# Joint T1 and T2 Mapping with Tiny Dictionaries and Subspace-Constrained Reconstruction

## TL;DR

This paper introduces an adaptive method for joint T1-T2 mapping that generates tiny dictionaries by approximating the Bloch-response manifold, enabling efficient subspace reconstruction with minimal loss of accuracy.

## Contribution

It proposes a novel approach that decouples dictionary size from accuracy by adaptively refining sampling grids based on local approximation error.

## Key findings

- Excellent agreement with traditional template matching
- Reduces dictionary sizes by one to two orders of magnitude
- Effective in phantom and in vivo studies

## Abstract

Purpose: To develop a method that adaptively generates tiny dictionaries for joint T1-T2 mapping. Theory: This work breaks the bond between dictionary size and representation accuracy (i) by approximating the Bloch-response manifold by piece-wise linear functions and (ii) by adaptively refining the sampling grid depending on the locally-linear approximation error. Methods: Data acquisition was accomplished with use of an 2D radially sampled Inversion-Recovery Hybrid-State Free Precession sequence. Adaptive dictionaries are generated with different error tolerances and compared to a heuristically designed dictionary. Based on simulation results, tiny dictionaries were used for T1-T2 mapping in phantom and in vivo studies. Reconstruction and parameter mapping were performed entirely in subspace. Results: All experiments demonstrated excellent agreement between the proposed mapping technique and template matching using heuristic dictionaries. Conclusion: Adaptive dictionaries in combination with manifold projection allow to reduce the necessary dictionary sizes by one to two orders of magnitude.