Two-Dimensional l₁-Norm Minimization in SAR Image Reconstriction

A nonconventional image algorithm, based on compressed sensing and l₁-norm minimization in Synthetic Aperture Radar (SAR) application is discussed. A discrete model of the earth surface relief and mathematical modeling of SAR signal formation are analytically described. Sparse decomposition in Fourier basis to solve the SAR image reconstruction problem is discussed. In contrast to the classical one-dimensional definition of l₁-norm minimization in SAR image reconstruction, applied to an image vector, the present work proposes a two-dimensional definition of l₁-norm minimization to the image. To verify the correctness of the algorithm, results of numerical experiments are presented.