Optimization of compressed sensing-based radio interferometric imaging: hyperparameter selection

Radio interferometric imaging samples visibility data in the spatial frequency domain and then reconstructs the image. Because of the limited number of antennas, the sampling is usually sparse and noisy. Compressed sensing based on convex optimization is an effective reconstruction method for sparse sampling conditions. The hyperparameter for the l₁ regularization term is an important parameter that directly affects the quality of the reconstructed image. If its value is too high, the image structure will be missed. If its value is too low, the image will have a low signal-to-noise ratio. The selection of hyperparameters under different levels of image noise is studied in this paper, and solar radio images are used as examples to analyze the optimization results of compressed sensing algorithms under different noise conditions. The simulation results show that when the salt-and-pepper noise density is between 10% and 30%, the compressed sensing algorithm obtains good reconstruction results. Moreover, the optimal hyperparameter value has a linear relationship with the noise density, and the mean squared error of regression is approximately 8.10\times 10^-8.