Spherically symmetric volume elements as basis functions for image reconstructions in computed laminography

Laminography is a tomographic technique that allows three-dimensional imaging of flat, elongated objects that stretch beyond the extent of a reconstruction volume. Laminography datasets can be reconstructed using iterative algorithms based on the Kaczmarz method.

The goal of this study is to develop a reconstruction algorithm that provides superior reconstruction quality for a challenging class of problems.

Images are represented in computer memory using coefficients over basis functions, typically piecewise constant functions (voxels). By replacing voxels with spherically symmetric volume elements (blobs) based on generalized Kaiser-Bessel window functions, we obtained an adapted version of the algebraic reconstruction technique.

Band-limiting properties of blob functions are beneficial particular in the case of noisy projections and if only a limited number of projections is available. In this case, using blob basis functions improved the full-width-at-half-maximum resolution from 10.2±1.0 to 9.9±0.9 (p value = 2.3·10-4). For the same dataset, the signal-to-noise ratio improved from 16.1 to 31.0. The increased computational demand per iteration is compensated for by a faster convergence rate, such that the overall performance is approximately identical for blobs and voxels.

Despite the higher complexity, tomographic reconstruction from computed laminography data should be implemented using blob basis functions, especially if noisy data is expected.