Methods and systems in a parallel magnetic resonance imaging (MRI) system utilize sensitivity-encoded MRI data acquired from multiple receiver coils together with spatially dependent receiver coil sensitivities to generate MRI images. The acquired MRI data forms a reduced MRI data set that is undersampled in at least a phase-encoding direction in a frequency domain. The acquired MRI data and auto-calibration signal data are used to determine reconstruction coefficients for each receiver coil using a weighted or a robust least squares method. The reconstruction coefficients vary spatially with respect to at least the spatial coordinate that is orthogonal to the undersampled, phase-encoding direction(s) (e.g., a frequency encoding direction). Values for unacquired MRI data are determined by linearly combining the reconstruction coefficients with the acquired MRI data within neighborhoods in the frequency domain that depend on imaging geometry, coil sensitivity characteristics, and the undersampling factor of the acquired MRI data. An MRI image is determined from the reconstructed unacquired data and the acquired MRI data.