# Sampling Theorem for images

A medical Image has a size of 8x8 inches. The sampling resolution is 5 cycles/mm. How many pixels are required? Will an image of size 256x256 be enough?

I know sampling in 1D signal but cannot get the intuition for a 2D image.

I first converted 5 cycles/mm to cycles/inch which came to be about 127 cycles/inch.

So as I understand it, this means we take 127 values for each inch of the input image and each of this is a pixel. So I figured for a 8x8 inch image, we would need

127*8x127*8 = 1016x1016 pixels

Am I right in my thinking or will Nyquist theorem have to be used?

Any kind of help is appreciated.

• // Am I right in my thinking or will Nyquist theorem have to be used? // ------ you are right in thinking that. But what you need is another factor that is greater than 2 for both vertical and horizontal. Nyquist says you need at least 2033 x 2033 pixels. and practicality says you need a bit more. Commented Apr 25, 2019 at 20:34
• maybe 2048 x 2048 would be just enough and it would make any FFT or DCT a bit more happy. Commented Apr 25, 2019 at 20:38
• i would, for practicality reasons, toss in another factor of two and make it 4096 x 4096 pixels. are you doing any FFT or DCT transformation to the image? Commented Apr 25, 2019 at 20:43
• Thanks, I got it. Can you point me to a resource which explains samping theorem for images? Commented Apr 25, 2019 at 20:43
• i just did a quick googley thing and found this. Commented Apr 25, 2019 at 20:44