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PreprintCC BY-NC-ND 4.0arXiv

Unimodality and Radial Monotonicity of the Magnetic Resonance Fingerprinting T1/T2 Matching Objective

  • Ze Wang
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Abstract

Magnetic resonance fingerprinting (MRF) estimates tissue parameters by matching an acquired MR signal time course to entries in a Bloch- or EPG-simulated dictionary. However, no study has yet proven the uniqueness of the matching results. In two earlier studies by exhaustive objective mapping I showed that for two widely used MRF sequences the normalized-correlation objective exhibits a single dominant peak at the true T1/T2 values and decreases smoothly away from that peak. These empirical properties motivated the fast MRF-ZOOM search algorithm even without using a pre-generated signal dictionary, but their theoretical basis has remained incomplete. The purpose of this work is to develop a mathematical framework for the MRF matching objective under normalized-correlation matching.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026unimodality,
  title = {{Unimodality and Radial Monotonicity of the Magnetic Resonance Fingerprinting T1/T2 Matching Objective}},
  author = {Ze Wang},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.30100},
  eprint = {2608.30100},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30100},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Unimodality and Radial Monotonicity of the Magnetic Resonance Fingerprinting T1/T2 Matching Objective
AU  - Ze Wang
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.30100
UR  - https://arxiv.org/abs/2608.30100
AB  - Magnetic resonance fingerprinting (MRF) estimates tissue parameters by matching an acquired MR signal time course to entries in a Bloch- or EPG-simulated dictionary. However, no study has yet proven the uniqueness of the matching results. In two earlier studies by exhaustive objective mapping I showed that for two widely used MRF sequences the normalized-correlation objective exhibits a single dominant peak at the true T1/T2 values and decreases smoothly away from that peak. These empirical properties motivated the fast MRF-ZOOM search algorithm even without using a pre-generated signal dictionary, but their theoretical basis has remained incomplete. The purpose of this work is to develop a mathematical framework for the MRF matching objective under normalized-correlation matching.
ER  -