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It has been found that radar returns of extended targets are not only sparsebut also exhibit a tendency to cluster into randomly located, variable sizedgroups. However, the standard techniques of Compressive Sensing as applied inradar imaging hardly considers the clustering tendency into account whilereconstructing the image from the compressed measurements. If the groupsparsity is taken into account, it is intuitive that one might obtain betterresults both in terms of accuracy and time complexity as compared to theconventional recovery techniques like Orthogonal Matching Pursuit (OMP). Inorder to remedy this, techniques like Block OMP have been used in the existingliterature. An alternate approach is via reconstructing the signal bytransforming into the Hough Transform Domain where they become point-wisesparse. However, these techniques essentially assume specific size andstructure of the groups and are not always effective if the exactcharacteristics of the groups are not known, prior to reconstruction. In thismanuscript, a novel framework that we call locally adapting matching pursuit(LAMP) have been proposed for efficient reconstruction of group sparse signalsfrom compressed measurements without assuming any specific size, location, orstructure of the groups. The recovery guarantee of the LAMP and its superioritycompared to the existing algorithms has been established with respect toaccuracy, time complexity and flexibility in group size. LAMP has beensuccessfully used on a real-world, experimental data set.

LAMP: A Locally Adapting Matching Pursuit Framework for Group Sparse Signatures in Ultra-Wide Band Radar Imaging