Superresolution of noisy band-limited data by data adaptive regularization and its application to seismic trace inversion, Proc. 1990 International Conference on Acoustics, Speech, and Signal Processing, vol.3, pp.1237-1240, IEEE Signal Processing Society, Apr. 1990, Albuquerque, NM.


Recovering a broadband object from noisy band-limited observations is an ill-posed problem. If the object has discontinuities, the solution by the conventional Tikhonov regularization method loses them though the solution can be stably obtained. We have 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 non-linear 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 to the conventional Tikhonov regularization method.

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