrik Garde, Nuutti Hyvonen
Summary: This study presents explicit series reversions for the solution of Calderon's problem and derives a family of numerical methods to improve the accuracy of the solution by reversing the Taylor series of the forward map. The convergence of these numerical methods is shown under conditions that ensure the invertibility of the Frechet derivative of the forward map. The introduced numerical methods have the same computational complexity as solving the linearized inverse problem.
MATHEMATICS OF COMPUTATION
(2022)
Article
Mathematics, Applied
Henrik Garde, Nuutti Hyvonen
Summary: We investigate the reconstruction of the support of an unknown perturbation to a known conductivity coefficient in Calderon's problem. We generalize a previous result by allowing the unknown coefficient to be the restriction of an A(2)-Muckenhoupt weight in parts of the domain, incorporating singular and degenerate behavior. Our main constructive result characterizes the outer shape of the support based on a local Neumann-to-Dirichlet map defined on an open subset of the domain boundary.
INVERSE PROBLEMS AND IMAGING
(2022)
Article
Mathematics, Applied
Antti Hannukainen, Nuutti Hyvonen, Lauri Perkkio
Summary: Iron loss determination in the magnetic core of electrical machines is treated as an inverse heat source problem, with sensor positions optimized for minimizing uncertainty in reconstruction. The study focuses on formulating the problem and efficiently solving the discretized sensor optimization and source reconstruction problems. A semi-realistic linear model is discretized using finite elements and numerically studied.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
