Uniqueness and convergence of MRF dictionary searching

Establish the uniqueness and convergence of magnetic resonance fingerprinting (MRF) dictionary-searching algorithms in general, beyond the sequence- and target-specific conditions supplied by the finite global certificates.

Background

Magnetic resonance fingerprinting estimates tissue parameters by matching measured signal time courses to Bloch- or EPG-simulated dictionary entries. The paper develops an analytic framework for the normalized-correlation matching objective and proves local strictness under positive-definite profiled Fisher information, as well as finite, sequence-specific certificates for global uniqueness and global radial monotonicity.

These results do not provide a universal guarantee for every acquisition schedule or parameter family. The authors explicitly identify the broader uniqueness and convergence theory of MRF dictionary searching as not fully established. A uniform result would require bounds on local curvature, derivative Lipschitz constants, and global separation margins across the relevant sequence and target families.