Systems and methods for pointwise encoding time reduction with radial acquisition (“PETRA”) magnetic resonance imaging (“MRI”) using a gradient modulation scheme to enable higher readout bandwidth while keeping the missing samples of the central region of k-space small are provided. This acquisition scheme allows independent selection of the excitation and readout bandwidths, which allows a higher readout bandwidth while keeping the required number of missing central k-space samples low. This flexibility in selecting the excitation and readout bandwidth settings can mitigate the peak radio frequency power and specific absorption rate limitations on flip angle in traditional PETRA imaging schemes.