The work aims to effectively remove Gauss noise from surface defect image of strip steel. Gauss noise is one of the main types of noise affecting strip image quality. To remove Gauss noise from the surface defect image, firstly the dictionary of traditional K-SVD (K-means and Singular Value Decomposition) algorithm was improved, then orthogonal matching pursuit (OMP, Orthogonal Matching Pursuit) algorithm was used to reconstruct the image and remove the noise, later this algorithm was applied to Gauss noise filter of the defect image. In order to verify de-noising effect of the proposed algorithm, several typical defect images (scratches, bubbles, oxidation tint, bond lines) were selected for test simulation, and were compared in various traditional filtering methods including median filtering, mean filtering, wavelet transform, Wiener filter, 3D block matching (BM3D). In the proposed algorithm, average value of PSNR (Peak Signal to Noise Ratio) was 33.976 dB, MSE (Mean Square Error) 27.607 and SSIM (Structural Similarity) 0.912. This algorithm provides clear edges and details of surface defect reconstructed images of steel strip. Performance indices PSNR, MSE and SSIM are significantly better than other traditional filtering algorithms, and they have favorable denoising effects.