Sparse-view X-ray CT based on a box-constrained nonlinear weighted anisotropic TV regularization.

Sparse-view computed tomography (CT) is an important way to reduce the negative effect of radiation exposure in medical imaging by skipping some X-ray projections. However, due to violating the Nyquist/Shannon sampling criterion, there are severe streaking artifacts in the reconstructed CT images that could mislead diagnosis. Noting the ill-posedness nature of the corresponding inverse problem in a sparse-view CT, minimizing an energy functional composed by an image fidelity term together with properly chosen regularization terms is widely used to reconstruct a medical meaningful attenuation image. In this paper, we propose a regularization, called the box-constrained nonlinear weighted anisotropic total variation (box-constrained NWATV), and minimize the regularization term accompanying the least square fitting using an alternative direction method of multipliers (ADMM) type method. The proposed method is validated through the Shepp-Logan phantom model, alongisde the actual walnut X-ray projections provided by Finnish Inverse Problems Society and the human lung images. The experimental results show that the reconstruction speed of the proposed method is significantly accelerated compared to the existing $ L_1/L_2 $ regularization method. Precisely, the central processing unit (CPU) time is reduced more than 8 times.

Low frequency conductivity reconstruction based on a single current injection via MREIT.

Conventional magnetic resonance electrical impedance tomography (MREIT) reconstruction methods require administration of two linearly independent currents via at least two electrode pairs. This requires long scanning times and inhibits coordination of MREIT measurements with electrical neuromodulation strategies. We sought to develop an isotropic conductivity reconstruction algorithm in MREIT based on a single current injection, both to decrease scanning time by a factor of two and enable MREIT measurements to be conveniently adapted to general transcranial- or implanted-electrode neurostimulation protocols. In this work, we propose and demonstrate an iterative algorithm that extends previously published MREIT work using two-current administration approaches. The proposed algorithm is a single-current adaptation of the harmonic B z algorithm. Forward modeling of electric potentials is used to capture changes of conductivity along current directions that would normally be invisible using data from a single-current administration. Computational and experimental results show that the reconstruction algorithm is capable of reconstructing isotropic conductivity images that agree well in terms of L 2 error and structural similarity with exact conductivity distributions or two-current-based MREIT reconstructions. We conclude that it is possible to reconstruct high quality electrical conductivity images using MREIT techniques and one current injection only.

Accelerating acquisition strategies for low-frequency conductivity imaging using MREIT.

We sought to improve efficiency of magnetic resonance electrical impedance tomography data acquisition so that fast conductivity changes or electric field variations could be monitored. Undersampling of k-space was used to decrease acquisition times in spin-echo-based sequences by a factor of two. Full MREIT data were reconstructed using continuity assumptions and preliminary scans gathered without current. We found that phase data were reconstructed faithfully from undersampled data. Conductivity reconstructions of phantom data were also possible. Therefore, undersampled k-space methods can potentially be used to accelerate MREIT acquisition. This method could be an advantage in imaging real-time conductivity changes with MREIT.

A method for MREIT-based source imaging: simulation studies.

This paper aims to provide a method for using magnetic resonance electrical impedance tomography (MREIT) to visualize local conductivity changes associated with evoked neuronal activities in the brain. MREIT is an MRI-based technique for conductivity mapping by probing the magnetic flux density induced by an externally injected current through surface electrodes. Since local conductivity changes resulting from evoked neural activities are very small (less than a few %), a major challenge is to acquire exogenous magnetic flux density data exceeding a certain noise level. Noting that the signal-to-noise ratio is proportional to the square root of the number of averages, it is important to reduce the data acquisition time to get more averages within a given total data collection time. The proposed method uses a sub-sampled k-space data set in the phase-encoding direction to significantly reduce the data acquisition time. Since the sub-sampled data violates the Nyquist criteria, we only get a nonlinearly wrapped version of the exogenous magnetic flux density data, which is insufficient for conductivity imaging. Taking advantage of the sparseness of the conductivity change, the proposed method detects local conductivity changes by estimating the time-change of the Laplacian of the nonlinearly wrapped data.

Noninvasive measurement of conductivity anisotropy at larmor frequency using MRI.

Anisotropic electrical properties can be found in biological tissues such as muscles and nerves. Conductivity tensor is a simplified model to express the effective electrical anisotropic information and depends on the imaging resolution. The determination of the conductivity tensor should be based on Ohm's law. In other words, the measurement of partial information of current density and the electric fields should be made. Since the direct measurements of the electric field and the current density are difficult, we use MRI to measure their partial information such as B1 map; it measures circulating current density and circulating electric field. In this work, the ratio of the two circulating fields, termed circulating admittivity, is proposed as measures of the conductivity anisotropy at Larmor frequency. Given eigenvectors of the conductivity tensor, quantitative measurement of the eigenvalues can be achieved from circulating admittivity for special tissue models. Without eigenvectors, qualitative information of anisotropy still can be acquired from circulating admittivity. The limitation of the circulating admittivity is that at least two components of the magnetic fields should be measured to capture anisotropic information.