In radio astronomy the sky is continuously scanned to collect frequency information about celestial objects. The inverse 2D Fourier transformation is used to generate images of the sky from the collected frequency information. We propose an algorithm that incrementally refines images by processing frequency information as it arrives in a temporal data stream. A direct implementation of the refinement with the discrete Fourier transformation requires O(N^2) complex multiplications to process an element of the stream. We propose a new algorithm that avoids recomputations and only requires O(N) complex multiplications.