SparseCT: System concept and design of multislit collimators

Abstract

Purpose: SparseCT, an undersampling scheme for compressed sensing (CS) computed tomography (CT), has been proposed to reduce radiation dose by acquiring undersampled projection data from clinical CT scanners (Koesters et al. in, SparseCT: Interrupted-Beam Acquisition and Sparse Reconstruction for Radiation Dose Reduction; 2017). SparseCT partially blocks the x-ray beam with a multislit collimator (MSC) to perform a multidimensional undersampling along the view and detector row dimensions. SparseCT undersamples the projection data within each view and moves the MSC along the z-direction during gantry rotation to change the undersampling pattern. It enables reconstruction of images from undersampled data using CS algorithms. The purpose of this work is to design the spacing and width of the MSC slits and the MSC motion patterns based on beam separation, undersampling efficiency, and image quality. The development and testing of a SparseCT prototype with the designed MSC will be described in a following paper.

Methods: We chose a few initial MSC designs based on the guidance from two metrics: beam separation and undersampling efficiency. Both beam separation and undersampling efficiency were measured from numerically simulated photon distribution with MSC taken into consideration. Beam separation measures the separation between x-ray beams from consecutive slits, taking into account penumbra effects on both sides of each slit. Undersampling efficiency measures the dose-weighted similarity between penumbra undersampling and binary undersampling, in other words, the effective contribution of the incident dose to the signal to noise ratio of the projection data. We then compared the initially chosen MSC designs in terms of their reconstruction image quality. SparseCT projections were simulated from fully sampled patient projection data according to the MSC design and motion pattern, reconstructed iteratively using a sparsity-enforcing penalized weighted least squares cost function with ordered subsets/momentum algorithm, and compared visually and quantitatively.

Results: Simulated photon distributions indicate that the size of the penumbra is dominated by the size of the focal spot. Therefore, a wider MSC slit and a smaller focal spot lead to increased beam separation and undersampling efficiency. For fourfold undersampling with a 1.2 mm focal spot, a minimum MSC slit width of three detector rows (projected to the detector surface) is needed for beam separation; for threefold undersampling, a minimum slit width of four detector rows is needed. Simulations of SparseCT projection and reconstruction indicate that the motion pattern of the MSC does not have a visible impact on image quality. An MSC slit width of three or four detector rows yields similar image quality.

Conclusion: The MSC is the key component of the SparseCT method. Simulations of MSC designs incorporating x-ray beam penumbra effects showed that for threefold and fourfold dose reductions, an MSC slit width of four detector rows provided reasonable beam separation, undersampling efficiency, and image quality.

Keywords: CT; SparseCT; Undersampling; compressed sensing; multislit collimator (MSC); penumbra.

Figure 1

SparseCT is a compressed sensing approach that undersamples along detector row direction within each view. It interrupts the continuous beam with a multislit collimator (MSC) to acquire projection data that are undersampled along the detector row direction. The MSC moves along the detector row direction as the gantry rotates to change the undersampling pattern for each view.

Figure 2

The finite size of the focal spot causes a significant penumbra on both sides of the undersampled beam.

Figure 3

Three types of photon distributions along detector row direction: no undersampling, penumbra undersampling, and binary undersampling. Penumbra undersampling and binary undersampling have different photon distributions but the same area under the curve. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 4

The numerically simulated photon distributions (blue curves) and experimentally measured photon distributions (red dots) at multiple multislit collimator (MSC) slit locations using two focal spot sizes (stdHR, large; superHR, small), normalized to the photon distribution without the MSC. Each peak corresponds to the simulation/measurement at one slit location. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 5

In the experimental validation of the photon distribution, each multislit collimator slit is mimicked by two plates of adaptive collimator in close proximity. Because the two plates are at uneven heights with the plate on cathode side being higher, the flux toward the anode is strongly blocked.

Figure 6

Photon distributions corresponding to six multislit collimator (MSC) designs and two focal spot sizes, normalized to the photon distribution without the MSC. Each peak is an undersampled beam passing through an MSC slit. The numbers in red are the FWHM of each undersampled beam, in units of detector rows. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 7

(a) Fully sampled patient projection, (b) regions where I0B/I0A > 0.2 (marked in white) based on a W4S16 multislit collimator and a large focal spot, (c) noise to be inserted, and (d) simulated undersampled SparseCT projection.

Figure 8

Comparison between different multislit collimator designs (W4S12, threefold dose reduction; W3S12, fourfold dose reduction; and W4S16, fourfold dose reduction) under the assumption of linear motion.

Figure 9

Comparison between different multislit collimator designs (W4S12, threefold dose reduction; W3S12, fourfold dose reduction; and W4S16, fourfold dose reduction) under the assumption of random motion.

Figure 10

(a) The prototype of SparseCT with multislit collimator (MSC) installed and (b) a zoomed view of W4S16 MSC. [Color figure can be viewed at wileyonlinelibrary.com]