Coded Aperture Optimization in X-ray Tomography via Sparse Principal Component Analysis

Coded aperture X-ray computed tomography (CAXCT) systems reconstruct high quality images of the inner structure of an object from a few coded illumination measurements. Since the CT system matrix is highly structured, random coded apertures lead to lower quality image reconstructions. In this paper, the noisy forward models of CAXCT in both Gaussian noise and Poisson noise are formulated and analyzed. In addition, a coded aperture optimization approach based on sparse principal component analysis is proposed to maximize the information sensed by a set of fan-beam projections. The complexity of the proposed optimization method is on the same order of magnitude as that of state-of-the-art methods but provide superior image quality. Computational experiments using simulated datasets and real datasets show gains up to $\sim$ 4.3dB with SNR = 25dB in the reconstruction image quality compared with that attained by random coded apertures.