Maximum-entropy and subspace methods for high-resolution relaxation-diffusion distribution estimation

Relaxation-diffusion distribution characterizes tissue microstructure using multi-contrast MRI data without using a multi-compartment model. This work applies and generalizes two nonlinear spectral estimation algorithms to compute relaxation-diffusion distributions and compares their performances with the standard linear inverse method. The first algorithm employs maximum entropy (MaxEnt) estimation, extending previous methods by incorporating measurement noise for improved robustness. The second algorithm is based on the MUltiple SIgnal Classification (MUSIC) subspace spectral estimation technique, enabling pseudo-spectral estimation of multi-exponential signals sampled on regular grids without solving optimization problems. Both methods were compared against the basis representation technique and the nonnegative least squares (NNLS) method using synthetic and <i>in vivo</i> data. MaxEnt demonstrated superior spectral resolution compared to other methods. Meanwhile, the multidimensional MUSIC algorithm provided accurate estimations but required a higher signal-to-noise ratio. MaxEnt and MUSIC improve computational efficiency, especially when a high-resolution sampling grid is required for the density functions.