This paper develops the theory for waveform-diverse moving-target synthetic-aperture radar. We assume that
the targets are moving linearly, but we allow an arbitrary flight path and (almost) arbitrary waveforms. We
consider the monostatic case, in which a single antenna phase center is used for both transmitting and receiving.
This work addresses the use of waveforms whose duration is sufficiently long that the targets and/or platform
move appreciably while the data is being collected.
In synthetic aperture radar (SAR) imaging, a scene of interest is illuminated by electromagnetic waves. The aim
is to reconstruct an image of the scene from the measurement of the scattered waves using airborne antenna(s).
There are many imaging systems which are built upon this notion such as mono-static SAR, bi-static SAR, and
hitchhiker SAR. For these modalities, there are analytic reconstruction algorithms based on backprojection.
Backprojection-based algorithms have the advantage of putting the visible edges of the scene at the right location
and orientation in the reconstructed images.
On the other hand, there is also a SAR imaging method based on the generalized likelihood-ratio test (GLRT).
In particular we consider the problem of detecting a target at an unknown location. In the GLRT, the presence
of a target in the scene is determined based on the likelihood-ratio test. Since the location of the target is not
known, the GLRT test statistic is calculated for each position in the scene and the location corresponding to the
maximum test statistic indicates the location of a potential target.
In this paper, we show that the backprojection-based analytic reconstruction methods include as a special
case the GLRT method. We show that the GLRT test statistic is related to the reflectivity of the scene when a
backprojection-based reconstruction algorithm is used.
We present a new image reconstruction method for distributed apertures operating in complex environments
with additive non-stationary noise. Our method is capable of exploiting information that we might have about:
multipath scattering in the environment; statistics of the objects to be imaged; statistics of the additive non-stationary
noise. The aperture elements are distributed spatially in an arbitrary fashion, and can be several
hundred wavelengths apart. Furthermore, our method facilitates multiple transmit apertures which operate
simultaneously, and is thus capable of handling a true multi-transmit-multi-receive scenario. We derive a set
of basis functions which is adapted to the given operating environment and sensor distribution. By selecting
an appropriate subset of these basis functions we obtain a sub-space reconstruction which is optimal in the
sense of obtaining the minimum-mean-square-error for the reconstructed image. Furthermore, as this subspace
determines which details will be visible in the reconstructed image, it provides a tool for evaluating the sensor
locations against the objects that we would like to see in the image. The implementation of our reconstruction
takes the form of a filter bank which is applied to the pulse-echo measurements. This processing can be performed
independently on the measurements obtained from each receiving element. Our approach is therefore well suited
for parallel implementation, and can be performed in a distributed manner in order to reduce the required
communication bandwidth between each receiver and the location where the results are merged into the final
image. We present numerical simulations which illustrate capabilities of our method.
We develop a linearized imaging theory that combines the spatial, temporal, and spectral aspects of scattered
waves. We consider the case of fixed sensors and a general distribution of objects, each undergoing linear
motion; thus the theory deals with imaging distributions in phase space. We derive a model for the data that is
appropriate for any waveform, and show how it specializes to familiar results when the targets are far from the
antennas and narrowband waveforms are used.
We develop a phase-space imaging formula that can be interpreted in terms of filtered backprojection or
matched filtering. For this imaging approach, we derive the corresponding point-spread function. We show
that special cases of the theory reduce to: a) Range-Doppler imaging, b) Inverse Synthetic Aperture Radar
(isar), c) Spotlight Synthetic Aperture Radar (sar), d) Diffraction Tomography, and e) Tomography of Moving
Targets. We also show that the theory gives a new SAR imaging algorithm for waveforms with arbitrary ridge-like
We present a new receiver design for spatially distributed
apertures to detect targets in an urban environment.
A distorted-wave Born approximation is used to model the scattering
environment. We formulate the received signals at different
receive antennas in terms of the received signal at the first
antenna. The detection problem is then formulated as a binary
hypothesis test. The receiver is chosen as the optimal linear filter
that maximizes the signal-to-noise ratio (SNR) of the
corresponding test statistic. The receiver operation amounts to
correlating a transformed version of the measurement at the first
antenna with the rest of the measurements. In the
free-space case the transformation applied to the measurement from the
antenna reduces to a delay operator. We evaluate the performance of
the receiver on a real data set collected in a multipath- and
clutter-rich urban environment and on simulated data corresponding to a simple
multipath scene. Both the experimental and simulation results show that
the proposed receiver design offers significant improvement in
detection performance compared to conventional matched
The idea of <i>preconditioning</i> transmit waveforms for optimal clutter rejection in radar imaging is presented.
