Constraint construction in convex set theoretic signal recovery via Stein´s principle [image denoising example]

Convex set theoretic estimation methods have been shown to be effective in numerous signal recovery problems due to their ability to incorporate a wide range of deterministic and probabilistic information in the form of constraints on the solution. To date, probabilistic information has been used exclusively to constrain statistics of the estimation residual to be consistent with known properties of the noise. In this paper, we propose a new technique to construct constraint sets from probabilistic information based on Stein´s identity. In this framework, probabilistic attributes of the signal to be recovered are estimated from the data. The proposed approach is applicable to signal formation models involving additive Gaussian noise and it leads to geometrically simple sets that can easily be handled via projection methods. An application to image denoising is demonstrated.