Abstract In this paper, the image processing capability of the CNN algorithm under the chaotic recursive diagonal model is explored from two aspects of medical image fusion and compression. By analyzing the structure of the chaotic recursive diagonal model, it is possible to combine it with a neural network. A convolutional neural network is used to automatically extract the focusing features of an image and output the probability of a pixel focusing. Combining the convolutional layer to extract image features with the activation function to nonlinearly map the feature map to achieve the effect of image fusion. Focusing on the exploration of the CNN algorithm for image fusion in image compression application processes. The results show that in the image fusion experiments, the CNN algorithm for image fusion data MI mean value is 6.1051, variance is 0.4418. QY mean value is 0.9859. The variance value is 0.0014. Compared to other algorithms, CNN in the image fusion effect has the effect of better distinguishing the edge details and making the appropriate decision. The CNN algorithm of the compression time is shorter. The time used in the compression of the X-chest image is 2.75s, which is 0.42 less than other algorithms. This study provides a new research perspective for medical image processing and is beneficial to improving the efficiency of medical image processing.