In recent decades, there has been a trend towards the collection, storage and processing of a large amount of data obtained from various sources. A significant bottleneck today is that the huge amounts of data being collected lead to prohibitively time-consuming optimization problems that are often difficult to solve in real time. The problem of data processing and pattern recognition also arises in medical applications. The International Agency for Research on Cancer (IARC) of the World Health Organization has published the 2020 Global Statistical Report, which notes that for the first time, breast cancer has officially ranked first in the world in the number of deaths from cancer. Breast cancer is a major disease that threatens women's life and quality of life, and its incidence ranks first among female malignant tumors in the world. Ultrasound computed tomography has many advantages in the early detection of breast cancer: safe, convenient, and reproducible. It can provide high-resolution reflection images and high-sensitivity sound speed images of dense breasts commonly seen in East Asian women, improving the accuracy of benign and malignant breast cancer identification. Recent advances in science and technology have made it possible to move on to the creation of high-precision ultrasonic equipment. A new type of ultrasonic equipment consists of a large number of sensors that emit a signal in a predetermined sequence. The use of a large set of sensors theoretically allows visualization of internal structures with high accuracy, but in practice leads to the need to process a huge data stream. A new generation ultrasound tomograph can be used for the prevention and early diagnosis of breast cancer, which can help increase life expectancy and reduce the overall mortality rate from cancer. Thus, the problem posed in the project of processing high-dimensional data and pattern recognition in real-time systems has academic, applied and social significance.

Existing solutions in the field of functional reconstruction based on data obtained during ultrasound examination from a new generation device consisting of a group of sensors have a number of significant problems in addition to processing a large number of measurements. To conduct a full-fledged analysis, three types of reconstruction are required: the speed of the signals, the degree of attenuation of the signals, and the reflection of the signals. There are many works devoted to this topic. However, due to the functional and technical features of the new ultrasonic equipment, as well as the specifics of the task itself, existing methods introduce significant errors in the recovery procedure. Significant difficulties are the high degree of heterogeneity of the unknown medium under study, in which a number of physical effects occur, including refraction and reflection of signals. The complexity of solving the project problem is determined by the presence of uncertainties inherent in ultrasonic data, namely: noisiness and low resolution compared to more expensive research methods, the use of which may be difficult or impossible due to the nature of the problem being solved. The project proposes the development of distributed optimization methods and big data mining to improve the existing developments of the Chinese side and move to a new technological level, as well as increase competitiveness compared to world analogues.

Huazhong University of Science and Technology, a participant in the project, has developed the first breast ultrasound computed tomography system based on circular probe with completely independent intellectual property rights in China. The cooperation with St. Petersburg State University is aimed at improving the developed system in terms of algorithmic enhancements through the development of new distributed stochastic optimization methods for high-dimensional problems. In particular, the cooperation includes joint debugging of the ultrasound computed tomography system and the acquisition system, sparse acquisition and reconstruction optimization of the ultrasound computed tomography system data based on the new stochastic optimization methods.

Expected outcomes:
A. New methods of stochastic distributed optimization for high-dimensional problems with application to ultrasonic computed tomography have been developed, their theoretical analysis has been carried out.
B. The research results of this project are applied to the actual ultrasound computed tomography system to provide high-resolution breast ultrasound tomography structural and functional images for clinical use.
C. The teams have applied for the external financial support: RSF-NSFC collaborative research project.
D. The teams have published 1 paper in Q1 or Q2 (SJR/JCR) journal.

The Chinese and Russian sides have carried out thorough preliminary research on the development of an ultrasound computed tomography system, data analysis and optimization algorithms. Both parties have the necessary hardware and software. These conditions ensure that the project achieves the expected results. The results of the project will be important for the social sphere and the development of scientific knowledge in the field of optimization. The planned results of the project will exceed the world level in the field of optimization theory and pattern recognition.