Related papers: Source reconstruction using a bilevel optimisation…
This paper investigates the inverse problems of determining a space-dependent source for thermoelastic systems of type III under adequate time-averaged or final-in-time measurements and conditions on the time-dependent part of the sought…
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required…
This paper is concerned with the state estimation problem for two-dimensional systems with asynchronous multichannel delays and energy harvesting constraints. In the system, each smart sensor has a certain probability of harvesting energy…
We present a convex-concave reformulation of the reversible Markov chain estimation problem and outline an efficient numerical scheme for the solution of the resulting problem based on a primal-dual interior point method for monotone…
Waveform inversion is theoretically a powerful tool to reconstruct subsurface structures, but a usually encountered problem is that accurate sources are very rare, causing the computation unstable and divergent. This challenging problem,…
Bilevel optimization is a central tool in machine learning for high-dimensional hyperparameter tuning. Its applications are vast; for instance, in imaging it can be used for learning data-adaptive regularizers and optimizing forward…
We study the inverse source problem for a class of viscoelastic systems from a single boundary measurement in a general spatial dimension. We give specific reconstruction formula and stability estimate for the source in terms of the…
We propose a deterministic-statistical method for an inverse source problem using multiple frequency limited aperture far field data. The direct sampling method is used to obtain a disc such that it contains the compact support of the…
Variational regularization techniques are dominant in the field of mathematical imaging. A drawback of these techniques is that they are dependent on a number of parameters which have to be set by the user. A by now common strategy to…
We propose a new heuristic goal-oriented a posteriori error estimator that connects the dual weighted residual method with equilibrated a posteriori error estimation. Our numerical experiments demonstrate the practical reliability of the…
This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal data. This theory finds applications in multi-wave imaging, greedy methods to…
This paper considers properties of an optimization based sampler for targeting the posterior distribution when the likelihood is intractable and auxiliary statistics are used to summarize information in the data. Our reverse sampler…
Low-cost air pollution sensors, offering hyper-local characterization of pollutant concentrations, are becoming increasingly prevalent in environmental and public health research. However, low-cost air pollution data can be noisy, biased by…
Bilevel optimisation is used in inverse imaging problems for hyperparameter learning/identification and experimental design, for instance, to find optimal regularisation parameters and forward operators. However, computationally, the…
Inversions for local helioseismology are an important and necessary step for obtaining three-dimensional maps of various physical quantities in the solar interior. Frequently, the full inverse problems that one would like to solve prove…
We improve a phase retrieval approach that uses correlation-based measurements with compactly supported measurement masks [27]. The improved algorithm admits deterministic measurement constructions together with a robust, fast recovery…
We study a class of algorithms for solving bilevel optimization problems in both stochastic and deterministic settings when the inner-level objective is strongly convex. Specifically, we consider algorithms based on inexact implicit…
Heteroscedastic regression is the task of supervised learning where each label is subject to noise from a different distribution. This noise can be caused by the labelling process, and impacts negatively the performance of the learning…
We propose a bilevel optimization approach for the estimation of parameters in nonlocal image denoising models. The parameters we consider are both the fidelity weight and weights within the kernel of the nonlocal operator. In both cases we…
This article studies Gauss-Newton-type methods for over-determined systems to find solutions to bilevel programming problems. To proceed, we use the lower-level value function reformulation of bilevel programs and consider necessary…