Coded Aperture Optimization in X-Ray Computed Tomography via Sparse Covariance Matrix Estimation

Coded aperture X-ray computed tomography (CAXCT) measures coded X-ray projections to reconstruct the inner structure of an object. Coded apertures, which determine the point spread function, can be designed to improve the reconstruction quality, but most approaches are computationally expensive, leading to very small images. In this paper, a sparse covariance matrix estimation approach is introduced to minimize the information loss sensed by projections corresponding to large tomographic images. The covariance matrix representing the map of the overlapping information of the projections is obtained by using block matrix multiplication and sparse estimation. A heuristic variant algorithm with a noise factor is presented to search the combinations of D projections leading to maximum non-overlapping information acquisition, where D is the number of unblocking elements on the coded apertures. Numerical experiments with simulated datasets show that the optimization performance of the proposed method is comparable to that of state-of-the-art methods with small images. Further, for the analyzed cases, coded aperture optimization was performed with 512 × 512 images by analyzing coefficients smaller than 0.02% in the covariance matrix.