Compressive Imaging of Subwavelength Structures II. Periodic Rough Surfaces

TL;DR

This paper introduces a compressed sensing approach for near-field imaging of periodic rough surfaces, enabling accurate surface profile recovery from sparse measurements even when traditional assumptions are invalid.

Contribution

It develops a novel compressed sensing scheme for subwavelength surface imaging that works under less restrictive conditions than previous methods.

Findings

Effective reconstruction of surface profiles from sparse measurements.

The scheme is robust even when the Rayleigh hypothesis does not hold.

Numerical results demonstrate high accuracy of the proposed method.

Abstract

A compressed sensing scheme for near-field imaging of corrugations of relative sparse Fourier components is proposed. The scheme employs random sparse measurement of near field to recover the angular spectrum of the scattered field. It is shown heuristically and numerically that under the Rayleigh hypothesis the angular spectrum is compressible and amenable to compressed sensing techniques. Iteration schemes are developed for recovering the surface profile from the angular spectrum. The proposed nonlinear least squares in the Fourier basis produces accurate reconstructions even when the Rayleigh hypothesis is known to be false.