Daniel J. Holland

Kezhi Li, Daniel Holland

A new iterative image reconstruction algorithm for electrical capacitance tomography (ECT) is proposed that is based on iterative soft thresholding of a total variation penalty and adaptive reweighted compressive sensing. This algorithm encourages sharp changes in the ECT image and overcomes the disadvantage of the $l_1$ minimization by equipping the total variation with an adaptive weighting depending on the reconstructed image. Moreover, the non-linear effect is also partially reduced due to the adoption of an updated sensitivity matrix. Simulation results show that the proposed algorithm recovers ECT images more precisely than existing state-of-the-art algorithms and therefore is suitable for the imaging of multiphase systems in industrial or medical applications.

Andrew Gordon Wilson, Yuting Wu, Daniel J. Holland et al.

Nuclear magnetic resonance (NMR) spectroscopy exploits the magnetic properties of atomic nuclei to discover the structure, reaction state and chemical environment of molecules. We propose a probabilistic generative model and inference procedures for NMR spectroscopy. Specifically, we use a weighted sum of trigonometric functions undergoing exponential decay to model free induction decay (FID) signals. We discuss the challenges in estimating the components of this general model -- amplitudes, phase shifts, frequencies, decay rates, and noise variances -- and offer practical solutions. We compare with conventional Fourier transform spectroscopy for estimating the relative concentrations of chemicals in a mixture, using synthetic and experimentally acquired FID signals. We find the proposed model is particularly robust to low signal to noise ratios (SNR), and overlapping peaks in the Fourier transform of the FID, enabling accurate predictions (e.g., 1% sensitivity at low SNR) which are not possible with conventional spectroscopy (5% sensitivity).