The article examines the influence of the data processing direction on the results of the discrete cosine transform (DCT). Based on the theory of groups, the symmetries of the basic functions of the DCT are considered, and the changes that occur when the direction of signal processing is changed are analyzed. It is shown that the antisymmetric components of the basis change sign in the reverse order of counts, while the symmetric ones remain unchanged. Modified expressions for block PREP are proposed, taking into account the change in the processing direction. The invariance of the frequency composition of the transform to the data processing direction has been experimentally confirmed. The results demonstrate the possibility of applying the proposed approach to the analysis of arbitrary signals, including image processing and data compression.

Keywords: discrete transforms, basic functions, invariance, symmetry, processing direction, matrix representation, correlation

This paper considers the problem of removing noise from an image based on the discrete cosine transform (DCT) algorithm. Despite its simplicity, the algorithm is still popular in image conversion. However, recently there has been a strong development of convolutional neural networks, leaving behind “traditional” signal processing methods. In this paper, we study image denoising using DCT and convolutional neural networks and creating an interpretable convolutional neural network to obtain accurate data. The basis was the Python programming language and the library for working with neural networks – PyTorch. Based on this, a neural network model was trained on The Berkeley Segmentation Dataset. Experiments have shown that the trained neural network shows results comparable to traditional image denoising algorithms.

Keywords: noise reduction, convolutional neural network, discrete cosine transform, machine learning, signal processing, Canny operator