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Simulation and in\u2010vivo results are compared to locally low\u2010rank (LLR) and compressed sensing reconstructions (CS) for reference.<\/jats:p><\/jats:sec><jats:sec><jats:title>Methods<\/jats:title><jats:p>Data were acquired using a 3D Cartesian pseudo\u2010spiral in\u2010out k\u2010t undersampling scheme (<jats:italic>R<\/jats:italic>\u00a0=\u200910) and reconstructed using MI\u2010LLR, which encompasses two stages. In the first stage, approximate displacement fields are derived from an initial LLR reconstruction to feed a motion\u2010compensated reference system to a second reconstruction stage, which reduces the rank of the inverse problem. For comparison, data were also reconstructed with LLR and frame\u2010by\u2010frame CS using wavelets as sparsifying transform (\u2010wavelet).<\/jats:p><jats:p>Reconstruction accuracy relative to ground truth was assessed using synthetic data for realistic ranges of breathing motion, heart rates, and SNRs. In\u2010vivo experiments were conducted in healthy subjects at rest and during adenosine stress. Myocardial blood flow (MBF) maps were derived using a Fermi model.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>Improved uniformity of MBF maps with reduced local variations was achieved with MI\u2010LLR. For rest and stress, intra\u2010volunteer variation of absolute and relative MBF was lower in MI\u2010LLR (\u00b10.17\u2009mL\/g\/min [26%] and \u00b11.07\u2009mL\/g\/min [33%]) versus LLR (\u00b10.19\u2009mL\/g\/min [28%] and \u00b11.22\u2009mL\/g\/min [36%]) and versus \u2010wavelet (\u00b11.17\u2009mL\/g\/min [113%] and \u00b16.87\u2009mL\/g\/min [115%]). At rest, intra\u2010subject MBF variation was reduced significantly with MI\u2010LLR.<\/jats:p><\/jats:sec><jats:sec><jats:title>Conclusion<\/jats:title><jats:p>The combination of pseudo\u2010spiral Cartesian undersampling and dual\u2010stage MI\u2010LLR reconstruction improves free\u2010breathing quantitative 3D myocardial perfusion CMR imaging under rest and stress condition.<\/jats:p><\/jats:sec>","DOI":"10.1002\/mrm.29295","type":"journal-article","created":{"date-parts":[[2022,6,17]],"date-time":"2022-06-17T10:14:59Z","timestamp":1655460899000},"page":"1575-1591","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Free\u2010breathing motion\u2010informed locally low\u2010rank quantitative 3D myocardial perfusion 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