Fast optimization of coded apertures in X-ray computed tomography.

Coded aperture X-ray computed tomography (CAXCT) is a novel X-ray imaging system capable of reconstructing high quality images from a reduced set of measurements. Coded apertures are placed in front of the X-ray source in CAXCT so as to obtain patterned projections onto a detector array. Then, compressive sensing (CS) reconstruction algorithms are used to reconstruct the linear attenuation coefficients. The coded aperture is an important factor that influences the point spread function (PSF), which in turn determines the capability to sample the linear attenuation coefficients of the object. A coded aperture optimization approach was recently proposed based on the coherence of the system matrix; however, this algorithm is memory intensive and it is not able to optimize the coded apertures for large image sizes required in many applications. This paper introduces a significantly more efficient approach for coded aperture optimization that reduces the memory requirements and the execution time by orders of magnitude. The features are defined as the inner product of the vectors representing the geometric paths of the X-rays with the sparse basis representation of the object; therefore, the algorithm aims to find a subset of features that minimizes the information loss compared to the complete set of projections. This subset corresponds to the unblocking elements in the optimized coded apertures. The proposed approach solves the memory and runtime limitations of the previously proposed algorithm and provides a significant gain in the reconstruction image quality compared to that attained by random coded apertures in both simulated datasets and real datasets.