WIPE is a regularized Fourier synthesis method recently developed in radio imaging and optical interferometry. The name of WIPE is associated with that of CLEAN, the well-known deconvolution method presented in the previous lecture, and intensively used by astronomers at IRAM as well as in many institutes, worldwide.
The regularization principle of WIPE refers to the Shannon sampling formula and to theoretical considerations related to multiresolution analysis. The notions of field and resolution appear via the definition of two key spaces: the object space and the object representation space (a subspace of the first). The complex visibilities define a function in another space: the data space. The functions lying in this space take their values on a frequency list which is the concatenation of the experimental frequency list and a regularization frequency list. The latter defines a virtual frequency coverage beyond the frequency coverage to be synthesized, up to the highest frequencies of the scaling functions generating the object space. This virtual sampling is performed at the Shannon rate corresponding to the synthesized field. The reconstructed image, also called the neat map, is defined as the function minimizing a regularized objective functional in which the data are damped appropriately. To describe WIPE we adopt a terminology derived from that of CLEAN.
In this lecture, we present the basic foundations of WIPE, and its implementation in the IRAM data processing software. The reader interested in the theoretical aspects and developments of WIPE is invited to consult the articles [Lannes et al. 1994], [Lannes et al. 1996], [Lannes et al. 1997].