Relation between one- and two-dimensional noise power spectra of magnetic resonance images

Our purpose in this study was to elucidate the relation between the one-dimensional (1D) and two-dimensional (2D) noise power spectra (NPSs) in magnetic resonance imaging (MRI). We measured the 1D NPSs using the slit method and the radial frequency method. In the slit method, numerical slits 1 pixel wide and L pixels long were placed on a noise image (128 × 128 pixels) and scanned in the MR image domain. We obtained the 1D NPS using the slit method (1D NPS_Slit) and the 2D NPS of the noise region scanned by the slit (2D NPS_Slit). We also obtained 1D NPS using the radial frequency method (1D NPS_Radial) by averaging the NPS values on the circumference of a circle centered at the origin of the original 2D NPS. The properties of the 1D NPS_Slits varied with L and the scanning direction in PROPELLER MRI. The 2D NPS_Slit shapes matched that of the original 2D NPS, but were compressed by L/128. The central line profiles of the 2D NPS_Slits and the 1D NPS_Slits matched exactly. Therefore, the 1D NPS_Slits reflected not only the NPS values on the central axis of the original 2D NPS, but also the NPS values around the central axis. Moreover, the measurement precisions of the 1D NPS_Slits were lower than those of the 1D NPS_Radial. Consequently, it is necessary to select the approach applied for 1D NPS measurements according to the data acquisition method and the purpose of the noise evaluation.