Browsing by Subject "inverse problems"

Now showing 1 - 9 of 9

Access status: Open Access ,
A loss function for box-constrained inverses problems
(2008) Yoneda, Kiyoshi
A loss function is proposed for solving box-constrained inverse problems. Given causality mechanisms between inputs and outputs as smooth functions, an inverse problem demands to adjust the input levels to make the output levels as close as possible to the target values; box-constrained refers to the requirement that all outcome levels remain within their respective permissible intervals. A feasible solution is assumed known, which is often the status quo. We propose a loss function which avoids activation of the constraints. A practical advantage of this approach over the usual weighted least squares is that permissible outcome intervals are required in place of target importance weights, facilitating data acquisition. The proposed loss function is smooth and strictly convex with closed-form gradient and Hessian, permitting Newton family algorithms. The author has not been able to locate in the literature the Gibbs distribution corresponding to the loss function. The loss function is closely related to the <i>generalized matching law</i> in psychology.
Access status: Open Access ,
A note on confidence intervals for deblurred images
(Wydawnictwa AGH, 2020) Biel, Michał; Szkutnik, Zbigniew
We consider pointwise asymptotic confidence intervals for images that are blurred and observed in additive white noise. This amounts to solving a stochastic inverse problem with a convolution operator. Under suitably modified assumptions, we fill some apparent gaps in the proofs published in [N. Bissantz, M. Birke, Asymptotic normality and confidence intervals for inverse regression models with convolution-type operators, J. Multivariate Anal. 100 (2009), 2364-2375]. In particular, this leads to modified bootstrap confidence intervals with much better finite-sample behaviour than the original ones, the validity of which is, in our opinion, questionable. Some simulation results that support our claims and illustrate the behaviour of the confidence intervals are also presented.
Access status: Open Access ,
A utility function to solve approximate linear equations for decision making
(2013) Yoneda, Kiyoshi; Celaschi, Walter
Suppose there are a number of decision variables linearly related to a set of outcome variables. There are at least as many outcome variables as the number of decision variables since all decisions are outcomes by themselves. The quality of outcome is evaluated by a utility function. Given desired values for all outcome variables, decision making reduces to »solving« the system of linear equations with respect to the decision variables; the solution being defined as decision variable values such that maximize the utility function. This paper proposes a family of additively separable utility functions which can be defined by setting four intuitive parameters for each outcome variable: the desired value of the outcome, the lower and the upper limits of its admissible interval, and its importance weight. The utility function takes a nonnegative value within the admissible domain and negative outside; permits gradient methods for maximization, is designed to have a small dynamic range for numerical computation. Small examples are presented to illustrate the proposed method.
Access status: Open Access ,
Elevator trip distribution for inconsistent passenger input-output data
(2007) Yoneda, Kiyoshi
Accurate traffic data are the basis for group control of elevators and its performance evaluation by trace driven simulation. The present practice estimates a time series of inter-floor passenger traffic based on commonly available elevator sensor data. The method demands that the sensor data be transformed into sets of passenger input-output data which are consistent in the sense that the transportation preserves the number of passengers. Since observation involves various behavioral assumptions, which may actually be violated, as well as measurement errors, it has been necessary to apply data adjustment procedures to secure the consistency. This paper proposes an alternative algorithm which reconstructs elevator passenger origin-destination tables from inconsistent passenger input-output data sets, thus eliminating the ad hoc data adjustment.
Access status: Open Access ,
Evolutionary multi-agent computing in inverse problem
(Wydawnictwa AGH, 2013) Wróbel, Krzysztof; Torba, Paweł; Paszyński, Maciej; Byrski, Aleksander
This paper tackles the application of evolutionary multi-agent computing to solve inverse problems. High costs of fitness function call become a major difficulty when approaching these problems with population-based heuristics. However, evolutionary agent-based systems (EMAS) turn out to reduce the fitness function calls, which makes them a possible weapon of choice against them. This paper recalls the basics of EMAS and describes the considered problem (Step and Flash Imprint Lithography), and later, shows convincing results that EMAS is more effective than a classical evolutionary algorithm.
Access status: Open Access ,
HP-HGS strategy for inverse AC/DC resistivity logging measurement simulations
(Wydawnictwa AGH, 2013) Gajda-Zagórska, Ewa; Paszyński, Maciej; Schaefer, Robert; Pardo, David
In this paper, we present resistivity-logging-measurement simulation with the use of two types of borehole logging devices: those which operate with zero frequency (direct current, DC) and those with higher frequencies (alternate current, AC). We perform simulations of 3D resistivity measurements in deviated wells, with a sharp angle between the borehole and formation layers. We introduce a hierarchical adaptive genetic strategy hp ? HGS interfaced with an adaptive finite element method. We apply a strategy for the solution of the inverse problem, where we identify the resistivities of the formation layers based on a given measurement. We test the strategy on both direct and alternate current cases.
Access status: Open Access ,
Maximization of an asymmetric utility function by the least squares
(2014) Yoneda, Kiyoshi; Moretti, Antonio Carlos
This note points out that a utility maximization procedure proposed in an earlier paper may be reduced to the least squares. The utility function is asymmetric in the sense that for each cue its ideal value and the permissible range are assigned in such a way that the ideal is not necessarily at the center of the range, like »a beer of 350 ml would be ideal, but acceptable if within [100, 500]«. A practical consequence of the observation is that very little programming will be needed to deploy the utility maximization since software for the least squares is widely available.
Access status: Open Access ,
On reconstructing an unknown coordinate of a nonlinear system of differential equations
(2014) Blizorukova, Marina; Kuklin, Aleksandr Anatol'evič; Maksimov, Vâčeslav
The paper discusses a method of auxiliary controlled models and the application of this method to solving problems of dynamical reconstruction of an unknown coordinate in a nonlinear system of differential equations. The solving algorithm, which is stable with respect to informational noises and computational errors, is presented.
Access status: Open Access ,
Stretching the least squares to embed loss function tables
(2015) Yoneda, Kiyoshi; Moretti, Antonio Carlos; Poker, Johan Hendrik