Radio Interferometric Image Reconstruction Algorithm Based on Primal Dual

Abstract

The last-standing ill-posed inverse problem of radio interferometric imaging is analyzed. A new convex optimization algorithm, Primal Dual, is applied to radio interferometric imaging to recover the emission structure from the incomplete sampling. The convex optimization problem is defined as the primal problem and its dual problem is calculated. According to the characteristics of these two problems, the final solution of the primal problem is solved and the image of radio sources are reconstructed by iteratively alternating between solving the primal problem and the dual problem by using moreau decomposition, forward-backward method and the proximity operator. The algorithm parameters are analyzed from the simulations based on experimental data. The algorithm is validated and the parameters are optimized. The comparison between the images inferred from the compressed sensing and classical CLEAN algorithms shows that the signal to noise ratio and the dynamic range in the reconstructed images from compressed sensing are significantly higher than the CLEAN images, and the sidelobe levels are much lower in the former based on the real data. Besides the obvious efficacy of the Primal Dual algorithm in reconstructing extended source images, the major attraction is that it is simple to parallelize to support large data sets.