Subrata Pal

Purpose: Personalized synthetic MRI (syn‐MRI) uses MR images of an individual subject acquired at a few design parameters (echo time, repetition time, flip angle) to obtain underlying parametric maps, from where MR images of that individual at other design parameter settings are synthesized. However, classical methods that use least‐squares (LS) or maximum likelihood estimators (MLE) are unsatisfactory at higher noise levels because the underlying inverse problem is ill‐posed. This article provides a pipeline to enhance the synthesis of such images in three‐dimensional (3D) using a deep learning (DL) neural network architecture for spatial regularization in a personalized setting where having more than a few training images is impractical.Methods: Our DL enhancements employ a Deep Image Prior (DIP) with a U‐net type denoising architecture that includes situations with minimal training data, such as personalized syn‐MRI. We provide a general workflow for syn‐MRI from three or more training images. Our workflow, called DIPsyn‐MRI, uses DIP to enhance training images, then obtains parametric images using LS or MLE before synthesizing images at desired design parameter settings. DIPsyn‐MRI is implemented in our publicly available Python package DeepSynMRI available at: https://github.com/StatPal/DeepSynMRI.Results: We demonstrate feasibility and improved performance of DIPsyn‐MRI on 3D datasets acquired using the Brainweb interface for spin‐echo and FLASH imaging sequences, at different noise levels. Our DL enhancements improve syn‐MRI in the presence of different intensity nonuniformity levels of the magnetic field, for all but very low noise levels.Conclusion: This article provides recipes and software to realistically facilitate DL‐enhanced personalized syn‐MRI.

Divergence measures have a long association with statistical inference, machine learning and information theory. The density power divergence and related measures have produced many useful (and popular) statistical procedures, which provide a good balance between model efficiency on one hand and outlier stability or robustness on the other. The logarithmic density power divergence, a particular logarithmic transform of the density power divergence, has also been very successful in producing efficient and stable inference procedures; in addition it has also led to significant demonstrated applications in information theory. The success of the minimum divergence procedures based on the density power divergence and the logarithmic density power divergence (which also go by the names β-divergence and γ-divergence, respectively) make it imperative and meaningful to look for other, similar divergences which may be obtained as transforms of the density power divergence in the same spirit.With this motivation we search for such transforms of the density power divergence, referred to herein as the functional density power divergence class. The present article characterizes this functional density power divergence class, and thus identifies the available divergence measures within this construct that may be explored further for possible applications in statistical inference, machine learning and information theory.

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