Wavelets are widely used in various fields of science and technology for processing 1D signals and multidimensional images. However, technical information processing devices are developing more slowly than the amount of digital data is growing. Computational latency is the most important characteristic of such devices. This paper proposes an implementation of the Winograd method with a convolution step 2 to reduce the latency of wavelet image processing. The proposed scheme for implementing calculations has reduced the asymptotic computational complexity of wavelet processing of 2D images to 53% compared to the direct implemettaion method. A theoretical assessment of the computing device characteristics showed a reduction in latency of up to 67%. A promising direction for further research is the hardware implementation of the proposed approach on modern microelectronic devices.

Keywords: image processing, Winograd method, digital filtering, computational delay, wavelet transform, convolution with step

In this paper, a physics-informed neural network containing natural gradient descent is proposed to solve the boundary value problem of the Poisson equation. Machine learning methods used in solving partial differential equations are an alternative to the finite element method. Traditional numerical methods for solving differential equations are not capable of solving arbitrary problems of mathematical physics with equivalent efficiency, unlike machine learning methods. The loss function of the neural network is responsible for the accuracy of solving initial and boundary value problems of partial differential equations. The more efficiently the loss function is minimized, the more accurate the resulting solution is. The most traditional optimization algorithm is adaptive moment estimation, which is still used in deep learning today. However, this approach does not guarantee achieving a global minimum of the loss function. We propose to use natural gradient descent with the Dirichlet distribution which increase the accuracy of solving the Poisson equation.

Keywords: natural gradient descent, Poisson equation, Fisher matrix, finite element method, neural networks

Diseases of the cardiovascular system are the main cause of death in the world. The main way to diagnose diseases of the cardiovascular system is to take an electrocardiogram of the patient. Automatic processing of electrocardiogram signals will allow doctors to quickly identify heart problems in a patient. This article presents a method for calculating the detail vector for neural network processing of a twelve-channel electrocardiogram signal. Adding a detail vector to the electrocardiogram signals improves the classification accuracy to 87.50%. The proposed method can be used to automatically classify two or more channel electrocardiogram signals.

Keywords: electrocardiogram, recurrent neural network, neural network with long-term short memory, detailing vector, PhysioNet Computing in Cardiology Challenge 2021