Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work, we propose a new regularization approach and a new regularization parameter selection approach for linear leastsquares discrete ill-posed problems. The propo...

We present a sequential noise compensation method based on the sequential Kullback proximal algorithm, which uses the Kullback-Leibler divergence as a regularization function for the maximum likelihood estimation. The method is implemented as filters. In contrast to sequential noise compensation method based on the sequential EM algorithm, the convergence rate of the method and estimation error...

In this paper we address two issues in modeling natural terrain using fractal geometry: estimation of fractal dimension, and fractal surface reconstruction. For estimation of fractal dimension, we extend the fractal Brownian function approach to accommodate irregularly sampled data, and we develop methods for segmenting sets of points exhibiting self-similarity over only certain scales. For fra...

We study multi-parameter Tikhonov regularization, i.e., with multiple penalties. Such models are useful when the sought-for solution exhibits several distinct features simultaneously. Two choice rules, i.e., discrepancy principle and balancing principle, are studied for choosing an appropriate (vector-valued) regularization parameter, and some theoretical results are presented. In particular, t...

Monitoring dynamical processes requires the estimation of the entire state, which is only partly accessible by measurements. Most quantities must be determined via model based state estimation, which in general is an ill-posed inverse problem. Regularization techniques have to be applied. In most of the literature the initial data are also regularized. However, the initial data are typically un...

The inverse problem of electrocardiography is usually analyzed during stationary rhythms. However, the performance of the regularization methods under fibrillatory conditions has not been fully studied. In this work, we assessed different regularization techniques during atrial fibrillation (AF) for estimating four target parameters, namely, epicardial potentials, dominant frequency (DF), phase...

In this paper we consider the problem of efficient computation of the stochastic MV-PURE estimator which is a reduced-rank estimator designed for robust linear estimation in ill-conditioned inverse problems. Our motivation for this result stems from the fact that the reduced-rank estimation by the stochastic MV-PURE estimator, while avoiding the problem of regularization parameter selection app...

This paper presents a new formulation of the problem of motion estimation which attempts to give solutions to classical problems in the field, such as detection of motion discontinuities and insufficiency of the optical flow constraint in areas with low intensity variation. An initial intensity segmentation phase partitions each frame into patches so that areas with low intensity variation are ...

We present a linear algebraic method, named the eXtended Fourier Transform (XFT), for spectral estimation from truncated time signals. The method is a hybrid of the discrete Fourier transform (DFT) and the regularized resolvent transform (RRT) (J. Chen et al., J. Magn. Reson. 147, 129-137 (2000)). Namely, it estimates the remainder of a finite DFT by RRT. The RRT estimation corresponds to solut...