MR fingerprinting (MRF) is a rapid multiparametric quantitative MRI technique that changes the acquisition parameters according to a pre-determined schedule aiming to obtain a unique temporal signal evolution for each set of tissue and system parameters (i.e. T1, T2, diffusion, B0 and B1) [1,2]. MRF has shown promise for measuring tissue changes in pathologies such as cancer [3]. For example, T1 and T2 maps obtained with MRF were shown to improve prostate cancer diagnosis in combination with the apparent diffusion coefficient (ADC) [[4], [5], [6], [7]]. In particular, quantitative T2 maps improved diagnostic power by separating intermediate/high-grade tumors from low-grade tumors [4]. However, longitudinal prostate imaging is challenging due to the deformable and dynamic anatomy of the prostate, its vulnerability to peristaltic motion and bladder filling effects, and distortions due to inherent magnetic susceptibility differences at the interface between different tissues. Most prostate MRF studies to date utilized variable density spiral k-space trajectories [8], which provides fast k-space traversal within a single excitation at the cost of long echo time (TE) and repetition time (TR) and B0-induced blurring.

Radial k-space sampling is an alternative acquisition technique that offers shorter TE/TR to minimize B0 blurring compared to spiral k-space sampling [9,10]. The utilization of the golden-angle acquisition scheme [11], where consecutive spokes are separated by the golden-angle, enables the acquisition of dynamic data with a different uniform k-space coverage in each temporal frame and thus provides enough temporal incoherence for MRF. However, in radial imaging each spoke provides limited k-space coverage, so the acquisition needs to be repeated until a sufficient coverage of k-space in each temporal frame is obtained. Since there are large correlations in the dynamic MRF data and the golden-angle radial acquisition is incoherent, the number of required spokes in each frame can be reduced by compressed sensing techniques [12,13]. A popular technique to accelerate the acquisition of MRF data is to enforce a low-rank condition in the space-time MRF matrix (each temporal frame is a column) [[14], [15], [16]]. Additionally, the MRF dictionary is known to be compressible, and several methods to compress the dictionary based on truncating singular value decomposition have been proposed to improve matching performance [17,18].

Inspired by the subspace reconstruction approach [19], where prior information about a dynamic process is used to build a model with reduced dimensionality (the subspace) and reconstruct undersampled k-space data, this work proposes to build a subspace MRF model using the dictionary entries for reconstruction of undersampled golden-angle radial MRF data. The subspace MRF model is similar to dictionary compression, but the reconstruction algorithm will enforce additional sparsity constraints in the subspace to further increase acceleration and/or improve reconstruction quality. The accuracy of the proposed reconstruction is evaluated in the ISMRM NIST phantom, a multicompartment phantom with different T1 and T2 relaxation values [20,21]. The in vivo utility of our approach is assessed in healthy subjects and reproducibility is tested by repeated scans over the course of a year. The potential use of the method for longitudinal treatment response assessment is demonstrated in a patient with prostate cancer undergoing high dose rate brachytherapy and external beam radiation therapy treatments.