Combining RF encoding with parallel imaging: a simulation study

Nunes, Rita G.; Hajnal, Joseph V.; Larkman, David J.

doi:10.1007/s10334-009-0191-1

Cited by 2 publications

(1 citation statement)

References 18 publications

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“…As an index for noise performance and stability of the reconstruction, the condition number

κ (E)

of the encoding matrix

E

, defined by

κ (E) = ‖ E^{- 1} ‖ \cdot ‖ E ‖

, is used to compare the conventional methods and the FRONSAC methods. The condition number is an upper bound to the error propagation from the measurements to the coefficients estimates. A minimum and optimal value is 1, in which case the information matrix is proportional to the identity matrix, such as in a complete DFT matrix.…”

Section: Discussionmentioning

confidence: 99%

Fast rotary nonlinear spatial acquisition (FRONSAC) imaging

Wang

Tam

Constable

et al. 2015

Magnetic Resonance in Med

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Purpose Nonlinear spatial encoding magnetic fields (SEMs) have been studied to reconstruct images from a minimum number of echoes. Previous work has also explored single shot trajectories in nonlinear SEMs. However, the search continues for optimal schemes that apply nonlinear SEMs to improve spatial encoding efficiency and image quality. Theory and Methods We enhance the encoding efficiency of standard linear gradient trajectories by adding a rapidly rotating nonlinear SEM of moderate amplitude, the so called FRONSAC (Fast ROtary Nonlinear Spatial ACquisition) imaging. This additional gradient greatly improves the image quality of highly undersampled single-shot trajectories, including EPI, Spiral, and Rosette trajectories. Results Our simulations, including noise and dephasing effects, test the effect of adding FRONSAC gradients, demonstrating the applicability of this approach. Performance is explained by demonstrating the additional k-space sampling the nonlinear gradient provides. Studies of the optimal amplitude and frequency of the additional FRONSAC field are presented, and the role of enhanced sampling during the readout demonstrated. Dynamic field mapping in a second-order gradient system shows the proposed gradient waveforms are feasible. Conclusions Images resulting from highly undersampled existing k-space trajectories, such as EPI, Spiral and Rosette, are greatly enhanced simply by adding a rotating nonlinear SEM field.

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“…As an index for noise performance and stability of the reconstruction, the condition number