Mean Risk Functional Minimization Based on Finite (Small) Amount of Experimental Data[1]

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

Deep Learning Techniques in Image Super-Resolution [2]

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.

[1]©M. V. Volkova, O. N. Granichin, 2017.

[2]©A. A. Senov, 2017.