DoG-HiT: A novel VLBI multiscale imaging approach

Abstract

Context. Reconstructing images from very long baseline interferometry (VLBI) data with a sparse sampling of the Fourier domain (uv-coverage) constitutes an ill-posed deconvolution problem. It requires application of robust algorithms, maximizing the information extraction from all of the sampled spatial scales, and minimizing the influence of the unsampled scales on image quality. Aims. We develop a new multiscale wavelet deconvolution algorithm, DoG-HiT, for imaging sparsely sampled interferometric data, which combines the difference of Gaussian (DoG) wavelets and hard image thresholding (HiT). Based on DoG-HiT, we propose a multistep imaging pipeline for analysis of interferometric data. Methods. DoG-HiT applies the compressed sensing approach to imaging by employing a flexible DoG wavelet dictionary, which is designed to adapt smoothly to the uv-coverage. It uses closure properties as data fidelity terms only, initially, and performs nonconvex, nonsmooth optimization by an amplitude-conserving and total-flux-conserving, hard thresholding splitting. DoG-HiT calculates a multiresolution support as a side product. The final reconstruction is refined through self-calibration loops and imaging with amplitude and phase information applied for the multiresolution support only. Results. We demonstrate the stability of DoG-HiT, and benchmark its performance against image reconstructions made with the CLEAN and regularized maximum-likelihood (RML) methods using synthetic data. The comparison shows that DoG-HiT matches the super-resolution achieved by the RML reconstructions and surpasses the sensitivity to extended emission reached by CLEAN. Conclusions. The application of regularized maximum likelihood methods, outfitted with flexible multiscale wavelet dictionaries, to imaging of interferometric data, matches the performance of state-of-the art convex optimization imaging algorithms and requires fewer prior and user-defined constraints.