Optimization of Compressed Sensing Based Radio Interferometric Imaging: Hyperparameter Selection

The radio interferometric imaging method obtains the visibility by sampling in the spatial frequency domain, and then reconstructs the image. Due to the limitation of antenna numbers, the sampling is usually sparse and noisy. Compressed sensing algorithm based on convex optimization is an effective reconstruction method under sparse sampling conditions. The hyperparameter of the $l_1$ regularization term is one important parameter that directly affects the quality of the reconstructed image. The parameter value is too highto miss the image structure. The parameter value is too lowto cause the image with low signal-to-noise ratio. The selection of hyperparameters under different image noise densities is researched in this paper, and solar radio images are used as examples to analyze the optimization results of compressed sensing algorithms under different noise densities. The simulation results shows that when the salt-and-pepper noise density is between $10\%$ and $30\%$, the compressed sensing algorithm has a good reconstruction effect, the optimal hyperparameter has a linear relationship with the noise density, and the regression mean square error is approximately $8.10×10^{-8}$.