Accelerating the CLEAN algorithm of radio interferometry with convex optimization

Context. In radio interferometry, images are recovered from incompletely sampled Fourier datasets. The de facto standard algorithm, the Cotton–Schwab CLEAN, iteratively switches between computing a deconvolution (minor loop) and subtracting the model from the visibilities (major loop). Aims. The next generation of radio interferometers is expected to handle much higher data rates, image sizes, and sensitivity, making acceleration of current data processing algorithms necessary. We aim to achieve this by evaluating the potential of various well-known acceleration techniques in convex optimization for the major loop. For the present manuscript, we limit our study of these techniques to the CLEAN framework. Methods. To this end, we identify CLEAN with a Newton scheme and work backwards through this chain of arguments to express Nesterov acceleration and conjugate gradient orthogonalization in the major and minor loop framework. Results. The resulting algorithms are simple extensions of the traditional framework. However, they converge multiple times faster than traditional techniques and reduce the residual significantly deeper. These improvements achieved by accelerating the major loop are competitive with other well-known improvements by replacing the minor loop with more advanced algorithms, but at lower numerical cost. The best performance is achieved by combining these two developments. Conclusions. CLEAN remains among the fastest and most robust algorithms for imaging in radio interferometry and can be easily extended to achieve an order of magnitude faster convergence speed and dynamic range. The procedure outlined in this manuscript is relatively straightforward and could be easily extended.