Superresolution of noisy band-limited data by data adaptive regularization and its application to seismic trace inversion

Recovering a broadband object from noisy bandlimited observations is an ill-posed problem. If the object has discontinuities, the solution by the conventional Tikhonov regularization method loses them, although the solution can be stably obtained. It is shown that a structural constraint such as the number of spikes/discontinuities in the solution plays an important role in recovering the missing frequency information in the presence of noise. This nonlinear constrained minimization problem has been solved by data adaptive regularization. Applications of this method to synthetic data have shown its superior resolving power and stability compared to the conventional Tikhonov regularization method