This article considers inverse problems of shape recovery from noisy boundary data, where the forward problem involves the inversion of elliptic PDEs. The piecewise constant solution, a scaling and translation of a characteristic function, is described in terms of a smoother level set function. A fast and simple dynamic regularization method has been recently proposed that has a robust stopping...

This paper focuses on linear classification using a fast and simple algorithm known as the Ho–Kashyap learning rule (HK). In order to avoid overfitting and instead of adding a regularization parameter in the criterion, early stopping is introduced as a regularization method for HK learning, which becomes HKES (Ho–Kashyap with Early Stopping). Furthermore, an automatic procedure, based on genera...

This handout addresses the errors in parameters estimated from fitting a function to data. Any sample of measured quantities will naturally contain some variability. Normal variations in data propagate through any equation or function applied to the data. In general we may be interested in combining the data in some mathematical way to compute another quantity. For example , we may be intereste...

Global optical flow estimation methods contain a regularization parameter (or prior and likelihood hyper-parameters if we consider the statistical point of view) which control the tradeoff between the different constraints on the optical flow field. Although experiments (see e.g. Ng et al. [Ng and Solo(1997)]) indicate the importance of the optimal choice of the hyper-parameters, only little at...

A novel parameter estimation algorithm is proposed. The inverse problem is formulated as a sequential data integration problem in which Gaussian process regression (GPR) is used to integrate the prior knowledge (static data). The search space is further parameterized using Karhunen–Loève expansion to build a set of basis functions that spans the search space. Optimal weights of the reduced basi...

Optical flow motion estimation from two images is limited by the aperture problem. A method to deal with this problem is to use regularization techniques. Usually, one adds a regularization term with appriopriate weighting parameter to the optical flow cost funtion. Here, we suggest a new approach to regularization for optical flow motion estimation. In this approach, all the regularization inf...

This paper presents a simple and efficient exogenous outlier detection & estimation algorithm introduced in a regularized version of the Kalman Filter (KF). Exogenous outliers that may occur in the observations are considered as an additional stochastic impulse process in the KF observation equation that requires a regularization of the innovation in the KF recursive equations. Regularizing wit...

Here we present an expository, general analysis of valid post-selection or post-regularization inference about a low-dimensional target parameter, α, in the presence of a very high-dimensional nuisance parameter, η, which is estimated using modern selection or regularization methods. Our analysis relies on high-level, easy-to-interpret conditions that allow one to clearly see the structures nee...

The presence of abrupt changes, such as impulsive and load disturbances, commonly occur in applications, but make the state estimation problem considerably more difficult than in the standard setting with Gaussian process disturbance. Abrupt changes often introduce a jump in the state, and the problem is therefore readily and often treated by change detection techniques. In this paper, we take ...