Adaptive coded aperture design for compressive computed tomography

Computed tomography (CT) is a non-invasive scanning technique that allows the visualization of the internal structure of an object from X-ray projections. These projections are frequently affected by different artifacts, including the beam hardening (BH) effect, among others. The BH effect is produced by high X-ray attenuation due to dense elements inside the object of interest. Traditionally, BH artifacts are addressed by applying oversampling techniques. However, the prolonged X-ray exposition represents a risk to the patient's health. To overcome this drawback, undersampling CT approaches have been developed, e.g., the coded aperture computed tomography (CA-CT) which is based on the compressive sensing (CS) theory. Nevertheless, CA-CT has not been extended for addressing the BH effect. This work proposes an adaptive coded aperture sensing methodology based on a fan-beam X-ray architecture to reduce the BH artifacts. The proposed methodology uses an initial sampling to identify high-density elements and an adaptive sampling to avoid the acquisition of those dense elements. Specifically, the proposed method is summarized into three main steps: (i) sensing matrix analysis via Gershgorin theorem; (ii) coded aperture optimization criteria based on view angles, pixels of the object, and dense elements; (iii) coded aperture optimization algorithm through the sensing matrix analysis and the proposed optimization criteria. Simulation results show that the reconstructed images by the proposed adaptive methodology gain up to 12[dB] in averaged peak signal-to-noise ratio (PSNR) compared to the traditional CA-CT approach which implements non-designed coded apertures.