Model-Based MR Parameter Mapping With Sparsity Constraints: Parameter Estimation and Performance Bounds

Abstract

MR parameter mapping (e.g., T1 mapping, T2 mapping, T2∗ mapping) is a valuable tool for tissue characterization. However, its practical utility has been limited due to long data acquisition times. This paper addresses this problem with a new model-based parameter mapping method. The proposed method utilizes a formulation that integrates the explicit signal model with sparsity constraints on the model parameters, enabling direct estimation of the parameters of interest from highly undersampled, noisy k-space data. An efficient greedy-pursuit algorithm is described to solve the resulting constrained parameter estimation problem. Estimation-theoretic bounds are also derived to analyze the benefits of incorporating sparsity constraints and benchmark the performance of the proposed method. The theoretical properties and empirical performance of the proposed method are illustrated in a T2 mapping application example using computer simulations.

Maximum Likelihood Reconstruction for Magnetic Resonance Fingerprinting

“…In MR fingerprinting, the contrast-weighted image I m ( x ) can be parameterized as [6], [20], [21]: $$I_m(\mathbf{x})=\rho (\mathbf{x}){\varphi }_m(T_1(\mathbf{x}),T_2(\mathbf{x}))),$$ for m = 1 , ⋯ , M , where ρ ( x ) denotes the spin density, T 1 ( x ) the longitudinal relaxation time, T 2 ( x ) the transverse relaxation time, and ϕ m (·) the contrast-weighting function associated with the m th acquisition parameter (e.g., the flip angle α m and repetition time TR m ). Note that ϕ m (·) in (1) is determined by the Bloch equation based magnetization dynamics, driven by the acquisition parameters ${\{({\alpha }_t,{\text{TR}}_t)\}}_{t=1}^m$.…”

“…Note that ϕ m (·) in (1) is determined by the Bloch equation based magnetization dynamics, driven by the acquisition parameters ${\{({\alpha }_t,{\text{TR}}_t)\}}_{t=1}^m$. However, distinct from conventional MR parameter mapping [20], [21], the analytical form of ϕ m (·) can be difficult to obtain in MR fingerprinting (though it is feasible to determine ϕ m numerically via Bloch simulations).…”

Accelerating t1ρ cartilage imaging using compressed sensing with iterative locally adapted support detection and JSENSE

“…Secondly, not all the data, such as low-intensity bone area that is adjacent to cartilage, fits into the T 1ρ parametric model due to the very low SNR in the later TSLs. So the model-based approaches such as (20) are not applicable here. Thirdly, specific ROIs need to be treated differently from other low SNR regions.…”

Model-based iterative reconstruction for magnetic resonance fingerprinting

“…Similar to conventional MR parameter mapping (e.g., [10,11]), there are a number of models that can be used for the parameter maps {ρ, T1, T2, f0} and/or the contrast-weighted images…”