Coded aperture optimization for single pixel compressive computed tomography

One of the main challenges in Computed Tomography (CT) is to obtain high-quality image reconstructions by using low-cost architectures. To alleviate this problem, the compressive sensing (CS) theory has been used to develop CT architectures with a partial reduction of the detector dimension by the inclusion of coded apertures. This dimensional reduction is possible, since, CS defy the conventional imaging notion that the detector dimension must match that of the object embedding space. Therefore, CS-CT architectures with low-resolution detectors have been developed in order to reduce the number of elements in the detector array, and so, the cost. However, in CT-CS architectures the approach of reducing the dimension of the detector array to the extreme case of a single pixel detector has not yet been studied. This work aims at studying the problem of obtaining high-quality CT images from coded projections acquired by a CS-CT architecture with a single pixel detector. Coded apertures are specially designed to enhance the peak signal-to-noise ratio of the reconstructed images. Simulation results show that the reconstructed images using the single pixel architecture gain up to 7.31 dB in average when random coded apertures are used and 14 dB in average using the designed codes with respect to a sparse view angle CS-CT architecture with full detector array, and a CS-CT architecture with modulated X-ray beam.