2008
DOI: 10.1137/070701583
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Postprocessing of the Linear Sampling Method by Means of Deformable Models

Abstract: The linear sampling method is a qualitative procedure for the visualization of both impenetrable and inhomogeneous scatterers, which requires the regularized solution of a linear illposed integral equation of the first kind. An open issue in this technique is the one of determining the optimal scatterer profile from the visualization maps in an automatic manner. In the present paper this problem is addressed in two steps. First, linear sampling is optimized by using a new regularization algorithm for the solut… Show more

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Cited by 11 publications
(18 citation statements)
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“…In Figure 5.4(c) we show the visualization of the unknown region as provided by the NSLSM: more precisely, we plot the values of the indicator function, chosen as the reciprocal of the squared norm of the regularized solution to the modified far-field equation (4.4). Next, we apply an active contour technique [1,10] to this visualization map: as a result, we extract the support of the unknown region T , which is the homogeneous inner domain shown in panel (d) of Figure 5.4. More precisely, in this panel we plot the pixel values of ε r characterizing the artificial background we need to consider for applying the inhomogeneous CSI in the investigation domain T (the plot of σ would be analogous and is not shown here).…”
Section: 2mentioning
confidence: 99%
“…In Figure 5.4(c) we show the visualization of the unknown region as provided by the NSLSM: more precisely, we plot the values of the indicator function, chosen as the reciprocal of the squared norm of the regularized solution to the modified far-field equation (4.4). Next, we apply an active contour technique [1,10] to this visualization map: as a result, we extract the support of the unknown region T , which is the homogeneous inner domain shown in panel (d) of Figure 5.4. More precisely, in this panel we plot the pixel values of ε r characterizing the artificial background we need to consider for applying the inhomogeneous CSI in the investigation domain T (the plot of σ would be analogous and is not shown here).…”
Section: 2mentioning
confidence: 99%
“…In this approach, from now on called no-sampling linear sampling, a single regularization procedure is applied to the functional equation (in particular, a single regularization parameter is selected by means of some optimality criterion) and therefore the computation of the method is notably faster. In [2] an edge detection algorithm is applied to no-sampling linear sampling in order to provide an automatic and optimal selection of the edges of the map visualized by the qualitative method. The resulting algorithm is able to visualize the profile of the scatterer in a fast and automatic manner from the far-field data.…”
Section: Introductionmentioning
confidence: 99%
“…In linear sampling a point on the boundary induces the norm of the regularized solution of the far-field equation to grow up. In [2], in a two-dimensional setting, an edge detection technique to highlight the contour of the scatterer is realized by means of deformable models. In principle, this technique could be extended to surfaces in 3D but, although active contours are reasonably fast, active surfaces [6] require a notable computational effort to converge to the boundary of the scatterer.…”
Section: Introductionmentioning
confidence: 99%
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