Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Efficient Minimization Methods of Mixed l2-l1 and l1-l1 Norms for Image Restoration
SIAM Journal on Scientific Computing
Blind and semi-blind deblurring of natural images
IEEE Transactions on Image Processing
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Systematic errors inevitably occur during the acquisition and processing of geophysical data because of measurement and discretization noise, as well as incorrect geophysical forward modeling, among other problems. Such errors commonly cause systematic degradations, including over-smoothing and decreased resolution of estimated geophysical models. In this paper, the relationship between systematic errors and an estimated geophysical estimated model is analyzed. A convolution model for systematic degradations is also derived. On the basis of the convolution model, we suggest using the inverse method to reduce systematic degradations and enhance estimated geophysical models. Accordingly, we propose a geophysical model enhancement algorithm based on blind deconvolution. The algorithm uses the mixed norm total variation regularizations to optimize the precision of the solution. We conduct experiments on 1D linear and 2D magnetotelluric geophysical model enhancement to confirm the validity of the proposed convolution approximation theory and model enhancement algorithm. Results indicate that the proposed method significantly improves geophysical models. In particular, the 2D enhancement experiment shows that the proposed algorithm increases overall model precision by 75%.