Interpolation Methods for SAR Backprojection at THz Frequencies

Abstract

The paper proposes the extensions of the available linear and cubic interpolation methods for backprojecting complex SAR data into an image plane. Due to the fact that the phase of complex SAR data is very sensitive to the shift in time, the proposed interpolations include the phase control of the interpolated complex values. The proposed methods are examined with the global backprojection algorithm that is used to process SAR data at THz frequencies. In numerical examples, a two-dimensional indoor THz SAR imaging for a point target is considered, where the developed interpolation methods are compared with the nearest neighbor approach.Index Terms-Complex-valued data interpolation, THz SAR, GBP.

Interpolation Methods with Phase Control for Backprojection of Complex-Valued SAR Data

“…Here, the interpolation kernel is represented by normalized sinc functions and T s is the sampling time. However, since the sinc function is infinite, it is difficult to implement an ideal reconstruction of a sampled signal via (24). Furthermore, the problem becomes even more complicated, when signal is complex-valued and phase control under reconstruction procedure is required.…”

“…Assume that the range time τ p defined in (4) satisfies the condition τ 0 < τ p < τ 1 , which is similar to the case for linear and cubic interpolations. To implement the reconstruction procedure, the normalized sinc kernel presented in (24) can be truncated up to a finite number of sinc functions 2L + 1, where L is a nonnegative integer, i.e., L ∈ Z and L ≥ 0. The functions are equally translated in both directions from the interpolation point and normalized with the sampling time T s to reach zero value at known range-time samples τ i .…”

“…In this paper, we introduce the extended versions of linear, cubic, and sinc interpolation algorithms that, in comparison with the interpolators described in [21][22][23], include the phase control procedure. The initial results on the phase control of complex SAR data under linear and cubic interpolation have been partially reported in [24]. The idea of the proposed control procedure is naturally related to the complex SAR data processing.…”

Phase Control in Interpolation for Backprojection of THz FMCW SAR Signals

“…3) The sinc interpolation with the phase control procedure is developed to interpolate complex-valued FMCW SAR data, so that it is ensured that information about the range distance between the SAR platform and the given point of space in the defned image plane is assigned into the phase of the interpolated complex-valued SAR data parameter. The extended sinc interpolator is based on the approach introduced for pulse radars in [18] and mathematically can be expressed as (13) where…”

“…The truncated sinc interpolator can be equipped with the Hanning window to improve coherency in SAR interferometry [17]. Recently, extended versions of linear and cubic interpolators with a phase control procedure that assigns information about the range distance between the SAR platform and the given point in space into the phase of interpolated complex-valued parameters have been introduced in [18] to process complexvalued SAR data for pulse radars. The results demonstrate that the proposed procedure provides an opportunity to obtain accurate imaging results with linear and cubic interpolators at the sampling rate f s = 2f max .…”