While conventional density compensation function(DCF) performs sufficiently well for filtered backprojection(FBP) and radial k-space MRI when the Nyquist sampling condition is met and/or evenly-spaced view angles are used, it may perform poorly when sub-sampling and/or irrational-view angles are used. We propose an optimized DCF for the aforementioned conditions by calculating the density weights based on geometric properties of radial k-space sampling in a discrete environment, regardless of scan conditions such as data sizes and view angles. Compared with standard DCF, the optimized DCF produces higher signal-to-noise ratio(SNR) in FBP (phantom) and more accurate flow metrics in 48-fold accelerated, phase-contrast MRI.
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