Why do we collect equispaced pixels when trying to sample an image at higher than Nyquist rate?
The Whittaker–Nyquist–Kotelnikov–Shannon theorem states that a bandlimited signal can be perfectly reconstructed if sampled at more than twice the bandwidth:
However, it does not specify that the samples, pixels, need to be equispaced. While some alternative schemes sampling schemes have been suggested, such as a hexagonal grid, I have not seen a justification for uniformity. While regularly spaced samples makes sense for periodic signals, it’s not clear to me why it makes sense for bounded signals such as an image from a microscope.
Because the image is acquired within a boundary, would it not make sense to increase sampling towards the boundary in order to have uniform rather than decaying image resolution? While we could retain resolution using regular sampling by oversampling the center of the image, this seems wasteful.
The impression that I am get between uniform sampling in image acquisition and Fourier analysis is that the field come into the habit of thinking of bounded images as periodic. Am I wrong?