The specks on the FFT were hand removed... I thought the following: he had an image obtained after a blur and sharpening filters. By replacing parts of the FFT

The specks on the FFT were hand removed... I thought the following: he had an image obtained after a blur and sharpening filters. By replacing parts of the FFT with black, he was just throwing away information. What would happen if instead of naively replacing the specks on the FFT with black he replaced those parts with the FFT from the blurred and sharpened image?