Fourier interpolation and reconstruction via shannon-type techniques II. Technical developments and applications

Abstract In the inverse problems of Fourier synthesis encountered in aperture synthesis, the data are complex quantities corresponding to an irregular sampling of the Fourier transform of some non-negative object function. CLEAN is a deconvolution method which is intensively used in this context. This series of two papers is meant to provide, as an alternative to CLEAN, a well-formulated deterministic method, in which the propagation of errors is under control. The method introduced in part I is referred to as FIRST or WIPE: FIRST for the principles (Fourier Interpolation and Reconstruction via Shannon-type Techniques), and WIPE for the corresponding deconvolution method (WIPE is reminiscent of CLEAN). The main purpose of part II is to complete the general framework presented in part I. In particular, we present a new method for computing the dusty map and the dirty beam. The related techniques of fast Fourier sampling and gridding are thoroughly analysed. We then explicitly describe the imaging kernel of...