It is shown that multiple blind deconvolution and phase retrieval in three or more dimensions are overdetermined problems if the image or Fourier amplitude, respectively, is measured continuously (or, equivalently, is sampled at the Nyquist rate). A sampling scheme is derived that removes the overdeterminancy and allows a measure of the redundancy to be defined. This indicates that phase retrieval and deconvolution are more stable, with respect to noise and partial information, with increasing dimensionality.
Rick P. Millane, Rick P. Millane,
"Redundancy in multidimensional deconvolution and phase retrieval", Proc. SPIE 1351, Digital Image Synthesis and Inverse Optics, (1 November 1990); doi: 10.1117/12.23637; https://doi.org/10.1117/12.23637