A Radio-interferometric Imaging Method Based on Adaptively Learned Sparsifying Basis

Abstract In radio interferometry, the process of reconstructing the signal from measured visibilities is an ill-posed inverse problem. Although the compressive sensing (CS) technology has been successfully applied in radio interferometry, the conventional CS methods use a fixed set of sparse bases for the entire astronomical image, which cannot achieve a sufficiently high degree of sparsity and thus affects the performance of CS reconstruction. This paper proposes a novel radio-interferometric imaging algorithm based on adaptively learned sparsifying basis. Considering that many signals in the universe are nonstationary, the proposed method uses an adaptive learning dictionary to sparsely represent overlapped image patches, which can effectively capture local features of the image and reduce the artifacts. Furthermore, the split Bregman iteration algorithm is employed to alternately solve the dictionary learning and image estimation. The effectiveness of the proposed method is validated through multiple simulation experiments.