Development of algorithms for digital image processing based on the Winograd method in general form and analysis of their computational complexity

The fast increase of quantitative and qualitative characteristics of digital visual data leads to the need to improve the performance of modern image processing devices. This article proposes a new algorithms for 2D digital image processing based on the Winograd method in a general form. An analysis of the obtained results showed that the Winograd method reduces the computational complexity of image processing by up to 84% compared to the traditional direct digital filtering method depending on the filter parameters and image fragments without affecting the quality of image processing. The resulting Winograd method transformation matrices and the developed algorithms can be used in image processing systems to improve the performance of modern microelectronic devices that carry out image denoising, compression, and pattern recognition. Hardware implementation on field-programmable gate array and application-specific integrated circuit, the algorithms development for digital image processing based on the Winograd method in a general form for 1D wavelet filter bank and for convolution with a step used in convolutional neural networks are a promising directions for further research.