Spectrally joint reconstruction and material classification from multi-energy CT

X-ray computed tomography (CT) is a popular technique for non-destructive examination of the interior of an object in medical diagnosis and security applications. This technique can reconstruct a high-resolution three-dimensional (3D) image of the object from projection data collected at different angles.

The emergence of energy-discriminating photon counting detectors (PCD) has paved the way to spectral (or multi-energy) X-ray CT which can simultaneously retrieve the linear attenuation coefficients (LAC) of materials as function of photon energy with polychromatic sources. The extraction of LACs at multiple energies can potentially enhance material separation than the traditional energy-integrating or dual energy detectors.

This thesis presents a new joint reconstruction algorithm and new classification methods which can classify materials into energy-independent features such as electron density (ρe) and effective atomic number (Zeff). The methods and the algorithm developed to address the challenges of spectral CT for security applications are briefly explained below.First, we propose a material classification method using a dual basis function decomposition which is based on the fact that the LAC of any material can be accurately reproduced by a linear combination of material- and energy-dependent components.

The method requires a calibration phase to register the energy-dependent basis functions of the decomposed LACs by employing a set of reference materials. Materials are then classified into ρe and Zeff , while these two parameters can completely identify the materials that may be found in the luggage.

The method is explored in the broad range of 6 ≤ Zeff ≤ 23 that includes the most materials important in explosive detection. Our method outperforms another state-of-the-art method called SRZE, providing up to 32 times better time efficiency for the image reconstruction with similar performance. Second, we present a new joint reconstruction algorithm called L∞ norm-based vectorial total variation (L∞-VTV), which utilizes the increased information from spectral LACs.

The algorithm is tested for experimental data acquired with the low signal-to-noise ratios (SNR) and few projections. It is demonstrated that the algorithm can outperform another state-of-the-art joint reconstruction in terms of reconstruction quality and classification from such data. Third, how the correction step for spectral distortions in a PCD influences the resulting material classification is analyzed.

This is because the spectra measured with PCDs are usually distorted by charge accumulation artifacts, such as pileup of photons and charge sharing between detector pixels. Fourth, we develop another classification method using a basis material decomposition which is based on the fact that the LAC of any material can be correctly restored by a linear combination of equivalent thicknesses and LACs of several basis materials.

The method requires a calibration phase in which a set of reference materials are measured to compute corresponding equivalent thicknesses. Equivalent thicknesses of the scanned unknown objects are found, and their Zeff values are calculated by interpolation or extrapolation with respect to the reference materials.

This method shows better accuracy in estimating Zeff than the first classification method mentioned above, when the number of projections is decreased or the data SNR is decreased. Both methods do not require a-priori knowledge of the sample. In the thesis, we address some challenges of spectral CT.

First, the division of photon counts into many energy bins significantly reduces data SNR in each bin. Second, if the widths of energy bins are lower than detector’s energy resolution, classification performance may not be improved further. Lastly, reconstructing many individual energy bins is computationally expensive.

Therefore, the experimental data is rebinned into smaller numbers of energy bins prior to reconstruction, which are optimized for each developed method in terms of classification performance.