Exploring non-negative solutions for the radar imaging inverse problem at Jicamarca

The radar imaging technique has been applied at the Jicamarca Radio Observatory for many years in order to observe how ionospheric structures evolve as function of space and time. Different algorithms have been proposed to invert the images from spatial cross correlation measurements that are conducted using a non-uniform distribution of antenna receivers. The algorithms, in general, estimate the inverse spatial Fourier transform of the correlation measurements in order to obtain the brightness function of the ionospheric structures that are of our interest. Among the different algorithms applied, Maximum Entropy has been widely used in the community showing to have a good performance. One of the main reasons for its use is that it naturally provides non-negative solutions of the brightness functions which is expected. In this work, we have explored some alternative algorithms to solve the radar imaging inverse problem imposing a non-negative constraint to the solution. Specifically, we have implemented two alternative algorithms, one based on Tikhonov regularization, and the other applying compressed sensing using a Daubechies basis functions. In both cases a non-negative constraint has been imposed providing solutions that are very similar to the ones obtained with maximum entropy. A statistical comparison between these different approaches based on simulated data will be presented in order to analyze their performance under different conditions.