Image Reconstruction Methods in Radio Astronomy

Abstract

An observation of a celestial source generally results in data which are insufficient for a unique reconstruction of the desired brightness profiles of the source. Two typical situations are considered here which pertain to the reconstruction of an object from the measurements of (A) an incomplete set of its Fourier components, and (B) of a diffraction limited image of the object. The inadequacy of classical restoring schemes is evident from the violation of prior knowledge, like positivity of the brightness profile. Various schemes have been developed over the last decade for obtaining a restoration, which agrees with the measurements, as well as our prior knoeledge about the source. Four such schemes are reviewed and critically discussed here. CLEAN is an iterative subtraction of point - components from a conventional map until the residual map is no longer significant above the noise-level. In Biraud's method, the Fourier components of the object are extrapolated in steps such that the object itself is described by a positive function. A 'Maximum Entropy Method' tries to define an 'entropy' characterising the observations as well as prior knowledge and them obtains a solution which leads to a maximum of this 'entropy'. The last scheme, an 'Optimum Deconvolution Method', attempts to optimize the solution by imposing prior knowledge as constraints on a least-squares solution which is also made to satisfy a smoothness requirement of a minimum variance of its second-differences. All these methods have been found to restore the object considerably better than the classical methods even in the presence of noise. Computationally, CLEAN is the most attractive method and it has been routinely used in processing two-dimensional maps with as large as ~ 10 (power 4) grid-points.