Model-based reconstruction approaches benefit from tight representation of the signal and from optimization on meaningful quantitative parameter maps, while requiring advanced algorithms and increased computational resources. We propose a generalized iterative thresholding algorithm with parameter splitting for model-based reconstruction, along with an efficient implementation. The approach is flexible and generalizable to problems in various MRI domains. We demonstrate it on the common image with phase evolution and signal decay model tackled with multi-echo GRE and Echo-Planar Time-resolved Imaging (EPTI), resulting in better image quality in comparison with GRAPPA and subspace constrained reconstruction, and increased z-scores in a low-SNR functional experiment.
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