3D shearlet-based regulariation for inverse problems with an application to industrial X-ray computed tomography

Various regularization terms have been proposed for inverse problems. In this work, we investigate the shearlet-based regularization in the context of sparse-view X-ray computed tomography(XCT) reconstruction of industrial parts. The shearlet transform is a multiscale and multidirectional representation that promotes sparsity in anisotropic features such as edges and textures. Consequently, the shearlet-based regularization effectively preserves fine details (e.g., pores) and texture information while suppressing under-sampling artifacts. The resulting regularized optimization problem is solved using the primal-dual algorithm Condat-Vũ, a very general algorithm that enables the incorporation of various regularization terms. While classical XCT reconstruction methods such as FDK tend to become highly unstable under sparse-view conditions, the proposed shearlet-based method outperforms the baseline method FDK, yielding improved reconstruction image quality and reduced streak artifacts. Fine details are preserved and under-sampling artifacts are mitigated. Moreover, when the number of X-ray projections is reduced to less than 10% of the full industrial acquisition, our results demonstrate that acceptable reconstruction quality can be achieved.