We investigate numerically the random scattering of two-dimensional (2-D) images and the visibility enhancement via stochastic resonance both in intensity and momentum spaces. The multiple scattering destroys the direct transmission of photons, but some ballistic photons carrying the image information still penetrate the scattering media. The underlying ballistic image signals exhibit an instability and are enhanced at the expense of scattering noise under self-focusing nonlinearity, which is described as a stochastic resonance. It is found that the higher ratio of ballistic signals to scattering noise triggers a stronger instability. The effect of visibility enhancement in different scattering conditions is discussed, and the 2-D quasiparticle motion model is designed to analyze the nonlinear dynamic evolution. Our results provide potential guidance for noisy image detection. ? 2019 Society of Photo-Optical Instrumentation Engineers (SPIE).