Aggregated convex regularization and variational analysis technique for enhancement of mm waveband remote sensing imagery

The statistical Bayesian and descriptive regularization approaches for high resolution radar image formation is detailed in many works; here we refer to [1]–[3] where such approach is adapted to the sm and mm waveband remote sensing (RS) applications considered in this paper. An alternative approach to image enhancement and noise suppression was proposed and detailed in [4] where the variational analysis (VA) paradigm was employed to incorporate a priori information regarding the image geometrical properties specified by its gradient flow over the image frame, while no particular model of the imaging system was employed. In view of this, the VA paradigm may be classified as a system model-free image enhancement approach [1], [4]. Some second order partial differential equation (PDE) models for specifying the gradient flow over the image frame were employed in different VA approaches to incorporate the intrinsic image geometry properties into the enhancement procedures [4], [6], [7]. The crucial limitation of all VA-based methods lies in their descriptive system-model-free deterministic regularization nature because these methods do not employ statistical optimization strategies. In view of this, the following problem arises: how to aggregate the statistically optimal Bayesian minimum risk (BME) convex regularization method with the VA formalism for enhanced RS imaging that incorporate the advantages of both the VA and the statistical convex regularization (CR) approaches. In this paper, we address a novel aggregated VA and statistical CR fusion paradigm that leads to a new method addressed to as the fused convex regularization variational analysis (CRVA) technique. The VA paradigm is adapted via incorporating the imaging scene spatial spectrum pattern (SSP) gradient norm preservation [1] into the overall CR image reconstruction problem to control the geometrical properties of the desired solution.