The X-ray images of Integrated Circuits （IC） generally have high noise and low contrast characteristics. Considering the different needs in detail preservation and noise removal of edge details and smooth regions， this paper proposes a multi-regularization image restoration method. Firstly， by employing a Fourier transform based Gauss high-pass filter and Gauss low-pass filter， the edge detail and smoothing filter results were obtained as new observed images for image restoration. Then， a TV-l₁ mixed regularization model， which takes full use of the advantages of l₁ regularization term in detail preservation and Total Variation （TV） regularization term in noise removal， was designed. The model is capable of addressing the problem of excessive smoothing or defective denoising caused by a single regularization term. Experiments on standard and IC X-ray images show that the proposed method can effectively remove noise while retaining more details， laying a foundation for subsequent defect detection of IC.