Sparsity-Based Multipath Exploitation for Through-the-Wall Radar Imaging by Michael Leigsnering

Author:Michael Leigsnering
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

Figure 4.3 illustrates the overlapping grouping of image pixels assuming an pixel image and possible propagation paths. The small number in the top left corner of each square indicates the pixel index, while the large number in the center represents the pixel weights of the depicted group. For example the index set for the group corresponding to the 12th pixel, as shown in the figure, would be , where the second half of the set corresponds to indices in the multipath image (). The corresponding weighing matrix would be . The index sets for all other groups are obtained similarly by shifting the cross-shaped mask to the appropriate pixel position. The weights should be chosen such that their sum is unity in order to avoid unintentional scaling of the reconstruction result.

Note that the regularizer (4.14) in reconstruction problem (4.15) is not separable. That is, it cannot be expressed as a summation of functions of disjoint sets of its variables, and thus, cannot be solved by SparSA [WNF09]. However, Fast overlapping Group Lasso (FoGLasso) [YLY13] allows for overlapping groups and is applied to the generalized group sparse reconstruction problem.

Fig. 4.4Measurement setup and room layout.

IEEE 2014. Reprinted, with permission, from M. Leigsnering, F. Ahmad, M. G. Amin, and A. Zoubir, “Multipath exploitation in through-the-wall radar imaging using sparse reconstruction,” IEEE Transactions on Aerospace and Electronic Systems, vol. 50, no. 2, pp. 920–939, Apr. 2014

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