A comparison of nonquadratic regularization implementations on the backhoe data set

A sparse-aperture imaging problem arises in synthetic aperture radar (SAR) when parts of the phase history data are corrupted or incomplete. The resulting images reconstructed from the sparse aperture SAR are degraded with elevated sidelobes. One effective method for enhancing these images has been nonquadratic regularization. Nonquadratic regularization employs a cost function which contains an image formation error term and a feature enhancement term. In the past, a quasi-Newton algorithm was applied to minimize the nonquadratic regularization cost function. Two alternatives employ the stochastic gradient method to minimize the nonquadratic regularization cost function. In this paper, these three algorithms based on the nonquadratic regularization cost function are applied to corrupted phase history data and evaluated based on output image quality and time required for image generation and enhancement. The phase history data will be from the Xpatch simulated backhoe data set.