Measuring information gain for frequency-encoded super-resolution MRI

Super-resolution (SR)-based methods that implement multiple data sets related by spatial translations in the frequency-encoding (FE) direction have recently been proposed for resolution enhancement in MRI. This approach, however, was initially received with controversy. It was suggested that when the shifts are applied in the FE direction, no new information was acquired after the first image. Recent developments suggest, however, that shifting the object between image acquisitions can introduce new information to each data set. For this reason, SRMRI may be possible in the FE direction.In this article, we point out that the presence of new information in each acquisition is not sufficient for an SR algorithm to be practical. Indeed, there are situations where the amount of new information is relatively small and possibly not even measurable in the presence of noise. We explore the question of how much new information can be present in each acquisition for FE SRMRI. In particular, we investigate the extent to which the effect of the spatial shift — applied before the object is imaged — can be undone using simple image-processing techniques.Visual comparisons and numerical measures are used to characterize the amount of new information that is acquired in each data set. It is shown that since the amount of new information can be relatively small, each image can be approximated by applying simple signal-processing techniques to a single data set. Ultimately, our research suggests that little progress may be possible by using this approach to perform resolution enhancement in the FE direction.