Sampling possible reconstructions of undersampled acquisitions in MR imaging
This addresses uncertainty estimation for MRI practitioners, offering a more comprehensive solution than traditional single-image reconstructions, though it is incremental as it builds on existing latent modeling and sampling techniques.
The paper tackles the problem of uncertainty in undersampled MRI reconstruction by proposing a method that generates multiple possible images rather than a single 'best' image, resulting in better k-space data matching and realistic structural variability compared to five alternative methods.
Undersampling the k-space during MR acquisitions saves time, however results in an ill-posed inversion problem, leading to an infinite set of images as possible solutions. Traditionally, this is tackled as a reconstruction problem by searching for a single "best" image out of this solution set according to some chosen regularization or prior. This approach, however, misses the possibility of other solutions and hence ignores the uncertainty in the inversion process. In this paper, we propose a method that instead returns multiple images which are possible under the acquisition model and the chosen prior to capture the uncertainty in the inversion process. To this end, we introduce a low dimensional latent space and model the posterior distribution of the latent vectors given the acquisition data in k-space, from which we can sample in the latent space and obtain the corresponding images. We use a variational autoencoder for the latent model and the Metropolis adjusted Langevin algorithm for the sampling. We evaluate our method on two datasets; with images from the Human Connectome Project and in-house measured multi-coil images. We compare to five alternative methods. Results indicate that the proposed method produces images that match the measured k-space data better than the alternatives, while showing realistic structural variability. Furthermore, in contrast to the compared methods, the proposed method yields higher uncertainty in the undersampled phase encoding direction, as expected. Keywords: Magnetic Resonance image reconstruction, uncertainty estimation, inverse problems, sampling, MCMC, deep learning, unsupervised learning.