Multi-scale and Multi-directional VLBI Imaging with CLEAN

Abstract: Very long baseline interferometry (VLBI) is a radio-astronomical technique in which the correlated signal from various baselines is combined into an image of highest angular resolution. Due to sparsity of the measurements, this imaging procedure constitutes an ill-posed inverse problem. For decades the CLEAN algorithm was the standard choice in VLBI studies, although having some serious disadvantages and pathologies that are challenged by the requirements of modern frontline VLBI applications. We develop a novel multi-scale CLEAN deconvolution method (DoB-CLEAN) based on continuous wavelet transforms that address several pathologies in CLEAN imaging. We benchmark this novel algorithm against CLEAN reconstructions on synthetic data and reanalyze BL Lac observations of RadioAstron with DoB-CLEAN. DoB-CLEAN approaches the image by multi-scalar and multi-directional wavelet dictionaries. Two different dictionaries are used. Firstly, a difference of elliptical spherical Bessel functions dictionary fitted to the uv-coverage of the observation that is used to sparsely represent the features in the dirty image. Secondly, a difference of elliptical Gaussian wavelet dictionary that is well suited to represent relevant image features cleanly. The deconvolution is performed by switching between the dictionaries. DoB-CLEAN achieves super-resolution compared to CLEAN and remedies the spurious regularization properties of CLEAN. In contrast to CLEAN, the representation by basis functions has a physical meaning. Hence, the computed deconvolved image still fits the observed visibilities, opposed to CLEAN. State-of-the-art multi-scalar imaging approaches seem to outperform single-scalar standard approaches in VLBI and are well suited to maximize the extraction of information in ongoing frontline VLBI applications.