# Possible to shift image pixel-wise with FFT?

I know we can shift an image entirely with FFT as

https://stackoverflow.com/questions/25827916/matlab-shifting-an-image-using-fft

However, is it possible to shift the image pixel-wise? I just found a similar description in a recently published paper: X. Wang, L. Li, and G. Hou, "High-resolution light field reconstruction using a hybrid imaging system," Appl. Opt. 55, 2580-2593 (2016). They use a subband approach that really confused me.

• What do you mean by "pixel-wise" in this context? As you mentioned, you do understand that a shift of the entire image is possible (i.e. a displacement of the image in $x$ and $y$ by a certain (not necessarily integer) number of pixels). What is the difference between this shift and your "pixel-wise" shift then?
– M529
Commented Apr 7, 2016 at 13:58
• "pixel-wise" means each pixel owns its own displacement that differs from others', in this case shifting the entire image is not equivalent to shifting pixel-wise. Commented Apr 8, 2016 at 5:18
• In this case, I do not see an efficient way to do this by an FFT. You could certainly chop up your image, displace each pixel individually and recombine the results then to achieve an shifted image. However, this is computationally certainly not the best option, and does also not solve the problem that you would generate "holes" (i.e. if you would shift one pixel to the left by exactely one pixel, you would have a hole/"missing value" in the original place, since no other pixels are dragged along with the originally shifted pixel).
– M529
Commented Apr 8, 2016 at 8:10
• Thanks for your comment, though I still don't understand the subband approach in the paper. Commented Apr 8, 2016 at 12:32