Iterative clustering material decomposition aided by empirical spectral correction for photon counting detectors in micro-CT

Abstract

Purpose: Photon counting detectors offer promising advancements in computed tomography (CT) imaging by enabling the quantification and three-dimensional imaging of contrast agents and tissue types through simultaneous multi-energy projections from broad X-ray spectra. However, the accuracy of these decomposition methods hinges on precise composite spectral attenuation values that one must reconstruct from spectral micro-CT. Errors in such estimations could be due to effects such as beam hardening, object scatter, or detector sensor-related spectral distortions such as fluorescence. Even if accurate spectral correction is done, multi-material separation within a volume remains a challenge. Increasing the number of energy bins in material decomposition problems often comes with a significant noise penalty but with minimal decomposition benefits.

Approach: We begin with an empirical spectral correction method executed in the tomographic domain that accounts for distortions in estimated spectral attenuation for each voxel. This is followed by our proposed iterative clustering material decomposition (ICMD) where clustering of voxels is used to reduce the number of basis materials to be resolved for each cluster. Using a larger number of energy bins for the clustering step shows distinct advantages in excellent classification to a larger number of clusters with accurate cluster centers when compared with the National Institute of Standards and Technology attenuation values. The decomposition step is applied to each cluster separately where each cluster has fewer basis materials compared with the entire volume. This is shown to reduce the need for the number of energy bins required in each decomposition step for the clusters. This approach significantly increases the total number of materials that can be decomposed within the volume with high accuracy and with excellent noise properties.

Results: Utilizing a (cadmium telluride 1-mm-thick sensor) Medipix detector with a $55\text{-}\mu m$ pitch, we demonstrate the quantitatively accurate decomposition of several materials in a phantom study, where the sample includes mixtures of soft materials such as water and poly-methyl methacrylate along with contrast-enhancing materials. We show improved accuracy and lower noise when all five energy bins were used to yield effective classification of voxels into multiple accurate fundamental clusters which was followed by the decomposition step applied to each cluster using just two energy bins. We also show an example of biological sample imaging and separating three distinct types of tissue in mice: muscle, fat, and bone. Our experimental results show that the combination of effective and practical spectral correction and high-dimensional data clustering enhances decomposition accuracy and reduces noise in micro-CT.

Conclusions: This ICMD allows for quantitative separation of multiple materials including mixtures and also effectively separates multi-contrast agents.

Keywords: clustering analysis; material decomposition; micro-computed tomography; photon counting detectors; signal-to-thickness calibration; soft tissue classification; spectral correction.

Fig. 1

Our data were acquired using the WidePix CdTe detector, a tiled assembly of five Medipix3RX single-chip units, in CSM mode. The detector features a CdTe sensor with square pixels of dimension $55\mu \mathrm{m}$ and a thickness of $1000\mu \mathrm{m}$, providing high spatial resolution. Its active area measures $1.408\times 7.040\mathrm{cm}$.

Fig. 2

(a) Cross-sectional schematic of a cylindrical PMMA phantom (27 mm diameter) with four cylindrical holes (4 mm diameter each). The holes contain 10% KI, 5% KI, 10% gadopentetic acid (${\mathrm{C}}_{14}{\mathrm{H}}_{20}{\mathrm{GdN}}_3{\mathrm{O}}_{10}-{\mathrm{H}}_2\mathrm{O}$), and 10% hydroxyapatite (${\mathrm{Ca}}_5({\mathrm{PO}}_4{)}_3\mathrm{OH}$) weight percent solution in water. (b) Slice of the reconstructed CT volume.

Fig. 3

Signal-to-thickness calibration for 100 randomly selected pixels based on 15 PMMA thickness measurements, ranging from 0.0 to 70.0 mm. These calibration curves, generated within a 26- to 32-keV energy window and a 1-s/frame acquisition rate, demonstrate the variability in inter-pixel response for the same photon counting detector.

Fig. 4

Comparison of GMM and $K$-means clustering for material segmentation in a multi-energy CT phantom. (a) Scatter plots showing the corrected mass attenuation values at two energy levels (energy 1: 20 to 26 keV; energy 2: 50 to 60 keV), representing true material labels (left), GMM clustering results (middle), and $K$-means clustering results (right). Yellow points correspond to potassium iodide (KI 5%), whereas purple points represent hydroxyapatite (HA 10%). (b) Visual segmentation maps from GMM (left) and $K$-means (right) clustering, illustrating the spatial distribution of KI and HA within the CT phantom. GMM achieves more accurate classification/segmentation than $K$-means, as evident from the better material separation.

Fig. 5

Workflow of the ICMD process. The process begins with multi-energy data acquisition, followed by signal-to-thickness calibration, CT reconstruction, and mass attenuation correction are performed for each energy window. Next, fundamental clusters are identified using GMM. Finally, material decomposition is applied to each fundamental cluster. The flowchart shows two fundamental clusters, but the process remains the same even with multiple fundamental clusters are found as in our examples.

Fig. 6

This figure compares the corrected and uncorrected mass attenuation coefficients from reconstructed voxels with the expected values from the NIST database. The plot demonstrates a strong agreement between the corrected mass attenuation coefficients and the expected NIST values.

Fig. 7

Comparison of CNR with (b) and without (a) signal-to-thickness calibration. The CNR was calculated as the difference in signal intensity between the region of interest and the PMMA background, normalized by the noise variance in the PMMA background region. Our results (c) show significant improvement in CNR which indicates a better image quality.

Fig. 8

Comparison of uncorrected (a) and corrected (b) mass attenuation values for 10% gadolinium (red) and hydroxyapatite (magenta) water solutions using five energy bins. Post-spectral correction, the measured values align more closely with the theoretical NIST values (marked with X).

Fig. 9

Illustration of fundamental clusters derived under three different conditions. (a) Flat-field correction applied to projection images with voxel clustering across all five energy windows. (b) With our empirical correction method but only using two energy windows: 26 to 32 and 32 to 42 keV. (c) With our empirical correction method using all five energy windows. Clusters are represented as PMMA (cyan), potassium iodide (red) of two concentrations, gadopentetic acid (yellow), and hydroxyapatite (blue).

Fig. 10

This diagram depicts the main steps of ICDM. The first step involves signal-to-thickness calibration and mass attenuation correction, aimed at reducing noise and enhancing contrast. The second step is iterative cluster analysis, streamlining the process by reducing the number of unknowns in each cluster. Finally, the third step applies material decomposition to each cluster, using a reduced basis of materials. The decomposition process is exemplified by separating the potassium iodide cluster into its constituent water and iodide components.

Fig. 11

Contrasting our ICMD method with single-step material decomposition using a four-material basis simultaneously. This graph underscores the advantages of limiting the number of material bases, which contributes to noise reduction and accuracy enhancement. It provides a clear comparison between our ICMD method and the conventional single-step material decomposition approach. The green dashed lines shows the ground truths for the lower and higher concentrations.

Fig. 12

Mouse tissue sample processed with our ICMD method. The GMM identifies three fundamental clusters, corresponding to bone, soft, and adipose tissue.

Fig. 13

Unsupervised segmentation of heterogeneous biological tissues into bone, soft, and adipose types using the GMM.

Fig. 14

Graph depicting measured mass attenuation for soft, adipose, and bone tissues. Experimental points represent the mean values of mass attenuation for each cluster at each energy window, whereas the dotted line indicates expected theoretical values from NIST. Deviations from theoretical values are attributed to the inherent inhomogeneity and complex composition of mouse tissue.