Purpose. Since fractal image coding is time-consuming and is prone to causing "blocking artifact", the article aims to combine fractal image coding, wavelet transform and compressed sensing to put forward a method which can shorten the coding time effectively and improve the quality of a reconstructed image. Methodology. The compressed sensing algorithm can quickly compress and highly restore sparse matrixes. The paper made use of this feature to conduct fractal coding for a low-frequency sub-image after wavelet transform, followed by recoding the samples of low-frequency differential sub-graphs and high-frequency sub-images by means of the compressed sensing algorithm for the purpose of compensating the quality of reconstructed images. Findings. Compared to the traditional fractal coding method, the algorithm in the paper (hereinafter referred to as "this Algorithm") can shorten the time considerably and get a maximum speed-up ratio by up to 6,45 times. Compared to the compressed sensing coding method, the quality of the reconstructed images is improved significantly. Originality. The innovation of the paper lies in applying the compressed sensing theory to the fractal coding algorithm to compensate the quality of the reconstructed images obtained by means of fractal coding based on wavelet transform. Practical value. This Algorithm can shorten the coding time on the basis of ensuring the quality of a reconstructed image, and has certain significance for promoting the fractal coding method.

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