This paper addresses the problem of optimizing computational costs in the modified Kalman filter used for suppressing autocorrelated noise in digital images. Such noise is a common feature of many practical applications, including medical imaging, Earth remote sensing, and real-time video processing. The classical discrete Kalman filter, while being optimal in terms of minimizing the mean square error, is insufficiently effective under autocorrelated disturbances. In this case, a solution to the discrete filtering problem can be obtained by extending the state vector through the inclusion of additional variables that describe the structure of the noise component. This approach enables more accurate signal restoration but leads to a sharp increase in computational complexity due to the growth of matrix dimensionality and memory requirements. To reduce these computational costs, three optimization strategies for optimizing the filtering algorithm are analyzed: the use of sparse matrix representations, which significantly reduce the number of operations for data storage and processing; multithreaded processing on CPUs to increase computational parallelism; and the transfer of computationally intensive procedures to graphics processing units (GPUs). The experimental study involves testing the developed algorithms on the CIFAR-10 dataset, to which artificially generated autocorrelated noise was added. The results demonstrate that the greatest performance gain is achieved with the GPU-based implementation (a 6–7× speedup compared to the baseline scheme), while the effectiveness of multithreading and sparse matrices depends on the dataset size and structure. The findings confirm the potential of the proposed solutions for practical use in high-performance image filtering systems and their integration into modern machine learning methods.
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Osipenko Igor Nikolaevich
Ulyanovsk State University
Ulyanovsk, Russian Federation
