Dealing with edge effects in least-squares image deconvolution problems

It is well-known that when an astronomical image is collected by a telescope, the measured intensities at pixels near the edge of the image may depend on the intensity of the object outside of the field of view (FOV) of the instrument. This makes the deconvolution of astronomical images troublesome. Standard approaches for solving this problem artificially extend the object outside the FOV via the imposition of boundary conditions (BCs). Unfortunately, in many instances the artificially extended object has little in common with the object itself outside of the FOV. This is most pronounced in the case of objects close to the boundary of the image and/or extended objects not completely contained in the image domain. In such cases, an inaccurate extension of the image outside of the FOV can introduce non-physical edge effects near the boundary that can degrade the quality of the reconstruction. For example, if the BCs used result in an extended image that is discontinuous at the boundary, these edge effects take the form of ripples (Gibbs oscillations). In this paper, we extend to least-squares (LS) algorithms a method recently proposed by Bertero & Boccacci (2005, A&A, 437, 369) in the context of the Richardson-Lucy (RL) algorithm for the restoration of images contaminated by Poissonian noise. The most important characteristic of the proposed approach is that it does not impose any kind of artificial BCs and is therefore free from edge effects. For this reason it can be considered the natural method for the restoration of images via LS algorithms.