Recently, the maximum a posteriori (MAP) probability rule has been proposed as an objective and quantitative method to detect atom columns and even single atoms from high-resolution high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) images. The method combines statistical parameter estimation and model-order selection using a Bayesian framework and has been shown to be especially useful for the analysis of the structure of beam-sensitive nanomaterials. In order to avoid beam damage, images of such materials are usually acquired using a limited incoming electron dose resulting in a low contrast-to-noise ratio (CNR) which makes visual inspection unreliable. This creates a need for an objective and quantitative approach. The present paper describes the methodology of the MAP probability rule, gives its step-by-step derivation and discusses its algorithmic implementation for atom column detection. In addition, simulation results are presented showing that the performance of the MAP probability rule to detect the correct number of atomic columns from HAADF STEM images is superior to that of other model-order selection criteria, including the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). Moreover, the MAP probability rule is used as a tool to evaluate the relation between STEM image quality measures and atom detectability resulting in the introduction of the so-called integrated CNR (ICNR) as a new image quality measure that better correlates with atom detectability than conventional measures such as signal-to-noise ratio (SNR) and CNR.

Magnetic resonance imaging (MRI) based T 1 mapping allows spatially resolved quantification of the tissue-dependent spin-lattice relaxation time constant T 1 , which is a potential biomarker of various neurodegenerative diseases, including Multiple Sclerosis, Alzheimer disease, and Parkinson's disease. In conventional T 1 MR relaxometry, a quantitative T 1 map is obtained from a series of T 1 -weighted MR images. Acquiring such a series, however, is time consuming. This has sparked the development of more efficient T 1 mapping methods, one of which is a super-resolution reconstruction (SRR) framework in which a set of low resolution (LR) T 1 -weighted images is acquired and from which a high resolution (HR) T 1 map is directly estimated.In this paper, the SRR T 1 mapping framework is augmented with motion estimation. That is, motion between the acquisition of the LR T 1 -weighted images is modeled and the motion parameters are estimated simultaneously with the T 1 parameters. Based on Monte Carlo simulation experiments, we show that such an integrated motion/relaxometry estimation approach yields more accurate T 1 maps compared to a previously reported SRR based T 1 mapping approach.

In this paper, we propose the use of Recurrent Inference Machines (RIMs) to perform T 1 and T 2 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 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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