Task-driven optimization of CT tube current modulation and regularization in model-based iterative reconstruction

Abstract

Tube current modulation (TCM) is routinely adopted on diagnostic CT scanners for dose reduction. Conventional TCM strategies are generally designed for filtered-backprojection (FBP) reconstruction to satisfy simple image quality requirements based on noise. This work investigates TCM designs for model-based iterative reconstruction (MBIR) to achieve optimal imaging performance as determined by a task-based image quality metric. Additionally, regularization is an important aspect of MBIR that is jointly optimized with TCM, and includes both the regularization strength that controls overall smoothness as well as directional weights that permits control of the isotropy/anisotropy of the local noise and resolution properties. Initial investigations focus on a known imaging task at a single location in the image volume. The framework adopts Fourier and analytical approximations for fast estimation of the local noise power spectrum (NPS) and modulation transfer function (MTF)-each carrying dependencies on TCM and regularization. For the single location optimization, the local detectability index (d') of the specific task was directly adopted as the objective function. A covariance matrix adaptation evolution strategy (CMA-ES) algorithm was employed to identify the optimal combination of imaging parameters. Evaluations of both conventional and task-driven approaches were performed in an abdomen phantom for a mid-frequency discrimination task in the kidney. Among the conventional strategies, the TCM pattern optimal for FBP using a minimum variance criterion yielded a worse task-based performance compared to an unmodulated strategy when applied to MBIR. Moreover, task-driven TCM designs for MBIR were found to have the opposite behavior from conventional designs for FBP, with greater fluence assigned to the less attenuating views of the abdomen and less fluence to the more attenuating lateral views. Such TCM patterns exaggerate the intrinsic anisotropy of the MTF and NPS as a result of the data weighting in MBIR. Directional penalty design was found to reinforce the same trend. The task-driven approaches outperform conventional approaches, with the maximum improvement in d' of 13% given by the joint optimization of TCM and regularization. This work demonstrates that the TCM optimal for MBIR is distinct from conventional strategies proposed for FBP reconstruction and strategies optimal for FBP are suboptimal and may even reduce performance when applied to MBIR. The task-driven imaging framework offers a promising approach for optimizing acquisition and reconstruction for MBIR that can improve imaging performance and/or dose utilization beyond conventional imaging strategies.

Fig.1

Illustration of the in-plane second order neighborhood over which the penalty is effective. Conventional penalty weighting scheme with ξ_jk = 1 for horizontal and vertical pairwise neighbors, and $\frac{1}{\sqrt{2}}$ for diagonal pairwise neighbors; r_jk is 1 for all directions (not shown).

Fig.2

(a) Polar plots of the Gaussian basis functions used for tube current modulation. The radial axis represents mAs per frame. Views 180^o apart are assigned the same weights in our investigations of a 360° circular scan. (b) A constant and a sinusoidal tube current modulation profiles represented by the Gaussian basis functions (solid) almost completely overlaps with ground truth (dashed).

Fig. 3

(a) The abdomen phantom with the stimulus inserted in the right kidney. (b) Discrimination task of a calcification cluster from a monolithic Gaussian. (c) The frequency domain task function of the imaging task illustrated in (b). (a), (b), and (c) are used for the six imaging strategies described in Sec.2.1. (d) A homogeneous ellipse phantom with a location of interest at the center. (e) Three task functions constructed directly in the Fourier domain presenting low, mid, and high-frequency content. (d) and (e) are used to investigate of the effect of β on the optimal tube current modulation.

Fig.4

The (a) tube current modulation, (b) directional penalty weights, and (c) β for the six imaging strategies detailed in Sec.B.1.6.

Fig.5

The local MTF (row 1) and NPS (row 2) around the location of the imaging task for the six imaging strategies. Theoretical predictions presented at the top half of each figure are compared with empirical estimations presented at the bottom half.

Fig.6

Optimal tube current modulation as a function of β for three imaging tasks presenting low-, mid-, and high-frequency components. For comparison, the α = 0.5 modulation pattern is plotted as red dotted lines in the first column. The β value that yields the highest d′ for each task is indicated by a green circle.

Fig. 7

(a) Test statistics distribution for the two hypotheses under the Task-Driven I₀(θ) + r_jk strategy. Values for the calcification cluster hypothesis were calculated from the 50 reconstructions following Eq.(19) and are shown as the bar plot. A Gaussian fit is superimposed as the solid curve. Distribution for the monolithic Gaussian signal is approximated for purposes of illustration. (b) Template for the Task-Driven I₀(θ) + r_jk strategy.

Fig.8

Reconstruction ROIs corresponding to the 100^th, 80^th, 50^th, and 20^th percentile from the respective test statistics distrubtion for each of the six imaging strategies. Relative d′ to the “Unmod” strategy are shown at the bottom.