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Table 1
Overview of the mathematical notations used throughout this paper.
| nx | number of pixels in the image domain. |
| nv. | number of visibilities (per single frequency). |
| np. | number of spatio-spectral parameters to model the sky. |
| I. | The unit matrix. |
 . |
The mean weighted sum of fi over a set of indices Ω. Weights are assumed to be normalized throughout. |
| b. | Index representing a baseline-time, i.e. a pair of antennas pq at time t. |
| bν. | Index representing a baseline-time-frequency (BTF) point. |
| Ων | The set of all BTFs bν (i.e. nv elements) for a given frequency ν. |
 . |
The 4-visibilities vector corresponding to bν. |
| xν. | The true sky vector (at frequency ν) of size  . |
| yν. | The dirty image vector (at frequency ν) of size  . |
 . |
The Fourier transform matrix of size  . Each column is the Fourier kernel mapping a given sky coordinate to all visibilities. |
 . |
The matrix of size  representing the operator that selects 4 out of 4nv visibilities. |
 . |
The 4 × 4 Mueller-like matrix of a given BTF point bν, for direction s. |
 . |
A block diagonal matrix of size  , representing the DDE effect over the image domain for BTF point bν. Each diagonal block i is a 4 × 4  matrix. |
 . |
The direction-dependent transfer function at frequency ν, mapping the sky vector xν onto the dirty image vector yν |
 . |
The image plane normalisation used to tranform  to a local convolution matrix. |
 . |
An object affected by the image plane normalisation  . |
 . |
Diagonal matrix of size  representing the data weighting for frequency ν. |
 |
The PSF corresponding to a single BTF bν. |
| Θ | A transfer function mapping the spatio-spectral sky model vector to the spectral dirty cube. |
 |
A (nx × np) matrix describing the transfer function between the spatio-spectral sky model vector around pixel i to the spectral dirty cube at frequency ν. |
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