Industrial radiography can help to detect discontinuities in welded objects, but the technique suffers some major disadvantages related to fog and noise, and there is also a need to impose some further processing to detect the discontinuities in the images. The dynamic range of foggy radiographs is narrow, making it difficult to maximize the contrast of an image. In this paper, we utilize an ℓ1 − ℓ0 minimization methodology that deconstructs X-ray images into a base layer and a detail layer. Afterward, to reconstruct the denoised image, an ℓ1 − ℓ0 reconstruction optimization problem will be solved. These results show that the algorithm reduces the foggy parts of radiographs in the base layer and enhances the structure in the detail layer. When compared with the original image, a clearer image can be produced, which can be used for discontinuity detection. Also, the reconstructed images show a very clear and visible discontinuity region in the radiographs.
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