Non-Cartesian MRI k-space trajectories provide faster and more motion-robust data acquisitions than those of Cartesian trajectories. In this paper, we focus on the rosette trajectory and generalize the weighted rosette trajectories for fast undersampled k-space data acquisition. However, single-slice imaging using the rosette trajectory will be affected by the off-resonance effect. To reduce the artifacts from offresonance slices, this paper introduced an adaptive iterative reconstruction

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... derived from the TV and nuclear norm regularization terms for raw MRI data reconstruction. This reconstruction problem was separated into two subproblems and solved with an adaptive regularization parameter. The results show that the weighted rosette trajectory that offers short acquisition times and good off-resonance behaviors with little blurring can be used for reconstruction with adaptive regularization parameters and achieve a superior performance. INDEX TERMS MRI, non-Cartesian trajectory, k-space, weighted rosette, adaptively, reconstruction. JIN XU received the B.S. degree from Sichuan University, in 2003, and the M.S. degree from the