Hyper-parameter selection in non-quadratic regularization-based radar image formation

We consider the problem of automatic parameter selection in regularization-based radar image formation techniques. It has previously been shown that non-quadratic regularization produces feature-enhanced radar images; can yield superresolution; is robust to uncertain or limited data; and can generate enhanced images in non-conventional data collection scenarios such as sparse aperture imaging. However, this regularized imaging framework involves some hyper-parameters, whose choice is crucial because that directly affects the characteristics of the reconstruction. Hence there is interest in developing methods for automatic parameter choice. We investigate Stein’s unbiased risk estimator (SURE) and generalized cross-validation (GCV) for automatic selection of hyper-parameters in regularized radar imaging. We present experimental results based on the Air Force Research Laboratory (AFRL) “Backhoe Data Dome,” to demonstrate and discuss the effectiveness of these methods

Multiplicative matrix-valued functionals and the continuity properties of semigroups correspondings to partial differential operators with matrix-valued coefficients

We define and examine certain matrix-valued multiplicative functionals with local Kato potential terms and use probabilistic techniques to prove that the semigroups of the corresponding partial differential operators with matrix-valued coefficients are spatially continuous and have a jointly continuous integral kernel. These partial differential operators include Yang-Mills type Hamiltonians and Pauli type Hamiltonians, with "electrical" potentials that are elements of the matrix-valued local Kato class.Comment: 26 pages; will appear in a slightly different form in the Journal of Mathematical Analysis and Application

Parameter selection in sparsity-driven SAR imaging

We consider a recently developed sparsity-driven synthetic aperture radar (SAR) imaging approach which can produce superresolution, feature-enhanced images. However, this regularization-based approach requires the selection of a hyper-parameter in order to generate such high-quality images. In this paper we present a number of techniques for automatically selecting the hyper-parameter involved in this problem. In particular, we propose and develop numerical procedures for the use of Stein’s unbiased risk estimation, generalized cross-validation, and L-curve techniques for automatic parameter choice. We demonstrate and compare the effectiveness of these procedures through experiments based on both simple synthetic scenes, as well as electromagnetically simulated realistic data. Our results suggest that sparsity-driven SAR imaging coupled with the proposed automatic parameter choice procedures offers significant improvements over conventional SAR imaging