Learning the Sampling Pattern for MRI

Abstract

The discovery of the theory of compressed sensing brought the realisation that many inverse problems can be solved even when measurements are "incomplete". This is particularly interesting in magnetic resonance imaging (MRI), where long acquisition times can limit its use. In this work, we consider the problem of learning a sparse sampling pattern that can be used to optimally balance acquisition time versus quality of the reconstructed image. We use a supervised learning approach, making the assumption that our training data is representative enough of new data acquisitions. We demonstrate that this is indeed the case, even if the training data consists of just 7 training pairs of measurements and ground-truth images; with a training set of brain images of size 192 by 192, for instance, one of the learned patterns samples only 35% of k-space, however results in reconstructions with mean SSIM 0.914 on a test set of similar images. The proposed framework is general enough to learn arbitrary sampling patterns, including common patterns such as Cartesian, spiral and radial sampling.

Inexact Derivative-Free Optimization for Bilevel Learning

“…As noted in [45], bilevel learning can require very highaccuracy solutions to the lower-level problem. We avoid this via the introduction of a dynamic accuracy model-based DFO algorithm.…”

“…While some theoretical results and heuristic choices have been proposed in the literature, see, e.g., [8,23] and references therein or the L-curve criterion [27], the appropriate choice of the regularization parameter in a practical setting remains an open problem. Similarly, other parameters in (1) have to be chosen by the user, such as smoothing of the total variation [14], the hyperparameter for total generalized variation [9] or the sampling pattern in magnetic resonance imaging (MRI), see, e.g., [25,45,46]. Instead of using heuristics for choosing all of these parameters, here we are interested in finding these from data.…”

“…Instead of using heuristics for choosing all of these parameters, here we are interested in finding these from data. A by-now common strategy to learn parameters of a variational regularization model from data is bilevel learning, see, e.g., [4,21,28,30,38,39,45] and references in [1] . Given labeled data (x i , y i ) i=1,...,n we find parameters θ ∈ ⊂ R m by solving the upper-level problem…”

“…While mathematically appealing, this nested optimization problem is computationally very difficult to handle since even the evaluation of the upper-level problem (2) requires the exact solution of the lower-level problems (3). This requirement is practically infeasible, and common algorithms in the literature compute the lower-level solution only to some accuracy, thereby losing any theoretical performance guarantees, see, e.g., [21,39,45]. One reason for needing exact solutions is to compute the gradient of the upper-level objective using the implicit function theorem [45], which we address by using upper-level solvers which do not require gradient computations.…”

“…This requirement is practically infeasible, and common algorithms in the literature compute the lower-level solution only to some accuracy, thereby losing any theoretical performance guarantees, see, e.g., [21,39,45]. One reason for needing exact solutions is to compute the gradient of the upper-level objective using the implicit function theorem [45], which we address by using upper-level solvers which do not require gradient computations.…”