Joint Statistical Iterative Material Image Reconstruction for Spectral Computed Tomography Using a Semi-Empirical Forward Model

Abstract

By acquiring tomographic measurements with several distinct photon energy spectra, spectral computed tomography (spectral CT) is able to provide additional material-specific information compared with conventional CT. This information enables the generation of material selective images, which have found various applications in medical imaging. However, material decomposition typically leads to noise amplification and a degradation of the signal-to-noise ratio. This is still a fundamental problem of spectral CT, especially for low-dose medical applications. Inspired by the success for low-dose conventional CT, several statistical iterative reconstruction algorithms for spectral CT have been developed. These algorithms typically rely on detailed knowledge about the spectrum and the detector response. Obtaining this knowledge is often difficult in practice, especially if photon counting detectors are used to acquire the energy specific information. In this paper, a new algorithm for joint statistical iterative material image reconstruction is presented. It relies on a semi-empirical forward model which is tuned by calibration measurements. This strategy allows to model spatially varying properties of the imaging system without requiring detailed prior knowledge of the system parameters. We employ an efficient optimization algorithm based on separable surrogate functions to accelerate convergence and reduce the reconstruction time. Numerical as well as real experiments show that our new algorithm leads to reduced statistical bias and improved image quality compared with projection-based material decomposition followed by analytical or iterative image reconstruction.

Feasibility of multi‐contrast imaging on dual‐source photon counting detector (PCD) CT: An initial phantom study

“…This was done to compare the underlying performance of the different approaches without potentially confounding the results by inclusion of other factors, such as iterative reconstruction. The material decomposition performance shown here most likely can be further improved if iterative reconstruction and material decomposition methods that include noise reduction techniques were to be used . Note that DS technology required image‐based decomposition methods, which were indeed used for this study.…”

“…The material decomposition performance shown here most likely can be further improved if iterative reconstruction and material decomposition methods that include noise reduction techniques were to be used. [43][44][45][46][47][48][49][50][51][52][53] Note that DS technology required image-based decomposition methods, which were indeed used for this study.…”

Comparison of five one-step reconstruction algorithms for spectral CT

“…The aberrant pixels observed after projection-based decomposition illustrate that loss of information: the reconstruction step cannot go back to the photon counts, and therefore must rely on aberrant decomposition results. Recently, several methods have been proposed which reconstruct material-specific volumes directly from the photon counts [5,19,37,3,22,7]. They are commonly referred to as "one-step inversion", or simply "one-step" methods.…”

Kullback-Leibler residual and regularization for inverse problems with noisy data and noisy operator

“…All of these methods are iterative: there is currently no analytical inversion formula for the material decomposition problem. They asssume a well-known detector response function [16,2,28,19]. In this work, we have used the Mechlem approach to minimize the regularization functional.…”

“…The minimization also integrates Ordered Subsets (OS) and Nesterov acceleration. The minimization method is described in detail in [19].…”