L1 Norm Minimization in ISAR Imaging

This work deals with an ISAR (Inverse Synthetic Aperture Radar) image enhancement algorithm using target's sparse image and image's
$l_{1}$
norm minimization. As calculation of
$l_{1}$
norm of two-dimensional (2D) image matrix is too complicated, target's image matrix is resized to one-dimensional (1D) one. According to ISAR theory, the ISAR signal matrix is a Fourier transform of the target's image matrix. Thus, the ISAR signal is obtained one dimensional one while modelling by Fourier transform of a certain target's image column matrix. In the image reconstruction algorithm, 12 norm constrained function and
$l_{12}$
objective function are defined. Simulation experimental results prove functionality of the developed algorithm.