Multi-domain constraint based one-step selective-reconstruction method for spectral micro-CT

X-ray micro-computed tomography (micro-CT) achieves a spatial resolution of micron or submicron and is well-applied in many fields such as biomedicine, materials and electronic packaging. However, it suffers from low contrast and weak material distinguishability because of its low power of the X-ray source comparing with industrial or medical X-ray source. Recently, we adapt a state-of-the-art photon-counting detector (PCD) in a micro-CT system, leading a spectral Micro-CT. By dividing the X-ray photons into different energy bins, the PCD well maintains the energy-dependent property of matter attenuation and then contributes to selective-reconstruction. The selective-reconstruction problems of spectral micro-CT are ill-posed, i.e., the solution is very sensitive to noise. Meanwhile, for each PCD energy channel, the corresponding photon number is only a small fraction of the emitted photons, which further increases the noise level. To overcome the ill-posedness, in this work, we propose a multi-domain constraint based optimization model for one-step selective-reconstruction. First, we measure the data fidelity in photon domain using the Kullback-Leibler distance (I-divergence) and derive an equivalent expression in channel projection domain. Then, we introduce multi-domain constraints to establish the relationship among channel projections, material projections, and material images. After that, we employ the Mumford-Shah (MS) functional to describe the prior knowledge in the material image domain, such as gradient sparsity and edge information. Finally, we develop an iterative algorithm and verify it with numerical simulations.