Sparsity based signal reconstruction and imaging methods

Sparsity based Compressive Sensing (CS) methods have gained high importance, since they have many application areas in real life. CS makes it possible to operate under Nyquist rate. CS techniques generally discretize the signal space and assume that the signal is sparse on the discretized grid. Due to continues nature of the signals, representing the signal on a discretized grid results in the off grid problem which causes performance degradation. Calibration performance is also another issue which can also cause performance degradation and thus must be addressed. Calibration aims to reduce the disruptive effects of the phase and the gain errors. In this thesis, novel Compressive Sensing based techniques are developed which are capable of the estimation of off grid signals and performing the calibration simultaneously. The thesis studies are firstly concentrated on developing sparsity based on joint imaging and autofocus techniques of Synthetic Aperture Radar (SAR) Spotlight mode. In SAR systems, the imaging of manmade scenes is a necessity. In addition, uncompensated platform motion errors cause performance degradation by defocusing the images. Discretizing the image space and assuming that the scene is sparse on the discretized grid is also another error source which results in the off grid problem. A novel Compressive Sensing based spotlight SAR imaging method is developed which is capable of simultaneously handling the off grid problem and phase errors due to uncompensated platform motion effects. The method solves the target reflectivities, platform induced phase errors and the off-grid target location perturbations iteratively. The technique allows reduced number of measurements and results in sparse SAR images. The results obtained by using both simulated and real SAR system data show that the proposed technique provides better SAR images. Sparsity based SAR image reconstruction and autofocus techniques usually require a predefined parameter and their performance are dependent on the accurate choice of the parameter. The parameter value itself is dependent on the actual scene which is to be estimated. So, there is a need for an automatic stopping criterion. In the thesis studies, a parameter free SAR image reconstruction and autofocus technique is developed. It uses a automatic stopping criterion which is based on cross validation. A sparsity based off grid blind sensor calibration method is also developed. This method performs the off grid signal reconstruction and calibration iteratively. For blind sensor calibration, the off grid signals are estimated first using multiple measurement sets. Then, using the reconstructed signals, the phase and the gain errors are estimated and calibrated. Lastly, this method is adopted to Group Sparsity and direction finding for the off grid signals. This method is capable of jointly off grid direction estimation and correction of the sensor phase and gain errors. By simulations studies using the synthetically generated data, it is shown that developed techniques can estimate jointly the off grid signals and perform blind calibration with high performance.