It is well known that one cannot image directly through a nonlinear medium, as intensity-dependent phase changes distort signals as they propagate. For this reason, nearly all nonlinear imaging techniques are point-by-point methods that rely on the frequency dependence of multi-photon effects, such as two-photon fluorescence and harmonic generation. Here, we focus on spatial effects by taking advantage of spatially dependent changes in the index of refraction. In particular, we apply wave mixing to (lensless) imaging by extending digital holography to the nonlinear domain. The method relies on propagation and provides a new means of super-resolution, e.g. by coupling low and high spatial frequencies. Using similar coupling, we then develop a technique to extract weak signals from noise. The method channels energy from plasma-like optical instabilities and represents a new, dynamical type of stochastic resonance.