We report on the implementation of an augmented Lagrangian approach for solving the inverse problems in diffuse optical tomography (DOT). The forward model of light propagation is the radiative transport equation (RTE). The inverse problem is formulated as a minimization problem with the RTE being considered as an equality constraint on the set of ‘optical properties—radiance’ pairs. This appro...

This work addresses inverse linear optimization, where the goal is to infer unknown cost vector of a program. Specifically, we consider data-driven setting in which available data are noisy observations optimal solutions that correspond different instances We introduce new formulation problem that, compared with other existing methods, allows recovery less restrictive and generally more appropr...

. The purpose of inverse problems is to identify the unknown causes or parameters based on observable effects measurements in a variety scientific and technical domains. To arrive at precise trustworthy solutions, numerical algorithms for must be designed optimised. creation optimisation specifically created solving issues are presented detail this abstract.The formulation mathematical models t...

Inverse optimization—determining parameters of an optimization problem that render a given solution optimal—has received increasing attention in recent years. Although significant inverse literature exists for convex problems, there have been few advances discrete despite the ubiquity applications fundamentally rely on decision making. In this paper, we present new set theoretical insights and ...

This paper discusses the construction of inverse solutions with optimal resolution kernels and applications of them in the reconstruction of the generators of the EEG/MEG. On the basis of the framework proposed by Backus and Gilbert [1967], we show how a family of well-known solutions ranging from the minimum norm method to the generalized Wiener estimator can be derived. It is shown that these...