  Photon counting detectors (PCDs) offer promising advancements in computed
tomography (CT) imaging by enabling the quantification and 3D imaging of
contrast agents and tissue types through multi-energy projections. However, the
accuracy of these decomposition methods hinges on precise composite spectral
attenuation values that one must reconstruct from spectral micro CT. Factors
such as surface defects, local temperature, signal amplification, and impurity
levels can cause variations in detector efficiency between pixels, leading to
significant quantitative errors. In addition, some inaccuracies such as the
charge-sharing effects in PCDs are amplified with a high Z sensor material and
also with a smaller detector pixels that are preferred for micro CT. In this
work, we propose a comprehensive approach that combines practical
instrumentation and measurement strategies leading to the quantitation of
multiple materials within an object in a spectral micro CT with a photon
counting detector. Our Iterative Clustering Material Decomposition (ICMD)
includes an empirical method for detector spectral response corrections,
cluster analysis and multi-step iterative material decomposition. Utilizing a
CdTe-1mm Medipix detector with a 55$\mu$m pitch, we demonstrate the
quantitatively accurate decomposition of several materials in a phantom study,
where the sample includes mixtures of material, soft material and K-edge
materials. We also show an example of biological sample imaging and separating
three distinct types of tissue in mouse: muscle, fat and bone. Our experimental
results show that the combination of spectral correction and high-dimensional
data clustering enhances decomposition accuracy and reduces noise in micro CT.
This ICMD allows for quantitative separation of more than three materials
including mixtures and also effectively separates multi-contrast agents.
