A theoretical framework for problems requiring robust behavior

This paper develops a generalized Cauchy density (GCD) based theoretical approach that allows the formulation of challenging problems in a robust fashion. The proposed framework subsumes the generalized Gaussian distribution (GGD) family based developments, thereby guaranteeing performance improvements over traditional problem formulation techniques. This robust framework can be adapted to a variety of applications in signal processing. We formulate two particular applications under this framework in this paper: (1) Robust reconstruction methods for compressed sensing and (2) robust estimation in sensor networks with noisy channels.