Abstract
Current popular methods for magnetic resonance fingerprint (MRF) recovery are bottlenecked by the heavy computations of a matched-filtering step due to the growing size and complexity of the fingerprint dictionaries in multi-parametric quantitative MRI applications. We address this shortcoming by arranging dictionary atoms in the form of cover tree structures and adopt the corresponding fast approximate nearest neighbour searches to accelerate matched-filtering. For datasets belonging to smooth low-dimensional manifolds cover trees offer search complexities logarithmic in terms of data population. With this motivation we propose an iterative reconstruction algorithm, named CoverBLIP, to address large-size MRF problems where the fingerprint dictionary i.e. discrete manifold of Bloch responses, encodes several intrinsic NMR parameters. We study different forms of convergence for this algorithm and we show that provided with a notion of embedding, the inexact and non-convex iterations of CoverBLIP linearly convergence toward a near-global solution with the same order of accuracy as using exact brute-force searches. Our further examinations on both synthetic and real-world datasets and using different sampling strategies, indicates between 2–3 orders of magnitude reduction in total search computations. Cover trees are robust against the curse-of-dimensionality and therefore CoverBLIP provides a notion of scalability—a consistent gain in time-accuracy performance—for searching high-dimensional atoms which may not be easily preprocessed (i.e. for dimensionality reduction) due to the increasing degrees of non-linearities appearing in the emerging multi-parametric MRF dictionaries.
Highlights
Quantitative Magnetic Resonance Imaging (Q-MRI) provides a powerful tool for measuring various intrinsic NMR properties of tissues such as the T 1, T 2 and T 2∗ relaxation times, field inhomogeneity, diffusion and perfusion [3]
Focusing on the non-compressed regime, we can see that Template Matching (TM) cannot achieve a good accuracy compared to the iterative methods (Figures 3 and 4(b))
We considered accelerating the iterative scheme for model-based Magnetic Resonance Fingerprint (MRF) reconstruction and for this purpose we approximated the matched-filtering step in each iteration using cover tree’s (1 + ε)-Approximate Nearest Neighbour Searches (ANNS) search scheme
Summary
Quantitative Magnetic Resonance Imaging (Q-MRI) provides a powerful tool for measuring various intrinsic NMR properties of tissues such as the T 1, T 2 and T 2∗ relaxation times, field inhomogeneity, diffusion and perfusion [3]. As occurs to any multi-parametric manifold enumeration, the main drawback of such approach is the size of this dictionary which grows exponentially in terms of the number of parameters and their quantization resolution This brings a serious (scalability) limitation to the current popular schemes to be applicable in the emerging multi-parametric MRF problems [15, 16, 17, 18, 19, 20], as the computational complexity of exact matchedfiltering using brute-force searches grows linearly with the dictionary size. To address this shortcoming we propose an iterative reconstruction method with inexact updates dubbed as Cover BLoch response Iterative Projection (CoverBLIP). This feature of robustness against the high-dimensionality of search spaces makes CoverBLIP a well-suited candidate to tackle multi-parametric MRF applications with increased non-linear dynamic complexity, where applying common subspace compression preprocessing becomes prohibitive for their unfavourable compromise in the final estimation accuracy
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