A magnetic resonance imaging system (1) includes a denoising unit (24), and a reconstruction unit (20). The denoising unit (24) denoises a partial image and provides a spatially localized measure of a denoising effectivity. The reconstruction unit (20) iteratively reconstructs an output image from the received MR data processed with a Fast Fourier Transform (FFT), and in subsequent iterations includes the denoised partial image and the spatially localized measure of the denoising effectivity.
