Low‐dose cone‐beam CT via raw counts domain low‐signal correction schemes: Performance assessment and task‐based parameter optimization (Part II. Task‐based parameter optimization)
Authors: Gomez‐Cardona Daniel , Hayes John W. , Zhang Ran , Li Ke , Cruz‐Bastida Juan Pablo , Chen Guang‐Hong 
Published: March 2018

Purpose

Different low‐signal correction (LSC) methods have been shown to efficiently reduce noise streaks and noise level in CT to provide acceptable images at low‐radiation dose levels. These methods usually result in CT images with highly shift‐variant and anisotropic spatial resolution and noise, which makes the parameter optimization process highly nontrivial. The purpose of this work was to develop a local task‐based parameter optimization framework for LSC methods.

Methods

Two well‐known LSC methods, the adaptive trimmed mean (ATM) filter and the anisotropic diffusion (AD) filter, were used as examples to demonstrate how to use the task‐based framework to optimize filter parameter selection. Two parameters, denoted by the set , for each LSC method were included in the optimization problem. For the ATM filter, these parameters are the low‐ and high‐signal threshold levels pl and ph; for the AD filter, the parameters are the exponents δ and γ in the brightness gradient function. The detectability index d′ under the non‐prewhitening (NPW) mathematical observer model was selected as the metric for parameter optimization. The optimization problem was formulated as an unconstrained optimization problem that consisted of maximizing an objective function , where i and j correspond to the i‐th imaging task and j‐th spatial location, respectively. Since there is no explicit mathematical function to describe the dependence of d′ on the set of parameters for each LSC method, the optimization problem was solved via an experimentally measured d′ map over a densely sampled parameter space. In this work, three high‐contrast–high‐frequency discrimination imaging tasks were defined to explore the parameter space of each of the LSC methods: a vertical bar pattern (task I), a horizontal bar pattern (task II), and a multidirectional feature (task III). Two spatial locations were considered for the analysis, a posterior region‐of‐interest (ROI) located within the noise streaks region and an anterior ROI, located further from the noise streaks region. Optimal results derived from the task‐based detectability index metric were compared to other operating points in the parameter space with different noise and spatial resolution trade‐offs.

Results

The optimal operating points determined through the d′ metric depended on the interplay between the major spatial frequency components of each imaging task and the highly shift‐variant and anisotropic noise and spatial resolution properties associated with each operating point in the LSC parameter space. This interplay influenced imaging performance the most when the major spatial frequency component of a given imaging task coincided with the direction of spatial resolution loss or with the dominant noise spatial frequency component; this was the case of imaging task II. The performance of imaging tasks I and III was influenced by this interplay in a smaller scale than imaging task II, since the major frequency component of task I was perpendicular to imaging task II, and because imaging task III did not have strong directional dependence. For both LSC methods, there was a strong dependence of the overall d′ magnitude and shape of the contours on the spatial location within the phantom, particularly for imaging tasks II and III. The d′ value obtained at the optimal operating point for each spatial location and imaging task was similar when comparing the LSC methods studied in this work.

Conclusions

A local task‐based detectability framework to optimize the selection of parameters for LSC methods was developed. The framework takes into account the potential shift‐variant and anisotropic spatial resolution and noise properties to maximize the imaging performance of the CT system. Optimal parameters for a given LSC method depend strongly on the spatial location within the image object.