Homogeneous Greens functions as a dictionary for wavefield reconstruction

Techniques for wavefield interpolation, extrapolation and regularization often rely on general-purpose dictionaries originating in the discipline of signal or image processing. However, the linearity of the Helmholtz equation suggests that a dictionary composed of homogeneous Greens functions may be specifically suitable for the reconstruction of the acoustic wavefields relevant to seismic exploration. Through such dictionary, data can be linearly mapped into a dual domain interpreted as an equivalent source distribution. The theoretical argument behind this mapping operation is constructed from first principles in this document. The scheme is then applied to the interpolation of a set of simple synthetic data.