  It has been argued that, for a spatially invariant imaging system, the
information one can gain about the separation of two incoherent point sources
decays quadratically to zero with decreasing separation, an effect termed
Rayleigh's curse. Contrary to this belief, we identify a class of point spread
functions with a linear information decrease. Moreover, we show that any
well-behaved symmetric point spread function can be converted into such a form
with a simple nonabsorbing signum filter. We experimentally demonstrate
significant superresolution capabilities based on this idea.
