  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.
