Purpose: Exploiting the x‐ray measurements obtained in different energy bins, spectral computed tomography (CT) has the ability to recover the 3‐D description of a patient in a material basis. This may be achieved solving two subproblems, namely the material decomposition and the tomographic reconstruction problems. In this work, we address the material decomposition of spectral x‐ray projection images, which is a nonlinear ill‐posed problem.Methods: Our main contribution is to introduce a material‐dependent spatial regularization in the projection domain. The decomposition problem is solved iteratively using a Gauss–Newton algorithm that can benefit from fast linear solvers. A Matlab implementation is available online. The proposed regularized weighted least squares Gauss–Newton algorithm (RWLS‐GN) is validated on numerical simulations of a thorax phantom made of up to five materials (soft tissue, bone, lung, adipose tissue, and gadolinium), which is scanned with a 120 kV source and imaged by a 4‐bin photon counting detector. To evaluate the method performance of our algorithm, different scenarios are created by varying the number of incident photons, the concentration of the marker and the configuration of the phantom. The RWLS‐GN method is compared to the reference maximum likelihood Nelder–Mead algorithm (ML‐NM). The convergence of the proposed method and its dependence on the regularization parameter are also studied.Results: We show that material decomposition is feasible with the proposed method and that it converges in few iterations. Material decomposition with ML‐NM was very sensitive to noise, leading to decomposed images highly affected by noise, and artifacts even for the best case scenario. The proposed method was less sensitive to noise and improved contrast‐to‐noise ratio of the gadolinium image. Results were superior to those provided by ML‐NM in terms of image quality and decomposition was 70 times faster. For the assessed experiments, material decomposition was possible with the proposed method when the number of incident photons was equal or larger than 10⁵ and when the marker concentration was equal or larger than 0.03 g·cm⁻³.Conclusions: The proposed method efficiently solves the nonlinear decomposition problem for spectral CT, which opens up new possibilities such as material‐specific regularization in the projection domain and a parallelization framework, in which projections are solved in parallel.

Electrical impedance tomography (EIT) has the potential to produce images during epileptic seizures. This might improve the accuracy of the localization of epileptic foci in patients undergoing presurgical assessment for curative neurosurgery. It has already been shown that impedance increases by up to 22% during induced epileptic seizures in animal models, using cortical or implanted electrodes in controlled experiments. The purpose of this study was to determine if reproducible raw impedance changes and EIT images could be collected during epileptic seizures in patients who were undergoing observation with video-electroencephalography (EEG) telemetry as part of evaluation prior to neurosurgery to resect the region of brain causing the epilepsy. A secondary purpose was to develop an objective method for processing and evaluating data, as seizures arose at unpredictable times from a noisy baseline. Four-terminal impedance measurements from 258 combinations were collected continuously using 32 EEG scalp electrodes in 22 seizure episodes from 7 patients during their presurgical assessment together with the standard EEG recordings. A reliable method for defining the pre-seizure baseline and recording impedance data and EIT images was developed, in which EIT and EEG could be acquired simultaneously after filtering of EIT artefact from the EEG signal. Fluctuations of several per cent over minutes were observed in the baseline between seizures. During seizures, boundary voltage changes diverged with a standard deviation of 1-54% from the baseline. No reproducible changes with the expected time course of some tens of seconds and magnitude of about 0.1% could be reliably measured. This demonstrates that it is feasible to acquire EIT images in parallel with standard EEG during presurgical assessment but, unfortunately, expected EIT changes on the scalp of about 0.1% are swamped by much larger movement and systematic artefact. Nevertheless, EIT has the unique potential to provide invaluable neuroimaging data for this purpose and may still become possible with improvements in electrode design and instrumentation.

Purpose:: Standard image reconstruction methods for fluorescence Diffuse Optical Tomography (fDOT) generally make use of L2‐regularization. A better choice is to replace the L2 by a total variation functional that effectively removes noise while preserving edges. Among the wide range of approaches available, the recently appeared Split Bregman method has been shown to be optimal and efficient. Furthermore, additional constraints can be easily included. We propose the use of the Split Bregman method to solve the image reconstruction problem for fDOT with a nonnegativity constraint that imposes the reconstructed concentration of fluorophore to be positive.Methods:: The proposed method is tested with simulated and experimental data, and results are compared with those yielded by an equivalent unconstrained optimization approach based on Gauss–Newton (GN) method, in which the negative part of the solution is projected to zero after each iteration. In addition, the method dependence on the parameters that weigh data fidelity and nonnegativity constraints is analyzed.Results:: Split Bregman yielded a reduction of the solution error norm and a better full width at tenth maximum for simulated data, and higher signal‐to‐noise ratio for experimental data. It is also shown that it led to an optimum solution independently of the data fidelity parameter, as long as the number of iterations is properly selected, and that there is a linear relation between the number of iterations and the inverse of the data fidelity parameter.Conclusions:: Split Bregman allows the addition of a nonnegativity constraint leading to improve image quality.

Magnetic induction tomography (MIT) is an imaging modality with a wide range of potential applications due to its non-contact nature. MIT is a member of the electrical tomography family that faces the most difficult imaging challenges, due to its demanding measurement accuracy requirements and its difficult forward and inverse problems. This paper presents for the first time split Bregman total variation (TV) regularization to solve the MIT inverse problem. Comparative evaluations are presented between proposed TV algorithm and more commonly used Tikhonov regularization method. Tikhonov regularization, which is based on the l ₂ -norm, is solved linearly, while TV is solved using the split Bregman formulation, which has been shown to be optimal for l ₁ -norm regularization. Experimental results are quantified by a number of image quality measurements, which show the superiority of the proposed TV method both on low conductivity and high conductivity MIT data. Significant improvement in MIT imaging results will make the proposed TV method a great candidate for both types of MIT imaging.

The state-of-the art for solving the nonlinear material decomposition problem in spectral computed tomography is based on variational methods, but these are computationally slow and critically depend on the particular choice of the regularization functional. Convolutional neural networks have been proposed for addressing these issues. However, learning algorithms require large amounts of experimental data sets. We propose a deep learning strategy for solving the material decomposition problem based on a U-Net architecture and a Sim2Real transfer learning approach where the knowledge that we learn from synthetic data is transferred to a real-world scenario. In order for this approach to work, synthetic data must be realistic and representative of the experimental data. For this purpose, numerical phantoms are generated from human CT volumes of the KiTS19 Challenge dataset, segmented into specific materials (soft tissue and bone). These volumes are projected into sinogram space in order to simulate photon counting data, taking into account the energy response of the scanner. We compared projection- and image-based decomposition approaches where the network is trained to decompose the materials either in the projection or in the image domain. The proposed Sim2Real transfer strategies are compared to a regularized Gauss-Newton (RGN) method on synthetic data, experimental phantom data and human thorax data.