In a PPA MRT method and apparatus, a selected region of k-space containing respective portions of some of the incomplete, measured data lines and respective portions of some of the complete, reconstructed data lines is designated. For each data line in the selected region, a level of the noise therein is identified. For each reconstructed, complete data line in the selected region, a scaling factor is calculated that is dependent on the noise level in that reconstructed, complete data line and the noise level in at least one neighboring incomplete, measured data line in the selected region. The scaling factor is then applied to the reconstructed, complete data line in question, so that the contribution of that line to the overall reconstructed image is adjusted according to the scaling factor. The scaling factor can be limited dependent on where the selected region is located in k-space.