Abstract

Compressive x-ray cone-beam computed tomography (CBCT) approaches rely on coded apertures (CA) along multiple view angles to block a portion of the x-ray energy traveling towards the detectors. Previous work has shown that designing CA patterns yields improved images. Most designs, however, are focused on multi-shot fan-beam (FB) systems, handling a 1:1 ratio between CA features and detector elements. In consequence, image resolution is subject to the detector pixel size. Moreover, CA optimization for computed tomography involves strong binarization assumptions, impractical data rearrangements, or computationally expensive tasks such as singular value decomposition (SVD). Instead of using higher-resolution CA distributions in a multi-slice system with a more dense detector array, this work presents a method for designing the CA patterns in a compressive CBCT system under a super-resolution configuration, i.e., high-resolution CA patterns are designed to obtain high-resolution images from lower-resolution projections. The proposed method takes advantage of the Gershgorin theorem since its algebraic interpretation relates the circle radii with the eigenvalue bounds, whose minimization improves the condition of the system matrix. Simulations with medical data sets show that the proposed design attains high-resolution images from lower-resolution detectors in a single-shot CBCT scenario. Besides, image quality is improved in up to 5 dB of peak signal-to-noise compared to random CA patterns for different super-resolution factors. Moreover, reconstructions from Monte Carlo simulated projections show up to 3 dB improvements. Further, for the analyzed cases, the computational load of the proposed approach is up to three orders of magnitude lower than that of SVD-based methods.

© 2021 Optical Society of America

Coded aperture optimization in compressive X-ray tomography: a gradient descent approach

Angela P. Cuadros and Gonzalo R. Arce
Opt. Express 25(20) 23833-23849 (2017)

Experimental demonstration and optimization of X-ray StaticCodeCT

Angela P. Cuadros, Xiaokang Liu, Paul E. Parsons, Xu Ma, and Gonzalo R. Arce
Appl. Opt. 60(30) 9543-9552 (2021)

Coded aperture optimization for compressive X-ray tomosynthesis

Angela P. Cuadros, Christopher Peitsch, Henry Arguello, and Gonzalo R. Arce
Opt. Express 23(25) 32788-32802 (2015)

Fast optimization of coded apertures in X-ray computed tomography

Tianyi Mao, Angela P. Cuadros, Xu Ma, Weiji He, Qian Chen, and Gonzalo R. Arce
Opt. Express 26(19) 24461-24478 (2018)

Improved resolution in x-ray tomography by super-resolution

Till Dreier, Niccolò Peruzzi, Ulf Lundström, and Martin Bech
Appl. Opt. 60(20) 5783-5794 (2021)