ABSTRACTS

M. V. Volkova, O. N. Granichin St. Petersburg State University
m.volkova@spbu.ru

o.granichin@spbu.ru

Key
words: mean risk functional, estimation, confidence set, sign-perturbed sums,
dynamic fracture, incubation time.

For many practical important problems of adaptive control, machine
learning, determining of implicit parameters of systems or materials the
solving processes are often based on the one or another search methods for the
adequacy of unknown regression function with experimental observation data.
Statistic methods of mean risk functional minimization are usually applied to
treatment of data with the noise. Its application is stipulated by great amount
of observations with sufficient diversity. However, in practice, it is very
dubiously to use them for the cases of finite (probably small) number of
observations. In this paper the problem to construct the confidence set with
given probability for a vector of unknown parameters are studied. The modified
sign-perturbed sums method (MSPS) is proposed. Theoretical results are applied
to the problem of fracture mechanics to determine the value of incubation time
characterizing the dynamic strength of materials.

Bibliogr.:
22 refs.

A. A. Senov

Saint Petersburg State University alexander.senov@gmail.com

Key
words: super-resolution, deep learning, parameter estimation, optimization.

Image analysis is an actively evolving research
area during the last decades. Particularly super-resolution is one of its
important subareas. Images with high resolution have better perception
characteristics and improve succeeding analysis quality. One of the most
important ways to achieve image resolution quality is to use better tools for
image capturing. However, this approach is limited by technical restrictions
and equipment cost. To overcome these obstacles, the super-resolution approach
was proposed — an approach based on constructing one high resolution image from
one or several low resolution images. We review algorithmic approaches for
image super-resolution problem. Special attention is paid to methods based on
deep learning which have shown competitive results in recent years.
Particularly, we discuss the problem of deep neural network parameters estimation
which is actual in the super-resolution problem

Bibliogr.: 38 refs.