Over the years there were several questions posted here at MathWorks about how to compute a radial profile (like average spectral density). The same answer was repeated every time: go in a for loop over all radii and average the data which lays in a circle. When dealing with an image of just 1024x1024 it starts to be faster to deconvolve an image than to compute a radial profile!
MatLab has a very fast own function accumarray which can do the trick with zero for loops. I have written a basic radial profiler which calls accumarray twice: first time to create radial ticks, and second time to create the average profile. In my application with 2048x1792 data I have ahieved 50x accelearation compared with the "for loop" approach.
If you need to speed-up this function even more, consider using bwdist instead of meshgrid.
This function can be further improved further in terms of accuracy of averaging by taking into account subpixel subtelties.