Use of marginal distributions constrained optimization (MADCO) for accelerated 2D MRI relaxometry and diffusometry

Measuring multidimensional (e.g., 2D) relaxation spectra in NMR and MRI clinical applications is a holy grail of the porous media and biomedical MR communities. The main bottleneck is the inversion of Fredholm integrals of the first kind, an ill-conditioned problem requiring large amounts of data to stabilize a solution. We suggest a novel experimental design and processing framework to accelerate and improve the reconstruction of such 2D spectra that uses a priori information from the 1D projections of spectra, or marginal distributions. These 1D marginal distributions provide powerful constraints when 2D spectra are reconstructed, and their estimation requires an order of magnitude less data than a conventional 2D approach. This marginal distributions constrained optimization (MADCO) methodology is demonstrated here with a polyvinylpyrrolidone-water phantom that has 3 distinct peaks in the 2D D-T1 space. The stability, sensitivity to experimental parameters, and accuracy of this new approach are compared with conventional methods by serially subsampling the full data set. While the conventional, unconstrained approach performed poorly, the new method had proven to be highly accurate and robust, only requiring a fraction of the data. Additionally, synthetic T1-T2 data are presented to explore the effects of noise on the estimations, and the performance of the proposed method with a smooth and realistic 2D spectrum. The proposed framework is quite general and can also be used with a variety of 2D MRI experiments (D-T2,T1-T2,D-D, etc.), making these potentially feasible for preclinical and even clinical applications for the first time.