Modern high sensitivity radio interferometric telescopes use ultra wide-band receivers on a large number of antenna elements to achieve the capability of imaging dynamic ranges in excess of 1:1,000,000. In practice, the imaging performance is limited by instrumental and ionospheric/atmospheric effects that corrupt the recorded data. Many of these effects are directionally dependent and vary with time and frequency. Correcting for them is therefore fundamentally more difficult and these effects have been ignored in classical image reconstruction algorithms. Few attempts in the past to correct for these effects in the image-domain did not deliver the required accuracy. Recent developments in new algorithms that can account for such direction dependent effects show promising results. In this paper I give a general mathematical description of these techniques, show that the resulting algorithms are more optimal in terms of imaging performance and computing requirements and show some results.
We describe a scale sensitive deconvolution algorithm for interferometric images. An ideal sky model should be able to pick up correlated emission on all scales and of all shapes. Though the problem can be well formulated mathematically, there are two issues: (1) it is computationally prohibitive, and (2) the choice of an appropriate basis to represent the image is not clear. The work presented here is an interim step towards developing a fully scale sensitive deconvolution algorithm which is computationally efficient as well. This approach, though restrictive as compared to the most general model for the sky, is an enormous improvement over other scale insensitive algorithms and forms the logical limit of multi-resolution CLEAN approach. The sky image is represented using parameterized basis functions with finite support and the algorithm solves for these parameters. The computational load in this approach is reduced by working with an analytical approximation of the Point Spread Function.