Designing an experiment to show blue noise not adding noise below nyquist and not aliasing above
Interesting! Please do share your results with us!

The reconstruction is indeed the difficult bit. Maybe you can look into NFFT (non-uniform FFT) to obtain the Fourier transform of your irregular sampled image and determine its frequency content. You’d expect a clear peak in the case of a sine wave below Nyquist, or an aliased sine wave. Noise would show up as additional (small) local maxima.