Compressed sensing applied to magnetic resonance imaging (MRI) allows to reduce the scanning time by enabling images to be reconstructed from highly undersampled data. In this paper, we tackle the problem of designing a sampling mask for an arbitrary reconstruction method and a limited acquisition budget. Namely, we look for an optimal probability distribution from which a mask with a fixed cardinality is drawn. We demonstrate that this problem admits a compactly supported solution, which leads to a deterministic optimal sampling mask. We then propose a stochastic greedy algorithm that (i) provides an approximate solution to this problem, and (ii) resolves the scaling issues of [1,2]. We validate its performance on in vivo dynamic MRI with retrospective undersampling, showing that our method preserves the performance of [1,2] while reducing the computational burden by a factor close to 200.
Deep image priors (DIP) offer a novel approach for the regularization that leverages the inductive bias of a deep convolutional architecture in inverse problems. However, the quality of DIP approaches often degrades when the number of iterations exceeds a certain threshold due to overfitting. To mitigate this effect, this work incorporates a plug-andplay prior scheme which can accommodate additional regularization steps within a DIP framework. Our modification is achieved using an augmented Lagrangian formulation of the problem, and is solved using an Alternating Direction Method of Multipliers (ADMM) variant, which can capture existing DIP approaches as a special case. We show experimentally that our ADMM-based DIP pairing outperforms competitive baselines in PSNR while exhibiting less overfitting.
In the last decade, Compressive Sensing (CS) has emerged as the most promising, model-driven approach to accelerate MRI scans. CS relies on the key sparsity assumption and proposes random sampling for data acquisition. The practical CS approaches in MRI employ variable-density (VD) sampling, where samples are drawn at random based on a parametric probability model which focuses on the center of the Fourier domain. In stark contrast to this model-driven sampling approaches, we propose a data-driven framework for optimizing sampling in parallel (multi-coil) MRI. Our approach does not assume any structure in the data, and instead optimizes a performance metric (e.g. PSNR) for any given reconstruction algorithm, based on our earlier learning-based sampling framework previously applied to 2D MRI which we also extend to 3D MRI setting in this work by employing lazy evaluations in the greedy algorithm. We show boosted performance for the parallel MRI based on this sampling approach and highlight the inefficiency of variable density approaches. This suggests that data-driven sampling methods could be the key to unlocking the full power of CS applied to MRI.
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