Shannon Nyquist Theorem

 What should be the ideal size of the pixel? should it be big or small?

The answer is given by the shannon nyquist theorem. As per this theorem, the sampling frequency should be greater than or equal to 2 ✕ fmax, where fmax is the highest frequency present in the image.

SubSampling 

The key idea in image sub-sampling is to throw away every other row and column to create a half-size image. When the sampling rate gets too low, we are not able to capture the details in the image anymore.

Instead, we should have a minimum signal/image rate, called the Nyquist rate.

Using Shannons Sampling Theorem, the minimum sampling should be such that :

$$f_s\ge 2f_{\max }$$