In this work we present a constrained reconstruction method that can produce either an R2- or R1- weighted image series, in tandem with the parameter map, from undersampled data. The method has been demonstrated in vivo for radial TSE, and radial TSE augmented with nonlinear encoding (O-space), and inversion recovery (IR) datasets. The algorithm iteratively calculates the entire series of T2 or T1 weighted images while enforcing the exponential decay posed as a geometric relationship between the images. Experimental brain images generated with these maps are in excellent agreement with the fully sampled images and show less undersampling artifact than images reconstructed from individual undersampled datasets.
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