tokens: GHz observations, respectively. 5.3. Computational aspects Each resolve run needs ≈500 000 evaluations of the response and ≈400 000 evaluations of its adjoint. That makes the response part of the imaging algorithm a factor of ≈50 000 more expensive compared to CLEAN approaches. The good news is that the implementation of the radio response Eq. ( 7 ) in the package ducc scales well with the number of data points and that the response calls can be parallelized over the sum in Eq. ( 26 ). The resolve runs have been performed on a single node with five MPI tasks, each of which needs ≈2.2 GB main memory. Each MPI task uses four threads for the parallelization of the radio response and the Fast Fourier Transforms. The wall time for each resolve run is between 80 and 90 h. Single-scale CLEAN takes below 30 min for imaging each channel on a modern laptop. Thus, resolve is approximately 180 times slower that single-scale CLEAN here. This comparison does not include that the resolve had five times the number of CPUs available. Multi-scale CLEAN takes about 2 hours during the final round of imaging on the 13 GHz data set. This number does not account for the time taken during the initial rounds of imaging used to tune the hyper parameters and construct the mask which can be a time-consuming process. However, it should be kept in mind that CLEAN scales much better when the dimensionality of the image is much smaller than that of the data, which is not the case here. This is because CLEAN only requires about 10–30 applications of the full measurement operator and its adjoint, even including all preprocessing steps. Taking 90 min for the average multi-scale CLEAN run, resolve is 60 times slower than multi-scale CLEAN . 6. Conclusions This paper compares the output of two algorithms traditionally applied in the radio interferometry community (single-scale CLEAN and multi-scale CLEAN ) with a Bayesian approach to imaging called resolve . We demonstrate that resolve overcomes a variety of problems present in traditional imaging: The sky brightness distribution is a strictly positive quantity, the algorithm quantifies the uncertainty on the sky brightness distribution, and the weighting scheme is determined non-parametrically. Additionally, resolve provides varying resolution depending on the position on the sky into account, which enables super-resolution. We find that single-scale CLEAN and multi-scale CLEAN give similar results. In contrast, resolve produces images with higher resolution: The 4.8 GHz map has comparable resolution to the 13.4 GHz CLEAN maps. These advantages are at the cost of additional computational time, in our cases ≈90 h wall time on a single node. Future work may extend resolve to multi-frequency reconstructions where the correlation structure in frequency axis is taken into account as well in order to increase resolution. Additionally, direction-independent and antenna-based calibration may be integrated into resolve . Finally, the
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