Charles Millard

Charles Millard, Mark Chiew

In recent years, there has been attention on leveraging the statistical modeling capabilities of neural networks for reconstructing sub-sampled Magnetic Resonance Imaging (MRI) data. Most proposed methods assume the existence of a representative fully-sampled dataset and use fully-supervised training. However, for many applications, fully sampled training data is not available, and may be highly impractical to acquire. The development and understanding of self-supervised methods, which use only sub-sampled data for training, are therefore highly desirable. This work extends the Noisier2Noise framework, which was originally constructed for self-supervised denoising tasks, to variable density sub-sampled MRI data. We use the Noisier2Noise framework to analytically explain the performance of Self-Supervised Learning via Data Undersampling (SSDU), a recently proposed method that performs well in practice but until now lacked theoretical justification. Further, we propose two modifications of SSDU that arise as a consequence of the theoretical developments. Firstly, we propose partitioning the sampling set so that the subsets have the same type of distribution as the original sampling mask. Secondly, we propose a loss weighting that compensates for the sampling and partitioning densities. On the fastMRI dataset we show that these changes significantly improve SSDU's image restoration quality and robustness to the partitioning parameters.

Charles Millard, Mark Chiew, Jared Tanner et al.

Magnetic Resonance Imaging (MRI) has excellent soft tissue contrast but is hindered by an inherently slow data acquisition process. Compressed sensing, which reconstructs sparse signals from incoherently sampled data, has been widely applied to accelerate MRI acquisitions. Compressed sensing MRI requires one or more model parameters to be tuned, which is usually done by hand, giving sub-optimal tuning in general. To address this issue, we build on previous work by the authors on the single-coil Variable Density Approximate Message Passing (VDAMP) algorithm, extending the framework to multiple receiver coils to propose the Parallel VDAMP (P-VDAMP) algorithm. For Bernoulli random variable density sampling, P-VDAMP obeys a "state evolution", where the intermediate per-iteration image estimate is distributed according to the ground truth corrupted by a zero-mean Gaussian vector with approximately known covariance. To our knowledge, P-VDAMP is the first algorithm for multi-coil MRI data that obeys a state evolution with accurately tracked parameters. We leverage state evolution to automatically tune sparse parameters on-the-fly with Stein's Unbiased Risk Estimate (SURE). P-VDAMP is evaluated on brain, knee and angiogram datasets and compared with four variants of the Fast Iterative Shrinkage-Thresholding algorithm (FISTA), including two tuning-free variants from the literature. The proposed method is found to have a similar reconstruction quality and time to convergence as FISTA with an optimally tuned sparse weighting and offers substantial robustness and reconstruction quality improvements over competing tuning-free methods.