Tomographic SAR Optimization by The Newton Iteration Algorithm Regularization - The Second Order Cone Programming Solution

In SAR tomography is often necessary to design tomographic acquisition geometries with the fewest number of repeated radar tracks. In all the cases where the data-set is corrupted, to adequately compensate the bad consequences due by an eventually under-sampled configuration, it is therefore necessary to process the observations with advanced Digital Signal Processing (DSP) that can be adapted for any physical environment, characterized to have inside coherent and non-coherent targets. In order to process forest by the SAR Tomography technique, in the above described configuration, is so necessary to implement algorithms that well works on point and distributed targets. Various Compressed Sensing (CS) DSP techniques that base their principal computational core on the sparse-set data condition, in most of the cases are unable to correctly process tomographic solutions if inputs consists of continuous environmental observations. This because in most of the cases inputs exists in a low sparse configuration. These algorithms are excellent methods for processing environments constituted by isolated point targets. This paper considers the Convex Optimization (CVX) tomographic solution in order to process multi-baseline data-sets with forested environments, in a Fourier under-sampled configuration. The DSP based on the CVX Second Order Cone Programming (SOCPs) has been tested by interior-point methods (IPM) defining a generic log-barrier algorithm, through a successfully computational bottleneck Newton calculation, searching general smooth problem solutions. This technique is validated on point, distributed targets and on real forested environments making a critical analysis of the vertical resolution and the radiometric accuracy for each classical Fourier, and SOCP DSP techniques.