Adaptive uniform weighting: Pre-conditioning to improve image fidelity

The 'dirty image' produced as a result of a direct Fourier inversion of visibility data is an important first step in inteferometric imaging. This is where we define the 'deconvolution problem', and the extent to which that problem is well- or ill-conditioned has direct consequences for the ultimate image fidelity that can be achieved in practise. An under-utilised degree of freedom during Fourier imaging pertains to the relative weights that are assigned to the visibility data. We explore the circumstances where some adjustment of the relative weights could provide improvements to the dirty image and, consequently, the ultimate post-deconvolution image fidelity. In this work, we specifically explored whether typical observations with current and upcoming facilities demonstrate a significant radial trend in the acquired data density. We modelled those trends and used them to calculate a distinct effective local density estimate for each data point. When the resulting local density estimate is used in conjunction with a uniform weight correction and the desired clean beam (e.g. Gaussian) tapering, it provides a significant improvement in the image quality over that provided by the current pixel-based density estimate. This distinction disappears in cases where the acquired visibility sampling is essentially complete. In many cases, particularly spectral-line observations (especially those with only limited sidereal tracking), this adaptive approach improves the beam quality by a factor of 2 to 10, as measured by the RMS residual relative to the best-fitting clean beam. This results in an improvement in the final image fidelity that is similar in terms of magnitude. An appealing aspect of this approach is that there are no 'knobs' for the user to adjust. Once the field size and pixel size are specified (guided by astrophysical aims), the method is considered to be fully adaptive to the acquired data and produces the 'cleanest possible' dirty beam in these circumstances.