  Reconstructing an object solely from its scattered intensity distribution is
a common problem that occurs in many applications. Currently, there are no
efficient direct methods to reconstruct the object, though in many cases, with
some prior knowledge, iterative algorithms result in reasonable
reconstructions. Unfortunately, even with advanced computational resources,
these algorithms are highly time consuming. Here we present a novel rapid
all-optical method based on a digital degenerate cavity laser, whose most
probable lasing mode well approximates the object. We present experimental
results showing the high speed (<100 ns) and efficiency of our method in
agreement with our numerical simulations and analysis. The method is scalable,
and can be applicable to any two dimensional object with known compact support,
including complex-valued objects.
