Significance of the spectral correction of photon counting detector response in material classification from spectral x-ray CT.

Purpose: Photon counting imaging detectors (PCD) has paved the way for spectral x-ray computed tomography (spectral CT), which simultaneously measures a sample's linear attenuation coefficient (LAC) at multiple energies. However, cadmium telluride (CdTe)-based PCDs working under high flux suffer from detector effects, such as charge sharing and photon pileup. These effects result in the severe spectral distortions of the measured spectra and significant deviation of the extracted LACs from the reference attenuation curve. We analyze the influence of the spectral distortion correction on material classification performance. Approach: We employ a spectral correction algorithm to reduce the primary spectral distortions. We use a method for material classification that measures system-independent material properties, such as electron density, ρ e , and effective atomic number, Z eff . These parameters are extracted from the LACs using attenuation decomposition and are independent of the scanner specification. The classification performance with the raw and corrected data is tested on different numbers of energy bins and projections and different radiation dose levels. We use experimental data with a broad range of materials in the range of 6 ≤ Z eff ≤ 15 , acquired with a custom laboratory instrument for spectral CT. Results: We show that using the spectral correction leads to an accuracy increase of 1.6 and 3.8 times in estimating ρ e and Z eff , respectively, when the image reconstruction is performed from only 12 projections and the 15 energy bins approach is used. Conclusions: The correction algorithm accurately reconstructs the measured attenuation curve and thus gives better classification performance.

Shape from projections via differentiable forward projector for computed tomography.

In computed tomography, the reconstruction is typically obtained on a voxel grid. In this work, however, we propose a mesh-based reconstruction method. For tomographic problems, 3D meshes have mostly been studied to simulate data acquisition, but not for reconstruction, for which a 3D mesh means the inverse process of estimating shapes from projections. In this paper, we propose a differentiable forward model for 3D meshes that bridge the gap between the forward model for 3D surfaces and optimization. We view the forward projection as a rendering process, and make it differentiable by extending recent work in differentiable rendering. We use the proposed forward model to reconstruct 3D shapes directly from projections. Experimental results for single-object problems show that the proposed method outperforms traditional voxel-based methods on noisy simulated data. We also apply the proposed method on electron tomography images of nanoparticles to demonstrate the applicability of the method on real data.

Adaptive Regularization of Some Inverse Problems in Image Analysis.

We present an adaptive regularization scheme for optimizing composite energy functionals arising in image analysis problems. The scheme automatically trades off data fidelity and regularization depending on the current data fit during the iterative optimization, so that regularization is strongest initially, and wanes as data fidelity improves, with the weight of the regularizer being minimized at convergence. We also introduce a Huber loss function in both data fidelity and regularization terms, and present an efficient convex optimization algorithm based on the alternating direction method of multipliers (ADMM) using the equivalent relation between the Huber function and the proximal operator of the one-norm. We illustrate and validate our adaptive Huber-Huber model on synthetic and real images in segmentation, motion estimation, and denoising problems.