Waveform preconditioning involves determining a map on the space of transmit waveforms, and then applying this
map to the waveforms before transmission. The work applies to systems with an arbitrary number of transmitand
receive-antenna elements, and makes no assumptions about the elements being co-located. Waveform
preconditioning for clutter rejection achieves efficient use of power and computational resources by distributing
power properly over a frequency band and by eliminating clutter filtering in receive processing.
Reconstruction algorithms for monostatic synthetic aperture radar (SAR) with poor antenna directivity
traversing straight and arbitrary flight trajectories have been developed by various authors<sup>1-5</sup>, while, to
our knowledge, the acquisition geometry of bistatic SAR studies for the case of poor antenna directivity
are limited to isotropic antennas traversing certain flight trajectories (straight<sup>6,7</sup> or circular<sup>8,9</sup> flight
trajectories) over flat topography.
In this paper, we present an approximate analytic inversion method for bistatic SAR (Bi-SAR).<sup>10</sup> In
particular, we present a new filtered-backprojection (FBP) type Bi-SAR inversion method for arbitrary,
but known, flight trajectories over non-flat, but known, topography. These FBP type reconstruction
methods have the advantage that they produce images that have the edges of the scene at the correct
location, orientation and strength. We demonstrate the performance of the new method via numerical
A <i>hitchhiker</i> is a passive radar receiver that relies on sources of opportunity to perform radar tasks.<sup>1-4</sup> In this paper, we consider a synthetic-aperture radar (SAR) system with static non-cooperative transmitters
and mobile receivers traversing arbitrary trajectories and present an analytic image formation
method. Due to its combined synthetic aperture and hitchhiking structure, we refer to the system
under consideration as <i>synthetic aperture hitchhiker </i>(SAH). Our approach is applicable to cooperative
and/or non-cooperative and static and/or mobile sources of opportunity.
Conventional SAR processing involves correlation of the received signal from a receiver with the
transmitted waveform as a first step of the image formation. For passive SAR, however, the transmitted
waveform is not necessarily known. Instead, we use spatio-temporal correlation of received signals.
Given a pair of receivers, the spatio-temporal correlation method compares the received signals to
identify a target within the illuminated scene. We combine this with microlocal techniques to develop
a filtered backprojection (FBP) type inversion method for passive SAR<sup>5</sup>. Combined correlation-FBP inversion method does not require the knowledge of the transmitter locations.
Furthermore, FBP inversion has the advantage of computational efficiency and image formation
under non-ideal conditions, such as arbitrary flight trajectories and non-flat topography.
This paper describes work that considered two Joint Time-Frequency
Transforms (JTFTs) for use in a SAR-based (single sensor/platform
Synthetic Aperture Radar) 3D imaging approach. The role of the
JTFT is to distinguish moving point scatterers that may become
collocated during the observation interval. A Frequency Domain
Velocity Filter Bank (FDVFB) was compared against the well-known
Short Time Fourier Transform (STFT) in terms of their maximal
Time-Frequency energy concentrations. The FDVFB and STFT energy
concentrations were compared for a variety of radar scenarios. In
all cases the STFT achieved slightly higher energy concentrations
while simultaneously requiring half the computations needed by the
This paper describes the development of an algorithm for detecting
multiple-scattering events in the 3D Geometric Theory of
Diffraction (GTD)-based Jackson-Moses scattering model. This
approach combines microlocal analysis techniques with
geometric-invariant theory to estimate multiple-scattering events.
After multiple-scattering returns were estimated, the algorithm
employed the Generalized Radon Transform to determine the
existence of multiple scattering within the measured data. The
algorithm was tested on an X-band simulation of isotropic point
scatterers undergoing unknown rotational motion.
We consider the problem of
imaging in a region where ultrasonic waves are multiply scattered.
A transducer emits ultrasonic pulses in tissue where they scatter
from a heterogeneity (e.g. a tumor) in the region of interest
(ROI). The reflected signals are recorded and used to produce an
image of tissue. Many of the conventional imaging methods assume
the wave has scattered just once (Born-approximation) from the
heterogeneity before returning to the sensor to be recorded. In
reality, waves can scatter several times before returning to the
detector. The purpose of this paper is to show how this
restriction (the Born approximation or weak, single-scattering
approximation) can be partially removed by incorporating a-priori
known environmental scatterers, such as a cavity wall or bones
into the background velocity model in the context of acoustic
medical imaging. We also show how the partial removal of the Born
approximation assumption leads to an enhanced angular resolution
of heterogeneities that are present. We will illustrate our method
using a locally planar scatterer, which is one of the simplest
possible environments for the scatterer.
