PSF-Informed Reconstruction: An Enhanced 2D Directional Filtered Backprojection Method for Cone-Beam Rotary Computed Laminography

Cone-beam rotary computed laminography (CL) presents a viable alternative to cone-beam CT for imaging objects with high aspect ratios. Conventional reconstruction techniques, such as CL-FBP and CL-FDK, often yield suboptimal results charac?terized by pronounced superimposition artifacts, reduced contrast,and blurred edges, primarily due to their reliance on 1D row-wise filtering along detector rows. To address these limitations and improve reconstruction quality, we proposed a novel 2D directional filtered backprojection (DFBP) method based on the point spread function (PSF). First, an exact expression for the projection process is derived by establishing the relationship between a reconstructed pixel and its corresponding projection point on the detector. Second, a revised backprojection process incorporating two weighting factors is introduced to counteract the nonlinearity inherent in conventional backprojection, leading to a simplified PSF formulation. Third, to circumvent the computational burden of 3D image space filtering,an approximate method by linearizing the coordinate relationship in Fourier space under some assumptions is developed that transfers the 3D filtering operation to the 2D projection space. This approach facilitates the derivation of a formally simple yet effective 2D direc?tional filter, which integrates a 2D von Hann window and a 2D sinc window. Experimental results demonstrate that the proposed method produces reconstructions with superior contrast, sharper boundaries,and fewer superimposition artifacts compared to CL-FBP and CL?FDK. Moreover, it enables more accurate recovery of internal structures, such as bubble defects and electronic components.