Este cursillo se realizará los días:
Viernes 8 de abril de 2011 a las 11:30 hrs en Sala 3 (sector Postgrado) Martes 12 de abril de 2011 a las 14:00 Hrs en Sala 3 (sector Postgrado) Viernes 15 de abril de 2011 a las 11:30Hrs en Sala 3 (sector Postgrado)
Abstract: In the mini-course we are going to discuss one of the most efficient methods for obtaining estimates of the eigenvalues for operators of the form H=A-qV where A is a non-negative operator in a functional Hilbert space, V is the operator of multiplication by a function and q is a coupling constant. We are interested in obtaining estimates of the number of negative eigenvalues of A, which are sharp in their behavior as the coupling constant grows. The leading examples are given by A being the Laplacian or its generalization, therefore the operators are called Schrödinger-like. The method is based upon considering the semigroup generated by A. We are going to present the necessary information on semigroups, explain two main abstract theorems, on estimates and on domination, and discuss numerous examples and applications, including the classical, magnetic and relativistic Schrödinger operators and operators on combinatorial and quantum graphs.
Accurate estimation of noise variance and correlations in tomographic reconstructions from real data is an important problem
for image quality assessment and thereby optimization of system parameters. Usually, this estimation is performed using repeated
scans of an anthropomorphic phantom along with the conventional unbiased estimator for the covariance matrix of image pixels.
Such an approach is robust, but very demanding in terms of number of scans because it has fairly low statistical power. In this talk, I
will present a new estimator for noise variance in tomographic images reconstructed using algorithms of the filtered backprojection type.
The new estimator operates on data acquired from repeated scans of the object under examination and is unbiased, as the usual
estimator, but it is shown to have significantly lower variance for many scenarios of practical interest. An extensive theoretical analysis of
this estimator will be presented, highlighting the circumstances under which it is most effective. This
analysis includes both general and specific data-correlation patterns. Moreover, performance of the estimator on X-ray
computed tomography data will be shown to demonstrate the efficacy of the new estimator in a medical imaging context.
Este minicurso se realizará durante los días:
Jueves 18 de noviembre de 2010 : 13.15 - 14.45 Jueves 25 de noviembre de 2010 : 13.15 - 14.45 Jueves 02 de diciembre de 2010 : 13.15 - 14.45