Testing the MCS Deconvolution Algorithm on Infrared Data

Magain, Courbin, and Sohy (MCS, 1998) [1] proposed a two-channel (separable point source plus extended background) method for astronomical image deconvolution. Unlike the two-channel Richardson-Lucy algorithm [2], [3], the MCS method does not require prior knowledge of point source amplitudes and positions. MCS claim that their method produces accurate astrometry and photometry in crowded fields and in the presence of variable backgrounds. This paper compares Midcourse Space Experiment (MSX) 8 μm Galactic plane images [4] deconvolved via the MCS method to Spitzer Space Telescope Glimpse Survey [5] 8 μm images of the same fields. The improved sampling and final image point spread function (PSF) for the deconvolved MSX image is chosen to match the Spitzer observation. In the parlance of MCS, this determines the light distribution from an 85 cm telescope (Spitzer) by deconvolving data taken with a 33 cm space telescope (MSX). Results are presented for varying degrees of background complexity and examine the limitations of the MCS method for use on infrared data in regions of high source density and bright complex backgrounds. 1. DECONVOLUTION WITH CORRECT SAMPLING Starck, Pantin, and Murtagh [6] in their 2002 review of deconvolution methods define super resolution as “recovering object spatial frequency information outside the spatial bandwidth of the image formation system.” Their review of the theoretical literature admits that true super-resolution is possible if the object to be resolved is nearly black – that is, most pixels in the data have zero values and the non-zero elements are well-spaced [7]. This is certainly true in many astronomical images, though it leads to difficulties in areas with structured backgrounds. While true super-resolution is not possible for extended objects that are not band-limited, the super-resolution techniques will provide image sharpening and contrast enhancement. [8] We may write the observed distribution of light from a source, d(x), as measured by a given instrument, as ) ( ) ( * ) ( ) ( x x x x n f p d + = where p(x) is the total system point response function (PRF), f(x) is the true light distribution, and n(x) is the noise inherent in the measured data. Deconvolution is the effort to remove the effect of the point response function, and our recovery of the higher spatial resolution image consistent with the true light distribution yields a superresolution image. Typical deconvolution algorithms seek to minimize the function