Image reconstruction algorithm regularized by anisotropic gradient sparsity and low rank for cone beam computed laminography

X-ray computed laminography (CL) has emerged as the preferred nondestructive imaging technique for inspecting plate-shell components. However, its unique scanning geometry inevitably leads to incomplete projection data, thereby causing significant aliasing artifacts and structural degradation in reconstructed images. To address this issue, we propose a novel CL reconstruction model that incorporates anisotropic gradient, sparse, and low-rank (AGSLR) regularization. The model leverages both the local smoothness and global spatial correlation of CL images. Specifically, local smoothness is captured through total variation (TV), while global spatial correlation is characterized by tensor nuclear norm (TNN). Furthermore, the model encodes the differential restoration capabilities of horizontal and vertical edges in CL images as a prior by introducing anisotropic TV terms. A numerical solver is devised utilizing the Chambolle-Pock (CP) algorithm. Experimental results on simulated and real data demonstrate that the proposed algorithm significantly outperforms existing methods in suppressing cone-beam artifacts, reducing noise, and recovering structural details.