Fast and scalable joint-LORAKS reconstruction and data-driven sampling optimisation of high-dimensional MRI datasets using a GPU-accelerated and learning-free differentiable framework: PyLORAKS

Magnetic resonance imaging (MRI) benefits significantly from parallel imaging and low-rank matrix completion approaches to reconstruct accelerated multidimensional acquisitions. As one such algorithm, low-rank matrix modelling of local k-space neighbourhoods (LORAKS) provides image reconstruction by exploiting sparsity in undersampled multichannel data acquisitions. Besides using spatial and multichannel redundancies, joint-reconstruction of multi-contrast data provides higher-quality reconstruction and enables higher acceleration factors. However, the computational demands of LORAKS limit its applicability for joint-reconstruction of modern multichannel multi-contrast high-resolution datasets, but methods to speed up the acquisition and reconstruction process are highly desired. In this work, we present PyLORAKS, a graphics processing unit (GPU) accelerated implementation of LORAKS built using the PyTorch framework. The framework employs efficient parallelisation, GPU compute strategies, and randomised singular value decomposition methods for increased computational efficiency in dealing with huge LORAKS matrix sizes encountered in modern high-resolution MRI. The computation speedup enabled parameter optimisation via Bayesian methods, while automated differentiable tracing of the LORAKS formulation was used for data-driven subsampling optimisation. In benchmark experiments, reduction in memory overhead was achieved, paired with approximately 5–6× speedup over the previous (MATLAB) LORAKS implementations using CPU computation, and a ~30-fold improvement using PyLORAKS on GPUs. While ensuring similar reconstruction performance, the computational efficiency allows for reconstruction of larger data matrices previously posing challenges to memory or computation time demands. Automated parameter optimisation of LORAKS parameters <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>λ</mml:mi> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>r</mml:mi> </mml:math> yielded better results than manual selection, avoiding inter-contrast leakage artefacts. Additionally, the highest reconstruction quality was achieved by using the maximal number of available contrasts for joint-reconstruction, exemplarily resulting in an increased structural similarity (SSIM) from 0.9468 to 0.9688 when doubling the number of echoes in joint-reconstruction of a 4-fold undersampled multi-echo acquisition. Furthermore, complementary sampling across echoes was found beneficial as reconstruction of the same sampling per echo achieved an SSIM of 0.955, whereas interleaving phase encode lines per echo increased the SSIM to 0.972 for the same acquisition and otherwise optimal parameter combinations. We further demonstrate superior performance of complementary sampling using an optimal sampling pattern obtained by backpropagation through the PyLORAKS algorithm. Overall, PyLORAKS enables fast and efficient reconstruction of multichannel multi-contrast high-resolution MRI data. It enables parameter and data-driven reconstruction and acquisition optimisation and provides a platform for physics-informed or artificial intelligence-augmented development. The framework is openly available, including containerised environments for large-scale deployment.