SAR tomography optimization by Interior Point Methods via atomic decomposition — The Convex Optimization approach

In the Multi-Baseline SAR tomography remote sensing technique, the tomographic resolution is proportional to the vertical aperture component of the synthetic antenna. In order to avoid the problem of obtaining aliased tomographic results when designing multi-baseline SAR acquisition geometries using the fewest number of repeated radar tracks, it is necessary to process the data-set by advanced signal processing techniques that can properly process coherent and distributed composed environments SAR data. In this paper the Digital Gabor Transform (DGT) decomposition for sparsity seeking and the Compressed Sensing (CS) for signal recovery techniques performance will be analyzed. Recovery in highly over-complete dictionaries leads to large-scale optimization problems that can be successfully reached specially because of recent advances in linear and quadratic programming by Interior Point Methods (IPM). This paper considers the Convex Optimization (CVX) tomographic solution in order to process multi-baseline datasets over forested environments, in a Fourier under-sampled configuration. In this situation, the vertical reflectivity function is in a smooth domain. The DGT is a suitable method in order to generate an over-complete dictionary for sparsity seeking. The CVX Second Order Cone Programming Solution (SOCPs) by IPM using a generic log-barrier algorithm has been tested in order to optimize the dictionary atoms. In particular the following recovery technique has been implemented: l1 norm minimization with quadratic constraints (L1QC). This technique has been validated over real forested areas pointing out the better performance of the proposed solution in such a particular environment.