ℓ2−ℓ1ℓ2−ℓ1 Structured descriptive experiment design regularization based enhancement of fractional SAR imagery

•A new framework for enhanced SAR imaging in harsh sensing environments is developed.•It aggregates the experiment design and the total variation regularization paradigms.•The method structures the l2 image and its l1 gradient metrics in the solution space.•Two regularization strategies for enhanced SAR imaging are l2–l1 optimally balanced.•The speeded-up convergence is attained via the projections onto convex solution sets.

Feature-enhanced reconstruction of the reflectivity maps (remotely sensed scene images) from the low-resolution fractional SAR imagery is treated for harsh sensing scenarios with uncertainties attributed to possible imperfect sensor calibration, atmospheric turbulence and uncontrolled carrier trajectory deviations. These effects lead to the randomly perturbed signal formation operator resulting in a partial coherence of the system. A low-resolution scene image formed using the conventional matched spatial filtering method serves as a starting point for the enhancement. We commence with the descriptive experiment design regularization (DEDR) approach for solving the image enhancement inverse problem based on the ℓ2ℓ2 -type squared error norm minimization strategy robust against the problem model uncertainties in the sense of the worst case statistical performance optimization. To exploit structural information on the desired image piecewise smoothness over the scene the ℓ1ℓ1 structured regularization level is incorporated via aggregating the image total variation (TV) minimization approach with DEDR. In the unified DEDR-TV framework, the image gradient magnitude map sparsity and the overall image texture anisotropy properties are structured by combining the ℓ2ℓ2 image metric with the ℓ1ℓ1 image gradient metric in the solution space. The incorporated projections onto convex solution sets guarantee the convergence and speed up the resulting implicit iterative enhancement scheme.