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Compressive Sensing as applied to Electromagnetic Inverse Scattering

 
 
The recontruction of the dielectric properties of unknow targets within an inaccessible investigation domain starting from non-invasive measurements of the electromagnetic field, it is of fundamental importance in various applications such as biomedical imaging, geophysical prospecting and non-destructive testing. Unfortunatly, since the aquired data of the electromagnetic field are usually limited and affected by errors and noise and the inverse problem results to be non-linear and ill-posed, it is quite difficult to achieve reliable and accurate solutions without a smart use of the information on the problem at hand. In this framework, Compressive Sensing approaches which exploit the a-priori knowledge on the unknowns' sparseness are currently object of study for the solution of inverse scattering problem thanks to their reliability, effectiveness and robustness to the noise.
   
Biomedical Imaging, geophysical prospecting, non-destructive testing


 
 
According to the CS theory, an unknown/signal phenomena can be enforced to be compressible with respect to suitable expansion bases (i.e., the corresponding vectors of expansion coefficients have few nonzero entries): exploiting the sparseness of the scatterer objects inside the investigation domain, members of ELEDIA Research Center have developed several techniques based on the CS theory aimed at reconstruct the phisical features of the objects under investigation, starting from the measurement of the elctromagnetic scattered fields. In particular, a Bayesian Compressive Sampling (BCS) approach has been considered: a "probabilistic" regularization has been used to reformulate the original inverse problem as a BCS one, and both the Contrast Source formulation and the Born & Rytov approximations has been investigated, exploiting either tranverse magnetic (TM) or transverse electric (TE) wave polarizations, for the reconstrution of the dielectric and conductivity properties of the unknown objects.
Cross-Shaped Object - BCS Reconstructed Profile
L-Shaped Object - BCS Reconstructed Profile

Keywords: Biomedical Imaging, Inverse Scattering, Compressive Sensing, Bayesian Compressive Sensing


See Also
  • G. Oliveri, P. Rocca, and A. Massa, "A Bayesian-compressive-sampling-based inversion for imaging sparse scatterers," IEEE Trans. Geosci. Remote Sens., vol. 49, no. 10, pp. 3993-4006, Oct. 2011.
    doi:10.1109/TGRS.2011.2128329
  • L. Poli, G. Oliveri, and A. Massa, "Microwave imaging within the first-order Born approximation by means of the contrast-field Bayesian compressive sensing," IEEE Trans. Antennas Propag., vol. 60, no. 6, pp. 2865-2879, Jun. 2012.
    doi:10.1109/TAP.2012.2194676
  • G. Oliveri, L. Poli, P. Rocca, and A. Massa, "Bayesian compressive optical imaging within the Rytov approximation," Optics Letters, vol. 37, no. 10, pp. 1760-1762, 2012.
    doi:10.1364/OL.37.001760
  • S. Ji, Y. Xue, and L. Carin, "Bayesian compressive sensing," IEEE Trans. Signal Process., vol. 56, no. 6, pp. 2346-2356, 2008. 10.1109/TSP.2007.914345L. Poli, G. Oliveri, F. Viani, and A. Massa, "MT-BCS-based microwave imaging approach through minimum-norm current expansion," IEEE Trans. Antennas Propag., vol. 61, no. 9, pp. 4722-4732, Sept. 2013.
    doi:10.1109/TAP.2013.2265254
  • L. Poli, G. Oliveri, P. Rocca, and A. Massa, "Bayesian compressive sensing approaches for the reconstruction of two-dimensional sparse scatterers under TE illumination," IEEE Trans. Geosci. Remote Sensing, vol. 51, no. 5, pp. 2920-2936, May. 2013.
    doi:10.1109/TGRS.2012.2218613
  • L. Poli, G. Oliveri, and A. Massa, "Imaging sparse metallic cylinders through a Local Shape Function Bayesian Compressive Sensing approach," Journal of Optical Society of America A, vol. 30, no. 6, pp. 1261-1272, 2013.
    doi:10.1364/JOSAA.30.001261
  • F. Viani, L. Poli, G. Oliveri, F. Robol, and A. Massa, "Sparse scatterers imaging through approximated multitask compressive sensing strategies," Microwave Opt. Technol. Lett., vol. 55, no. 7, pp. 1553-1558, Jul. 2013.
    doi:10.1002/mop.27612