Localized X-ray compressive computer tomography reconstruction by designing measurement matrix

X-ray computed tomography (CT) is a noninvasive process for acquiring 3D images from the internal structure of an object. Traditionally, the number of samples needed to recover images from X-ray projections is due to the Nyquist criteria. Recently, a sampling protocol based on compressive sampling (CS) theory has been proposed for reducing the number of required samples. The compressive CT system measures coded projections by using coded apertures that can be adjusted to increase the quality of the retrieved information. In areas such as medicine, geology, and industry, there are applications where it is important the high resolution in only specific parts of the scene, and the additional information is ignored. The compressive CT system allows taking more compressive information of some part of the scene by designing the sensing matrix. This work formulates a localized reconstruction approach in compressive CT by downsampling the non-interest regions selectively and designing the coded apertures for ensuring a uniform sampling for the regions of interest. This process decreases the number of samples required to reconstruct all the data with a high resolution and to preserve a high quality only in the regions of interest. Simulation results, of real and synthetic data, show that the reconstruction algorithms based on CS theory allow the CT images reconstruction for selectively subsampled data and the regions of interest reconstructions have comparable quality to traditional results without selectivity.