5 papers
Tikhonov regularization-based reconstruction of partial scattering functions obtained from contrast variation small-angle neutron scattering
Manabu Machida, Koichi Mayumi
Contrast variation small-angle neutron scattering (CV-SANS) has been widely employed for nano structural analysis of multicomponent systems. In CV-SANS experiments, scattering inte…
Iterative inversion schemes for the Born series and the reduced inverse Born series
Akari Ishida, Manabu Machida
Nonlinear inverse problems have complicated landscapes. Hence the calculation with naive iterative schemes (e.g., Gauss-Newton or conjugate gradients) is trapped in local minima. T…
Shape optimization for piecewise parameter identification in inverse diffusion problems with a single boundary measurement
Manabu Machida, Hirofumi Notsu, Julius Fergy Tiongson Rabago
This paper proposes a unified shape and coefficient optimization approach for inverse problems governed by diffusion equations. The associated forward problem is considered with a…
Lecture note on inverse problems and reconstruction methods
Manabu Machida
The area of inverse problems in mathematics is highly interdisciplinary. In various fields of science, engineering, medicine, and industry, there arises a need to reconstruct infor…
Rotated reference frames in radiative transport theory
Manabu Machida
Rotated reference frames offer fast algorithms for the radiative transport equation (RTE). We review the singular-eigenfunction approach and related numerical methods for the multi…