Reggio Calabria (RC), 89124, Italy

Qualitative methods

Qualitative methods restrict the problem’s scope to reconstruction of the morphological properties of the unknown targets, by considering a simplified mathematical model with a lower computational burden and thus avoiding dealing with the problem in its full non-linearity. In such framework, LEMMA’s researchers have proposed different qualitative methods. In particular, [1] introduces a simple and original physical interpretation of the linear sampling method and shows its relationship with electromagnetic focusing problems, thus extending the method to the case of near field data. On the other hand, in [2] a generalized formulation of LSM is proposed, wherein the LSM equation is turned into a family of equations by considering at its right-hand side a generic term of the multipole series. [3] proposes a new method based on joint sparsity and equivalence principles able to retrieve the boundary of unknown targets, while in [4] a comparison is performed amongst three different qualitative methods, i.e., the linear sampling method, the orthogonality sampling method, and method in [3]. Finally, [5] gives a general physical understanding of orthogonality sampling method, a recently introduced qualitative method, which is characterized by simplicity of implementation and the applicability to various measurement configurations.

  1. I. Catapano, L. Crocco, and T. Isernia, “On simple methods for shape reconstruction of unknown scatterers,” IEEE Transactions on Antennas and Propagation, vol. 55, no. 5, pp. 1431-1436, 2007. [click here]
  2. L. Crocco, L. Di Donato, I. Catapano and T. Isernia, “An Improved Simple Method for Imaging the Shape of Complex Targets,” IEEE Transactions on Antennas and Propagation, vol. 61, no. 2, pp. 843-851, 2013. [click here
  3. M. T. Bevacqua and T. Isernia, “Shape Reconstruction via Equivalence Principles, Constrained Inverse Source Problems and Sparsity Promotion”, Progress In Electromagnetics Research, vol. 158, pp. 37-48, 2017. [click here]
  4. M. T. Bevacqua and R. Palmeri, “Qualitative Methods for the Inverse Obstacle Problem: A Comparison on Experimental Data”, Journal of Imaging, vol. 5, no. 4, p. 47, 2019. [click here]
  5. M. T. Bevacqua, T. Isernia, R. Palmeri, M. N. Akinci, L. Crocco, “Physical Insight Unveils New Imaging Capabilities of Orthogonality Sampling Method,” IEEE Transactions on Antennas and Propagation, vol. 68, no. 5, pp. 4014-4021, 2020. [click here]