  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 to 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.
