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The edge information of a medical image is the basis of the analysis and processing of that medical image. The medical image contains the muscle, blood vessels and other interference information, which is large but leads the edge detection to become very difficult. So the research into an image edge detection algorithm has become one of the key technologies in image processing, and has important significance in the field of practical application. A new edge detection algorithm based on wavelet transform is proposed in this paper on the basis of regression analysis. Firstly, the signal is decomposed into approximate part and detailed part by the wavelet transform. Secondly, the wavelet coefficients of the detailed part are influenced by the threshold. Finally, the regression function of the signal is obtained by reconstructing wavelet coefficients. The experimental results show that the signal-noise ratio of the improved algorithm is clearly higher than the original, and it is helpful for improving the regression accuracy in terms of the wavelet transform. The algorithm can effectively remove noise, and the local feature of the signals is fully retained.