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

TL;DR

CoverBLIP introduces a scalable, fast iterative algorithm for Magnetic Resonance Fingerprint reconstruction that significantly reduces computational complexity by using cover tree structures for approximate nearest neighbor searches, enabling efficient handling of large, high-dimensional dictionaries.

Contribution

The paper presents CoverBLIP, a novel iterative reconstruction method that accelerates matched-filtering in MRF by employing cover trees, achieving linear convergence and substantial computational savings.

Findings

Achieves 2 to 3 orders of magnitude reduction in search computations.

Provides linear convergence to near-global solutions under certain conditions.

Demonstrates robustness and scalability on synthetic and real datasets.

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 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.