Abstract
Computed tomography (CT) allows the three-dimensional internal structure reconstruction of an object illuminated with X-ray light. In CT, a set of twodimensional projections are taken to reconstruct the underlying object structure. The number of projections needed for sensing a CT scene is determined by the Nyquist limit. In some cases, the imposed projections number is excessive. Compressive sensing (CS) has emerged as a new sampling technique requiring fewer projections than those specified by the Nyquist criterion. Instead of measuring the samples directly, they are encoded before being integrated into the detector. This paper describes a CS system for CT based on coded apertures. An optimized value of transmittance and an aperture distribution are selected such that the quality of reconstruction is maximized. Simulations show that results in reconstruction with 50% of measurements are comparable with the traditional CT method based on Nyquist criterion. Similarly, results indicate that the PSNR of reconstructed images can be controlled according to the number of projections taken.
Highlights
Computed tomography (CT) is a technology established for the non-invasive acquisition of images from the internal structure of the objects in three dimensions (3D) [1]
Simulations show that results in reconstruction with 50% of measurements are comparable with the traditional CT method based on Nyquist criterion
The CT image reconstruction algorithms have been restricted by the Nyquist theorem [5]; in some CT applications, the established number of projections is excessive since high X-ray dose could be destructive or carcinogenic for human beings [6]
Summary
Computed tomography (CT) is a technology established for the non-invasive acquisition of images from the internal structure of the objects in three dimensions (3D) [1]. The CT image reconstruction algorithms have been restricted by the Nyquist theorem [5]; in some CT applications, the established number of projections is excessive since high X-ray dose could be destructive or carcinogenic for human beings [6]. For this reason, it appears the interest to find acquisition methods for reducing the object exposure to the X-ray radiation, without sacrificing the quality of the images. Compressed sensing (CS) has recently emerged as a branch of signal processing. In CS, the samples are coded in order to reduce the data redundancy in a scene; these coded measurements are enough to reconstruct the signal with a comparable quality of the signal sampled following the Nyquist theorem [8]
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