Multiscale and multidirectional VLBI imaging with CLEAN
by Hendrik Müller
Very long baseline interferometry (VLBI) is a radio-astronomical technique whereby the correlated signal from various baselines is combined into an image of the highest possible angular resolution. Due to the sparsity of the measurements, this imaging procedure constitutes an ill-posed inverse problem. For decades, the CLEAN algorithm has been the standard choice in VLBI studies. However, the continued development of interferometric instruments and increasing demands on robustness and structural range of image reconstruction from VLBI data have been gradually highlighting important limitations of CLEAN: CLEAN introduces a disparity between the recovered model and the final convolved image, its resolution limit is too conservative, the representation of extended emission is suboptimal, CLEAN has spurious regularization properties (the interpolation into the gaps of the uv-coverage in the Fourier domain is only weakly constrained), and the imaging process is highly supervised introducing a considerable human bias.
Recently, forward modeling techniques were proposed and demonstrated to be superior in terms of accuracy, resolution, and dynamic range. Particularly multiscale methods, e.g. DoG-HiT, were successful in reducing the need for human interaction significantly. We transfer these ideas to a CLEAN framework and develop a novel multiscale CLEAN deconvolution method: DoB-CLEAN. The DoB-CLEAN method approaches the image via multiscalar and multidirectional wavelet dictionaries. Two different dictionaries are used: 1) a difference of elliptical spherical Bessel functions dictionary fitted to the uv-coverage and its defects that is used to sparsely represent the features in the dirty image, i.e. that distinguishes structural information of Fourier coefficients covered by observations from gaps in the uv-coverage; 2) a difference of elliptical Gaussian wavelet dictionary that is well suited to represent relevant image features cleanly. The deconvolution is performed by alternating between these two dictionaries within the major loop of DoB-CLEAN.
The representations of the image and the visibilities by continuous wavelet transforms address successfully several pathologies in CLEAN imaging. DoB-CLEAN achieves a super-resolution compared to CLEAN and remedies the spurious regularization properties of CLEAN. In contrast to CLEAN, the representation via basis functions has a physical meaning. Hence, the computed deconvolved image still fits the observed visibilities, in contrast to CLEAN, and a final convolution with a restoring beam is not necessary.
We benchmarked this novel algorithm against CLEAN reconstructions on synthetic data. State-of-the-art multiscalar imaging approaches outperform single-scalar standard approaches in VLBI and are well suited to maximize the extraction of information in ongoing frontline VLBI applications. As a demonstrating example we reanalyze BL Lac observations of RadioAstron with DoB-CLEAN uncovering new features that were not detectable with CLEAN.