Before revision:  In this paper, we investigate "approximating the Fourier Transform of the input image" as a potential alternative, in the hope that it may further boost the performances on the primary task or introduce novel constraints not well covered by image reconstruction.
After revision:  In this paper, we investigated "approximating the Fourier Transform of the input image" as a potential alternative, in the hope that it may further boost the performances on the primary task or introduce novel constraints not well covered by image reconstruction.