Is it possible to restore an optical object from its low-pass spectrum and its truncated image?

Abstract

Let our observations on an arbitrary L₂-space optical object f(x) consist of its low-pass spectrum and its truncated image, i.e., F(ω)rect(ω/2b) and f(x)rect(x/a), respectively. Can f(x) be restored from the given data? We show that, in general, such a restoration is not possible.