Uniqueness and sampling conditions for image reconstruction from the Hartley-transform intensity

Using a constructive proof, I show that a real two-dimensional image is uniquely determined by theintensity of its Hartley transform if the latter is sampled on a particular set of points whose density is approximately half the Nyquist density for the intensity. This result indicates that image reconstruction from the Hartleytransform intensity is in general overdetermined and sub-Nyquist sampled.