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

Scattering the geometry of weighted graphs

Given two weighted graphs $(X,b_k,m_k)$, $k=1,2$ with $b_1\sim b_2$ and $m_1\sim m_2$, we prove a weighted $L^1$-criterion for the existence and completeness of the wave operators $W_{\pm}(H_{2},H_1, I_{1,2})$, where $H_k$ denotes the natural Laplacian in $\ell^2(X,m_k)$ w.r.t. $(X,b_k,m_k)$ and $I_{1,2}$ the trivial identification of $\ell^2(X,m_1)$ with $\ell^2(X,m_2)$. In particular, this entails a very general criterion for the absolutely continuous spectra of $H_1$ and $H_2$ to be equal

q-parabolicity of stratified pseudomanifolds and other singular spaces

The main result of this paper is a sufficient condition in order to have a compact Thom-Mather stratified pseudomanifold endowed with a $\hat{c}$-iterated edge metric on its regular part $q$-parabolic. Moreover, besides stratified pseudomanifolds, the $q$-parabolicity of other classes of singular spaces, such as compact complex Hermitian spaces, is investigated.Comment: 21 pages; Version 3: Several new results have been added, and everything has been specialized to the Riemannian setting. To appear in the Annals of Global Analysis and Geometr

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