In this work a new deblurring algorithm for a special deconvolution problem, where a parameter describes the degree of blurring, is considered. The algorithm is based on the Conjugate Gradient technique and uses the so-called weighted L2-norm regularizer to obtain a reasonable solution. In order to avoid the necessity of determining the appropriate regularization parameter for this regularizer, this regularizer is included as a multiplicative constraint. In this way, the appropriate regularization parameter will be controlled by the inversion process itself. Numerical testing shows that the proposed algorithm works very effectively.
In this paper the contrast source inversion method using a multiplicative weighted L2-norm total variation regularizer is applied to image reconstructions from electromagnetic microwave tomography experiments. This iterative method avoids solving a full forward problem in each iteration which makes the method suitable to handle a large scale computational problem. The numerical results from experimental data with high contrast biological phantom are presented and discussed.
In this paper the nonlinear iterative algorithm, the so-called Extended Contrast Source Inversion is applied to subsurface sensing problem where the number of measured data are very limited and the unknown objects/layers are illuminated from only one side. Some numerical results obtained from synthetic and real data are presented to illustrate the strengths and the weakness of the method.
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