We formulate a solution to the diffuse optical tomography (DOT) inverse problem as the minimization of an energy functional of the solution and the data. For the solution prior we introduce a local diffusion regularization potential with a threshold based on robust statistics (the Hubert function). We compare results on simulated data for the Hubert function and two other standard regularizatio...

We explain some basic theoretical issues regarding nonparametric statistics applied to inverse problems. Simple examples are used to present classical concepts such as the white noise model, risk estimation, minimax risk, model selection and optimal rates of convergence, as well as more recent concepts such as adaptive estimation, oracle inequalities, modern model selection methods, Stein’s unb...

The problem of incomplete and noisy information in profile reconstruction from neutron reflectometry data is considered. In particular methods of Bayesian statistics in combination with modelling or inverse scattering techniques are considered in order to properly include the required a priori knowledge to obtain quantitatively reliable estimates of the reconstructed profiles. Applying Bayes th...

Factors thought to be related to lung cancer include smoking, radon, and educational attainment. These factors were analyzed in the present ecological study for Oregon with correlation and linear regression statistics. A moderate, inverse, and statistically significant correlation was found with educational attainment while surprisingly, negligible and statistically insignificant correlations w...

From a probabilistic point-of-view, the solution to an inverse problem can be seen as a combination of independent states of information quantified by probability density functions. Typically, these states of information are provided by a set of observed data and some a priori information on the solution. The combined states of information (i.e. the solution to the inverse problem) is a probabi...

This paper studies the application of the theory and algorithms of blind signal extraction to solve the problem of the detection of the desired users in a DS-CDMA communications system. Typically, the uplink in this system is characterized by users that transmit asynchronously and propagation channels that are multipath. We address inverse filter criterion introduced by Tugnait in [1] and we sh...

We present a new family of estimators of the Weibull tail-coefficient. The Weibull tail-coefficient is defined as the regular variation coefficient of the inverse failure rate function. Our estimators are based on a linear combination of log-spacings of the upper order statistics. Their asymptotic normality is established and illustrated for two particular cases of estimators in this family. Th...

Inverse problem typically deal with the identification of unknown quantities from indirect measurements and appear in many areas in technology, medicine, biology, finance, and econometrics. The computational solution of such problems is a very active, interdisciplinary field with close connections to optimization, control theory, differential equations, asymptotic analysis, statistics, and prob...

The problem of reconstructing a function and/or its domain given its moments is encountered in many areas. Several applications from diverse areas such as probability and statistics [4], signal processing [10], computed tomography [8, 9], and inverse potential theory [1, 11] (magnetic and gravitational anomaly detection) can be cited, to name just a few. We can expound on some of these applicat...

in the linear system ax = b the points x are sometimes constrained to lie in a given subspace s of column space of a. drazin inverse for any singular or nonsingular matrix, exist and is unique. in this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of drazin inverse in solving such systems is investigated. constrained linear system arise ...