evaluating individual terms of 2D DFT (Goertzel?)
The 2D DFT is separable, so you can conceptually compute it by applying 1D DFTs in both directions. For the Goertzel algorithm you can first apply it for a specific column for each row, and then use that column and apply it again to obtain the individual term. Most likely, you can rewrite the Goertzel algorithm to do this in one go, but the computational savings are quite small (for an $N \times N$ image, you would need $N^2 + N$ multiplications using the separable approach, while a 2D version would give $N^2$ multiplications).