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 5 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 32% of k-space, however results in reconstructions with mean SSIM 0.956 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.

J-MoDL: Joint Model-Based Deep Learning for Optimized Sampling and Reconstruction

“…Early approaches that rely on compressed sensing algorithms [10], [11] optimize the sampling pattern Θ such that…”

“…These experiment design strategies often rely on the Cramer-Rao (CR) bound, assuming the knowledge of the image support or location of the sparse coefficients. Algorithm-dependent schemes such as [10], [11] optimize the sampling pattern, assuming specific reconstruction algorithms (e.g., TV or wavelet sparsity). These approaches [10], [11] only consider single-channel settings with undersampled Fourier transform as a forward model.…”

“…Algorithm-dependent schemes such as [10], [11] optimize the sampling pattern, assuming specific reconstruction algorithms (e.g., TV or wavelet sparsity). These approaches [10], [11] only consider single-channel settings with undersampled Fourier transform as a forward model. They utilize a subset of discrete sampling locations using greedy or continuous optimization strategies to minimize the reconstruction error.…”

“…The main focus of this work is to jointly optimize the sampling pattern and the deep network parameters for parallel MRI reconstruction. Most of the previous optimization strategies [10], [11], [20]- [22] are only restricted to the single-channel setting. We rely on an algorithm-dependent strategy to search for the best sampling pattern in the multichannel setting.…”

“…We rely on an algorithm-dependent strategy to search for the best sampling pattern in the multichannel setting. The main difference of the proposed scheme from [10], [11], [20], [21] is that we do not constrain the sampling pattern to be a subset of the Cartesian sampling pattern. Specifically, we assume the sampling locations to be continuous variables.…”