Radio-interferometric imaging aims to estimate a sky intensity image from degraded undersampled Fourier measurements. At the dynamic range of interest to modern radio telescopes, the image reconstruction quality will be limited by the unknown time-dependent calibration kernels. Hence the need of performing joint image reconstruction and calibration, and consequently of solving a non-convex blind deconvolution problem. Extending our recent work where the calibration kernels are assumed to be smooth in space, we further assume in this work that the calibration kernels are smooth in time. In addition, an average sparsity prior is used for the estimation of the image of interest. The resulting high dimensional non-convex non-smooth minimization problem is then solved by leveraging an alternating forward-backward algorithm which benefits from well-established convergence guarantees. Our results show that time-regularization is effective in enhancing imaging quality.
The codes made available here represent a proof of concept MATLAB implementation of the proposed algorithm.
P.-A. Thouvenin, A. Repetti, A. Dabbech, and Y. Wiaux - Time-Regularized Blind Deconvolution Approach for Radio Interferometry, Proc. IEEE Sensor Array and Multichannel Signal Process. Workshop (SAM), pp. 475-479, Sheffield, United-Kingdom, 8--11 July 2018.