A mathematical perspective on radar interferometry

Abstract

<p style='text-indent:20px;'>Radar interferometry is an advanced remote sensing technology that utilizes complex phases of two or more radar images of the same target taken at slightly different imaging conditions and/or different times. Its goal is to derive additional information about the target, such as elevation. While this kind of task requires centimeter-level accuracy, the interaction of radar signals with the target, as well as the lack of precision in antenna position and other disturbances, generate ambiguities in the image phase that are orders of magnitude larger than the effect of interest.</p><p style='text-indent:20px;'>Yet the common exposition of radar interferometry in the literature often skips such topics. This may lead to unrealistic requirements for the accuracy of determining the parameters of imaging geometry, unachievable precision of image co-registration, etc. To address these deficiencies, in the current work we analyze the problem of interferometric height reconstruction and provide a careful and detailed account of all the assumptions and requirements to the imaging geometry and data processing needed for a successful extraction of height information from the radar data. We employ two most popular scattering models for radar targets: an isolated point scatterer and delta-correlated extended scatterer, and highlight the similarities and differences between them.</p>

Vertical autofocus for the phase screen in a turbulent ionosphere

“…Finally, we note that in SAR interferometry [31][32][33]38], some averaging of the interferometric data is usually required. The latter is justified by a certain statistical model of the target.…”

“…It is shown that the effect of the perturbations can be evaluated in terms of the variance and expectation of the CINT image: Accordingly, we require l ≫ 1 (recall that the azimuthal resolution ∆ A is chosen as the nondimensionalization unit in ( 9) and ( 10)). As (31) requires l/ℓ ≲ 1, we obtain the following double inequality:…”

“…Since we intend to preserve the main characteristics of the CINT approach, we always take l ≲ ℓ, see (31). Then, similar to (19), we can use…”

“…The reconstruction of ionospheric parameters may also exploit the difference between two distortions of the signal phase for a pair of SAR images that realize the scenario of radar interferometry [31]. There are, in fact, different kinds of radar interferometry.…”

Denoising Convolution Algorithms and Applications to SAR Signal Processing

“…Note that lower values of ∆ x correspond to better resolution because SAR can tell between the targets located closer to one another. It can also be shown that as ∆ x → 0 the GAF given by (3.1) converges to the δ-function in the sense of distributions [7,Section 3.3]. In this case, the image, which is a convolution of the ground reflectivity with the GAF, coincides with ground reflectivity.…”