We show how to apply the techniques of microlocal analysis to the Potter-Moses attributed scattering center model, which is based on the
Geometrical Theory of Diffraction (GTD). The microlocal methods enable us to determine how scattering centers will appear in the radar data. We show also how to extend the model to some multiple-scattering events, and we apply the microlocal techniques to the extended model.
This paper develops a method for making an image of an object when there are extra point-like scatterers in the environment. Once the location of these scatterers is known, they can be exploited in the imaging process.
Here the extra point scatterers are assumed to lie between the sensor and the object of interest. A single-scattering model is used for the object itself. Detailed analysis is carried out for the case of a single extra scatterer in the foreground; the extension to the case of many scatterers is expected to be similar.
Conventional Synthetic Aperture Radar combines high range resolution waveforms collected from disparate directions/locations to form an image in range and cross-range. If the radar bandwidth is narrow, then range resolution will suffer and the overall image will be degraded. (This necessarily happens when the radar's carrier frequency is small, for instance.) There is, however, a complementary imaging mode in which very narrow frequency-domain pulses are collected by a platform in relative motion with the target and combined to form an image. Such systems rely on Doppler frequency shift measurements (instead of range information). For various practical reasons, this kind of imaging has not been well examined, but there are situations where the scheme is useful (in principle).
We develop the theory of radar imaging from data measured by a moving antenna emitting a single-frequency waveform. We show that, under a linearized (Born) scattering model, the signal at a given Doppler shift is due to a superposition of returns from stationary scatterers on a cone whose axis is the flight velocity vector. This cone reduces to a hyperbola when the scatterers are known to lie on a planar surface. In this case, reconstruction of the scatterer locations can be accomplished by a tomographic inversion in which the scattering density function is reconstructed from its integrals over hyperbolas. We give an approximate reconstruction formula and analyze the resolution of the resulting image. We provide a numerical shortcut and show results of numerical tests in a simple case.
This paper develops a method for forming a synthetic-aperture image of a flat surface seen through a homogeneous layer of a material that is dispersive, i.e., its wave speed varies with frequency.
We outline first a simplified scalar model for electromagnetic wave propagation in a dispersive medium; the resulting equation could also be used for acoustics. We show that the backscattered signal can be viewed as a Fourier integral operator applied to the ground reflectivity funciton. The reconstruction method, which is based on backprojection, can be used for arbitrary sensor paths and corrects for the radiated beam pattern, the source waveform, and geometrical spreading factors. The method correctly reconstructs the singularities (such as edges) that are visible from the sensor.
We consider the problem of identification of airborne objects from high-range-resolution radar data. We use high-frequency asymptotics to show that certain features of the object-correspond to identifiable features of the radar data. We study the cases of single scattering and scattering from re-entrant structures such as ducts. This work suggests a method for target identification that circumvents the need to create an intermediate radar image from which the object's characteristics are to be extracted. As such, this scheme may be applicable to efficient machine-based radar identification programs.
In order to improve our ability to use electromagnetic fields to diagnose and treat disease, it would be helpful to know the electric conductivity in the interior of the body. In order to obtain this information, our group of Rensselaer has built devices, which we call Adaptive Current Tomograph (ACT) systems, that apply small currents to the body through electrodes stuck to the skin. The ACT systems measure the induced voltages, and send all the current and voltage information to the computer, which uses an algorithm to process the data and reconstruct approximate images of the conductivity and permittivity in the interior.
Diagnosis and treatment of some disease states of the heart can be facilitated with knowledge of the electrical activity and resistivity properties within the heart muscle. A method of obtaining such information is through the use of electrical impedance tomography. Impedance imaging systems apply current patterns to the exterior of an object, measure the resulting voltages, and from these measurements construct an approximation to the spatially varying resistivity of the interior. By placing electrodes on the exterior of the heart or thorax as well as inside one of the heart chambers, using a catheter or by other means, it may be possible to construct images which reflect the resistivity distribution of the heart wall. In this work, we consider a simple model of the heart and thorax where electrodes are situated on both the interior and exterior boundaries of an annulus. The optimal current patterns to be applied are determined for the case of a homogeneous resistivity distribution and for the case of a single inhomogeneous layer. The question of the measurement precision required to distinguish between a homogeneous resistivity distribution and an inhomogeneous resistivity distribution is also discussed.
Electrical impedance imaging systems1,2,3 make electrical measurements on the surface S of a body B, and from these measurements reconstruct an approximation to the electrical properties of the interior. Mathematically, the problem can be formulated as follows. The electric potential u satisfies the equations