  It has been found that radar returns of extended targets are not only sparse
but also exhibit a tendency to cluster into randomly located, variable sized
groups. However, the standard techniques of Compressive Sensing as applied in
radar imaging hardly considers the clustering tendency into account while
reconstructing the image from the compressed measurements. If the group
sparsity is taken into account, it is intuitive that one might obtain better
results both in terms of accuracy and time complexity as compared to the
conventional recovery techniques like Orthogonal Matching Pursuit (OMP). In
order to remedy this, techniques like Block OMP have been used in the existing
literature. An alternate approach is via reconstructing the signal by
transforming into the Hough Transform Domain where they become point-wise
sparse. However, these techniques essentially assume specific size and
structure of the groups and are not always effective if the exact
characteristics of the groups are not known, prior to reconstruction. In this
manuscript, a novel framework that we call locally adapting matching pursuit
(LAMP) have been proposed for efficient reconstruction of group sparse signals
from compressed measurements without assuming any specific size, location, or
structure of the groups. The recovery guarantee of the LAMP and its superiority
compared to the existing algorithms has been established with respect to
accuracy, time complexity and flexibility in group size. LAMP has been
successfully used on a real-world, experimental data set.
