Superresolution with the zero-phase imaging condition

Wave-based imaging techniques use wavefield data from receivers on the boundary of a domain to produce an image of the underlying structure in the domain of interest. These images are defined by the imaging condition, which maps recorded data to their reflection points in the domain. In this paper, we introduce a nonlinear modification to the standard imaging condition that can produce images with resolutions greater than that ordinarily expected using the standard imaging condition. We show that the phase of the integrand of the imaging condition, in the Fourier domain, has a special significance in some settings that can be exploited to derive a super-resolved modification of the imaging condition. Whereas standard imaging techniques can resolve features of a length scale of $\lambda$, our technique allows for resolution level $R < \lambda$, where the super-resolution factor (SRF) is typically $\lambda/R$. We show that, in the presence of noise, $R \sim \sigma$.