Related papers: General regularization schemes for signal detectio…

Distribution shifts are problems where the distribution of data changes between training and testing, which can significantly degrade the performance of a model deployed in the real world. Recent studies suggest that one reason for the…

We provide estimators for a large class of inverse problems, including nonlinear inverse problems. Using complexity regularization technics we provide adaptive estimators achieving the best rate over the collection of models.

It's well-known that inverse problems are ill-posed and to solve them meaningfully one has to employ regularization methods. Traditionally, popular regularization methods have been the penalized Variational approaches. In recent years, the…

We deal with the solution of a generic linear inverse problem in the Hilbert space setting. The exact right hand side is unknown and only accessible through discretised measurements corrupted by white noise with unknown arbitrary…

Inverse problems are inherently ill-posed, suffering from non-uniqueness and instability. Classical regularization methods provide mathematically well-founded solutions, ensuring stability and convergence, but often at the cost of reduced…

Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…

Despite huge successes on a wide range of tasks, neural networks are known to sometimes struggle to generalise to unseen data. Many approaches have been proposed over the years to promote the generalisation ability of neural networks,…

Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…

Usage of multiprocessor and multicore computers implies parallel programming. Tools for preparing parallel programs include parallel languages and libraries as well as parallelizing compilers and convertors that can perform automatic…

The idea of adversarial learning of regularization functionals has recently been introduced in the wider context of inverse problems. The intuition behind this method is the realization that it is not only necessary to learn the basic…

Finding a point in the intersection of a collection of closed convex sets, that is the convex feasibility problem, represents the main modeling strategy for many computational problems. In this paper we analyze new stochastic reformulations…

Calculation of the log-normalizer is a major computational obstacle in applications of log-linear models with large output spaces. The problem of fast normalizer computation has therefore attracted significant attention in the theoretical…

Forward and inverse models are used throughout different engineering fields to predict and understand the behaviour of systems and to find parameters from a set of observations. These models use root-finding and minimisation techniques…

We introduce inverse transport networks as a learning architecture for inverse rendering problems where, given input image measurements, we seek to infer physical scene parameters such as shape, material, and illumination. During training,…

There has been a recent interest in imitation learning methods that are guaranteed to produce a stabilizing control law with respect to a known system. Work in this area has generally considered linear systems and controllers, for which…

Random projections offer an appealing and flexible approach to a wide range of large-scale statistical problems. They are particularly useful in high-dimensional settings, where we have many covariates recorded for each observation. In…

A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. However, these so-called filter methods are generally restricted to monotonic transformations,…

The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…

We study the linear ill-posed inverse problem with noisy data in the statistical learning setting. Approximate reconstructions from random noisy data are sought with general regularization schemes in Hilbert scale. We discuss the rates of…

Solving inverse problems \(Ax = y\) is central to a variety of practically important fields such as medical imaging, remote sensing, and non-destructive testing. The most successful and theoretically best-understood method is convex…