Estimating first order finite-difference information in image restoration problems

First-order finite-difference information has been exploited in a variety of image and signal restoration settings. These approaches typically require - implicitly or explicitly - that certain attributes of the finite-difference images be known a priori. We propose a new statistical framework in which such attributes are estimated a posteriori from the observed data under the assumption that the noise is additive and Gaussian. Our analysis can be directly applied to the construction of property sets in set theoretic estimation methods. The proposed framework is illustrated through an application to image denoising.