Exploitation of any available a priori information can considerably reduce the false solution occurrence through convenient starting points, regularization techniques or multifrequency and/or multiresolution procedures. The principle of the regularization methods is indeed to use the additional a priori information on the contrast function in an explicit way to construct from the beginning a solution both compatible with the data and which exhibit some specific physical features. The kind of additional information includes (but it is not limited to):
- an upper bound on the dimensionality of the space where the unknown function is looked for. Such a strategy can be defined ‘regularization by projection’. While in [1],[3] the unknown contrast profile is projected onto a finite number of spatial Fourier harmonics, in [4] Haar wavelets are considered;
- the knowledge that the punctual value of the unknown function only can belong to a given finite alphabet of values. In this respect, in [4] a ‘binary’ regularization is introduced.
- exploit the concept of ‘sparsity’ or ‘compressibility’ of the unknown function. In this respect, in [5] two different sparsity promoting approaches are introduced for the solution of non-linear inverse scattering problems. Differently from the other sparsity promoting approaches proposed in the literature, the two methods in [5] tackle the problem in its full non-linearity, by adopting a contrast source inversion scheme.
Finally, in [2] an interesting alternative to deal with the occurrence of the false solutions which exploits multifrequency data is discussed.
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