  The desire for wide-field of view, large fractional bandwidth, high
sensitivity, high spectral and temporal resolution has driven radio
interferometry to the point of big data revolution where the data is
represented in at least three dimensions with an axis for spectral windows,
baselines, sources, etc; where each axis has its own set of sub-dimensions. The
cost associated with storing and handling these data is very large, and
therefore several techniques to compress interferometric data and/or speed up
processing have been investigated. Unfortunately, averaging-based methods for
visibility data compression are detrimental to the data fidelity, since the
point spread function (PSF) is position-dependent, i.e. distorted and
attenuated as a function of distance from the phase centre. The position
dependence of the PSF becomes more severe, requiring more PSF computations for
wide-field imaging. Deconvolution algorithms must take the distortion into
account in the major and minor cycles to properly subtract the PSF and recover
the fidelity of the image. This approach is expensive in computation since at
each deconvolution iteration a distorted PSF must be computed. We present two
algorithms that approximate these position-dependent PSFs with fewer
computations. The first algorithm approximates the position-dependent PSFs in
the $uv$-plane and the second algorithm approximates the position-dependent
PSFs in the image-plane. The proposed algorithms are validated using simulated
data from the MeerKAT telescope.
