In this paper, we propose the use of Recurrent Inference Machines (RIMs) to perform T₁ and T₂ mapping. The RIM is a neural network framework that learns an iterative inference process based on the signal model, similar to conventional statistical methods for quantitative MRI (QMRI), such as the Maximum Likelihood Estimator (MLE). This framework combines the advantages of both data-driven and model-based methods, and, we hypothesize, is a promising tool for QMRI. Previously, RIMs were used to solve linear inverse reconstruction problems. Here, we show that they can also be used to optimize non-linear problems and estimate relaxometry maps with high precision and accuracy. The developed RIM framework is evaluated in terms of accuracy and precision and compared to an MLE method and an implementation of the Residual Neural Network (ResNet). The results show that the RIM improves the quality of estimates compared to the other techniques in Monte Carlo experiments with simulated data, test-retest analysis of a system phantom, and in-vivo scans. Additionally, inference with the RIM is 150 times faster than the MLE, and robustness to (slight) variations of scanning parameters is demonstrated. Hence, the RIM is a promising and flexible method for QMRI. Coupled with an open-source training data generation tool, it presents a compelling alternative to previous methods.

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In this work, a recently developed quantitative approach based on the principles of detection theory is used in order to determine the possibilities and limitations of High Resolution Scanning Transmission Electron Microscopy (HR STEM) and HR TEM for atom-counting. So far, HR STEM has been shown to be an appropriate imaging mode to count the number of atoms in a projected atomic column. Recently, it has been demonstrated that HR TEM, when using negative spherical aberration imaging, is suitable for atom-counting as well. The capabilities of both imaging techniques are investigated and compared using the probability of error as a criterion. It is shown that for the same incoming electron dose, HR STEM outperforms HR TEM under common practice standards, i.e. when the decision is based on the probability function of the peak intensities in HR TEM and of the scattering cross-sections in HR STEM. If the atom-counting decision is based on the joint probability function of the image pixel values, the dependence of all image pixel intensities as a function of thickness should be known accurately. Under this assumption, the probability of error may decrease significantly for atom-counting in HR TEM and may, in theory, become lower as compared to HR STEM under the predicted optimal experimental settings. However, the commonly used standard for atom-counting in HR STEM leads to a high performance and has been shown to work in practice.@en

Quantification of the spin-lattice relaxation time, T1, of tissues is important for characterization of tissues in clinical magnetic resonance imaging (MRI). In T1 mapping, T1 values are estimated from a set of T1-weighted MRI images. Due to the limited spatial resolution of the T1-weighted images, one voxel might consist of two tissues, causing partial volume effects (PVE). In conventional mono-exponential T1 estimation, these PVE result in systematic errors in the T1 map. To account for PVE, single-voxel bi-exponential estimators have been suggested. Unfortunately, in general, they suffer from low accuracy and precision. In this work, we propose a joint multi-voxel bi-exponential T1 estimator (JMBE) and compare its performance to a single-voxel bi-exponential T1 estimator (SBE). Results show that, in contrast to the SBE, and for clinically achievable single-voxel SNRs, the JMBE is accurate and efficient if four or more neighboring voxels are used in the joint estimation framework. This illustrates that, for clinically realistic SNRs, accurate results for quantitative biexponential T1 estimation are only achievable if information of neighboring voxels is incorporated.@en

In the present paper, the optimal detector design is investigated for both detecting and locating light atoms from high resolution scanning transmission electron microscopy (HR STEM) images. The principles of detection theory are used to quantify the probability of error for the detection of light atoms from HR STEM images. To determine the optimal experiment design for locating light atoms, use is made of the so-called Cramér–Rao Lower Bound (CRLB). It is investigated if a single optimal design can be found for both the detection and location problem of light atoms. Furthermore, the incoming electron dose is optimised for both research goals and it is shown that picometre range precision is feasible for the estimation of the atom positions when using an appropriate incoming electron dose under the optimal detector settings to detect light atoms.@en