The effect of free parameter estimates on the reconstruction of turbulence corrupted images using the bispectrum

In a previous work we quantified the performance improvement resulting from using the bispectrum to reconstruct extended scenes from image sets corrupted by atmospheric seeing over horizontal paths. Here we expand on that work and explore how image reconstruction quality is effected when poor or inaccurate estimates of the point spread function and other free parameters are used for amplitude estimation. We also examine how the number of paths used in the bispectrum phase estimate similarly impacts reconstruction quality. The performance bounds of each of these parameters are explored in terms of the MSE in intensity per pixel of the resulting reconstructions relative to a diffraction-limited reference image. We have found that using more than six distinct phase paths in the bispectrum phase estimate does not result in improvement enough to justify the additional computation time. Similarly, estimates of the turbulence strength used to develop the inverse filter used in may deviate from the optimum by 50% or more while incurring only a 10% reduction in MSE improvement over a range of turbulence values.