Currently, image compression algorithms are an integral part of modern information systems in various industries and spheres of human activity, including telecommunications, medicine, artificial intelligence, and defense technologies. This paper deals with a novel image compression method based on nonlinear multiscale decomposition with fractional-rational approximation, providing a compact representation of image components while preserving reconstruction quality. The proposed algorithm consists of five steps, including image preprocessing, discretization, nonlinear multiscale decomposition, quantization, and arithmetic compression. The method was evaluated using 1000 test images and demonstrated an average compression ratio of 13.2, with reconstructed image quality of 41.5 dB, outperforming classical wavelet-based approaches under comparable  conditions  (approximately by 8-10% in average). The computational complexity of the proposed algorithm remains suitable for practical implementation, making it a promising solution for efficient image compression in modern digital systems.