Optimal Sampling & Reconstruction: Theory and Applications

TL;DR

This paper discusses the challenges and methods for optimizing MRI data sampling and reconstruction by defining appropriate metrics and exploring various theoretical and practical approaches.

Contribution

It provides a comprehensive overview of optimal sampling and reconstruction strategies in MRI, considering multiple perspectives and the importance of choosing suitable evaluation metrics.

Findings

Highlights the subjective nature of defining optimality in MRI methods.

Explores information and estimation theory approaches to optimization.

Emphasizes the importance of metric selection in the optimization process.

Abstract

The optimization of MRI data sampling and image reconstruction methods has been a priority for the MRI community since the very early days of the field. Designing an "optimal" method requires the definition of an optimality metric (i.e., a quantitative evaluation of the "goodness" of different competing approaches that allows an objective comparison between them). However, a key challenge is that there are many different possible ways of quantitatively evaluating the "goodness" of a data sampling scheme or a reconstruction result, and there are no acquisition or reconstruction methods that are known to be universally optimal with respect to all of these possible metrics simultaneously. Thus, optimization of MRI methods requires a subjective choice about what aspects of quality matter most in the context of a given MRI experiment, and subsequently the subjective choice of an optimality metric that hopefully does a reasonable job of quantifying those aspects of quality. Once these choices are made, the optimization problem becomes well-defined, and it remains to choose an algorithm that can identify data sampling or image reconstruction methods that are optimal with respect to the chosen metric. All of these choices are generally nontrivial. In this presentation, we will discuss optimal sampling and reconstruction designs from multiple different perspectives, including ideas from information and estimation theory and various practical perspectives.