A universal filter for enhanced imaging with small arrays

We analyze in detail directivity enhancement in imaging with small arrays of closely spaced sensors, in homogeneous media. Imaging is done with Kirchhoff or travel time migration of the array data after applying an inverse filter that increases the resolution of the image. In general, the construction of such a filter requires invasive measurements on a control array in the vicinity of the object to be imaged, which we assume are not available. The form of the filter is, however, universal when the control array encloses the imaging sensor array. It is the inverse of the finite Fourier transform operator, which has the sinc function as its kernel. We analyze the dependence of resolution enhancement on the signal-to-noise ratio both with narrow and broadband signals.