Sensor Arrangement in Through-the Wall Radar Imaging

Abstract

In this paper, the problem of how to spatially sample the scattered field in microwave through-the wall imaging is addressed. To this end, a two-dimensional scalar configuration for a three-layered back-ground medium is considered under a linearized scattering model. The aim is to collect as low as possible measurements by maintaining the same performance in the reconstructions. Accordingly, the number and the positions of the spatial measurement points are determined so that the point-spread function of the resulting semi-discrete problem approximates well the one of the ideal continuous case (i.e., when data space is not sampled at all). It is shown that the resulting measurement spatial positions must be non-uniformly arranged across the measurement domain and their number is generally much lower than the one returned by some literature sampling criteria. Also, the measurement points can be analytically determined by taking into account the geometrical parameters as well as the wall features. Numerical examples are included to check the theoretical arguments.

An Insight into the Warping Spatial Sampling Method in Subsurface Radar Imaging and Its Experimental Validation

“…In [37,39,40], some numerical examples are provided that show how the warping sampling method reduces the number of data without affecting the reconstruction performance. However, each theoretical approach must pass experimental verification to prove its effectiveness.…”

An Insight into the Warping Spatial Sampling Method in Subsurface Radar Imaging and Its Experimental Validation

“…In [37,39,40], some numerical examples are provided that show how the warping sampling method reduces the number of data without affecting the reconstruction performance. However, each theoretical approach must pass experimental verification to prove its effectiveness.…”

ACCOR: Attention-Enhanced Complex-Valued Contrastive Learning for Occluded Object Classification Using mmWave Radar IQ Signals

“…This is mainly due to the lack of publicly available datasets with complex-valued radar IQ signals, as opposed to their pre-processed counterparts, even though these pre-processing steps commonly remove information for a better visualization of the signal. Furthermore, the penetration ability of mmWave radar applies not only to rain and fog but also to light materials such as cardboard or thin drywall [15], [29], [30]. Due to its popularity surge, mmWave radar also arrived as very helpful perception assistance in robotics and automation, as extensive surveyed in [31].…”

Transverse Resolution in Through-the-Wall Radar Imaging

“…Equation (1) in operator notation is written as The function v(x) ¼ (e s (x) À e 0 )/e 0 is the so-called contrast function, with e s being the dielectric permittivity of the unknown scatterer, representing the unknown solution of the problem. The function G 2 (x o , x,) is the square of G(x o , x,), that is, the Green function accounting for a three-layered background medium whose spectral representation is reported in [2]. If it is assumed that L. k 0 n and z À L À z o .…”

“…where cðxÞ ¼ ½/ðÀX 0 ; xÞ þ /ðX 0 ; xÞ and gðxÞ ¼ ½/ ðÀX 0 ; xÞ À /ðX 0 ; xÞ To make explicit the dependence of g(x) in terms of x, we need to determine the two refraction points x m1 and x m2 by solving (4). This issue can be simplified by exploiting an equivalent two-layered model (see [2]). This allows one to reexpress the phase term in (3) as…”

An Insight into the Warping Spatial Sampling Method in Subsurface Radar Imaging and Its Experimental Validation

“…In [37,39,40], some numerical examples are provided that show how the warping sampling method reduces the number of data without affecting the reconstruction performance. However, each theoretical approach must pass experimental verification to prove its effectiveness.…”

ACCOR: Attention-Enhanced Complex-Valued Contrastive Learning for Occluded Object Classification Using mmWave Radar IQ Signals

“…This is mainly due to the lack of publicly available datasets with complex-valued radar IQ signals, as opposed to their pre-processed counterparts, even though these pre-processing steps commonly remove information for a better visualization of the signal. Furthermore, the penetration ability of mmWave radar applies not only to rain and fog but also to light materials such as cardboard or thin drywall [15], [29], [30]. Due to its popularity surge, mmWave radar also arrived as very helpful perception assistance in robotics and automation, as extensive surveyed in [31].…”

Transverse Resolution in Through-the-Wall Radar Imaging

“…Equation (1) in operator notation is written as The function v(x) ¼ (e s (x) À e 0 )/e 0 is the so-called contrast function, with e s being the dielectric permittivity of the unknown scatterer, representing the unknown solution of the problem. The function G 2 (x o , x,) is the square of G(x o , x,), that is, the Green function accounting for a three-layered background medium whose spectral representation is reported in [2]. If it is assumed that L. k 0 n and z À L À z o .…”

“…where cðxÞ ¼ ½/ðÀX 0 ; xÞ þ /ðX 0 ; xÞ and gðxÞ ¼ ½/ ðÀX 0 ; xÞ À /ðX 0 ; xÞ To make explicit the dependence of g(x) in terms of x, we need to determine the two refraction points x m1 and x m2 by solving (4). This issue can be simplified by exploiting an equivalent two-layered model (see [2]). This allows one to reexpress the phase term in (3) as…”

An Insight into the Warping Spatial Sampling Method in Subsurface Radar Imaging and Its Experimental Validation

“…In [37,39,40], some numerical examples are provided that show how the warping sampling method reduces the number of data without affecting the reconstruction performance. However, each theoretical approach must pass experimental verification to prove its effectiveness.…”

ACCOR: Attention-Enhanced Complex-Valued Contrastive Learning for Occluded Object Classification Using mmWave Radar IQ Signals

“…This is mainly due to the lack of publicly available datasets with complex-valued radar IQ signals, as opposed to their pre-processed counterparts, even though these pre-processing steps commonly remove information for a better visualization of the signal. Furthermore, the penetration ability of mmWave radar applies not only to rain and fog but also to light materials such as cardboard or thin drywall [15], [29], [30]. Due to its popularity surge, mmWave radar also arrived as very helpful perception assistance in robotics and automation, as extensive surveyed in [31].…”

Transverse Resolution in Through-the-Wall Radar Imaging

“…Equation (1) in operator notation is written as The function v(x) ¼ (e s (x) À e 0 )/e 0 is the so-called contrast function, with e s being the dielectric permittivity of the unknown scatterer, representing the unknown solution of the problem. The function G 2 (x o , x,) is the square of G(x o , x,), that is, the Green function accounting for a three-layered background medium whose spectral representation is reported in [2]. If it is assumed that L. k 0 n and z À L À z o .…”

“…where cðxÞ ¼ ½/ðÀX 0 ; xÞ þ /ðX 0 ; xÞ and gðxÞ ¼ ½/ ðÀX 0 ; xÞ À /ðX 0 ; xÞ To make explicit the dependence of g(x) in terms of x, we need to determine the two refraction points x m1 and x m2 by solving (4). This issue can be simplified by exploiting an equivalent two-layered model (see [2]). This allows one to reexpress the phase term in (3) as…”