CoverBLIP: accelerated and scalable iterative matched-filtering for Magnetic Resonance Fingerprint reconstruction

Current popular methods for Magnetic Resonance Fingerprint (MRF) recovery are\nbottlenecked by the heavy computations of a matched-filtering step due to the\ngrowing size and complexity of the fingerprint dictionaries in multi-parametric\nquantitative MRI applications. We address this shortcoming by arranging\ndictionary atoms in the form of cover tree structures and adopt the\ncorresponding fast approximate nearest neighbour searches to accelerate\nmatched-filtering. For datasets belonging to smooth low-dimensional manifolds\ncover trees offer search complexities logarithmic in terms of data population.\nWith this motivation we propose an iterative reconstruction algorithm, named\nCoverBLIP, to address large-size MRF problems where the fingerprint dictionary\ni.e. discrete manifold of Bloch responses, encodes several intrinsic NMR\nparameters. We study different forms of convergence for this algorithm and we\nshow that provided with a notion of embedding, the inexact and non-convex\niterations of CoverBLIP linearly convergence toward a near-global solution with\nthe same order of accuracy as using exact brute-force searches. Our further\nexaminations on both synthetic and real-world datasets and using different\nsampling strategies, indicates between 2 to 3 orders of magnitude reduction in\ntotal search computations. Cover trees are robust against the\ncurse-of-dimensionality and therefore CoverBLIP provides a notion of\nscalability -- a consistent gain in time-accuracy performance-- for searching\nhigh-dimensional atoms which may not be easily preprocessed (i.e. for\ndimensionality reduction) due to the increasing degrees of non-linearities\nappearing in the emerging multi-parametric MRF dictionaries.\n