Coded aperture design for super-resolution compressive X-ray tomography

Computed tomography obtains the inner structure of an object. However, obtaining an accurate image reconstruction while keeping a low radiation dose is a challenging problem. For this purpose, compressed sensing has been studied to reduce the number of measurements required. In this work, we present an algorithm for the design of high-resolution coded apertures for compressed sensing computed tomography. The aim is to combine high-resolution apertures with low-resolution detectors in order to achieve super-resolution. To design the coded apertures, the proposed method iteratively improves random coded apertures using a gradient descending algorithm subject to constraints on the homogeneity induced by the coded aperture of the compressive sensing process. Computational experiments using synthetic data show a significant improvement in the quality of CT image reconstructions achieved with the designed coded apertures over the random coded apertures up to 3dB in terms of PSNR. Further simulations are performed with different transmittances and shots to assess the robustness of the proposed approach.