Reggio Calabria (RC), 89124, Italy

Other Methods

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):

  1. 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;
  2. 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.
  3. 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.

  1. T. Isernia, V. Pascazio and R. Pierri, “A nonlinear estimation method in tomographic imaging,” IEEE Transactions on Geoscience and Remote Sensing, vol. 35, no. 4, pp. 910-923, 1997. [click here]
  2. O. M. Bucci, L. Crocco, T. Isernia and V. Pascazio, “Inverse scattering problems with multifrequency data: reconstruction capabilities and solution strategies,” IEEE Transactions on Geoscience and Remote Sensing, vol. 38, no. 4, pp. 1749-1756, 2000. [click here]
  3. T. Isernia, V. Pascazio, and R. Pierri. “On the local minima in a tomographic imaging technique”, IEEE Transactions on Geoscience and Remote Sensing, vol. 39, pp. 1596-1607, 2001. [click here]
  4. L. Crocco and T. Isernia, “Inverse scattering with real data: detecting and imaging homogeneous dielectric objects,” Inverse Problems, vol. 17, no. 6, p. 1573, 2001. [click here
  5. M. T. Bevacqua, L. Crocco, L. Di Donato, T. Isernia, “Non-linear Inverse Scattering via Sparsity Regularized Contrast Source Inversion”, IEEE Transactions on Computational Imaging, vol. 3, no. 2, pp. 296-304, 2017. [click here]