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.
ABSTRACT
Compressive spectral imaging (CSI) systems sense 3D spatio-spectral data cubes with just a few two-dimensional (2D) projections by using a coded aperture, a dispersive element, and a focal plane array (FPA). The coded apertures in these systems, whose main function is the modulation of the data cube, are often implemented through photomasks attached to piezoelectric devices. A remarkable improvement on this configuration has been recently proposed, the replacement of the block-unblock coded apertures by patterned optical filter arrays, referred to as "colored" coded apertures, which allow spatial and spectral modulation. When using these colored coded apertures, its real implementation in terms of cost and complexity directly depends on the number of filters to be used, as well as the number of shots to be captured. A shifting colored coded aperture optimization featuring these observations is proposed, with the aim to improve the imaging quality reconstruction and to generate an achievable optical implementation with a limited number of filters requiring only one mask to acquire any number of shots. The mathematical model of the computational imaging strategy to overcome the practical limitations of actual CSI systems is presented along with a testbed implementation. Simulations, as well as experimental results, will prove the accuracy and performance of the proposed shifting colored coded aperture design over the current literature designs.
