We consider passive airborne receivers that use backscattered signals from sources of opportunity transmitting
fixed-frequency waveforms, which we refer to as Doppler Synthetic Aperture Hitchhiker (DSAH). We present a
novel image formation method for DSAH. Our method first correlates the windowed signal obtained from one
receiver with the windowed, filtered, scaled and translated version of the received signal from another receiver,
and then uses the microlocal analysis to reconstruct the scene radiance by the weighted-backprojection of the
correlated signal. This imaging algorithm can put the visible edges of the scene radiance at the correct location,
and under appropriate conditions, with correct strength. We show that the resolution of the image is directly
related to the length of the support of the windowing function and the frequency of the transmitted waveform.
We present numerical experiments to demonstrate the performance of the proposed method.
The Chirp-Scaling Algorithm (CSA) is one of the most widely used synthetic aperture radar (SAR) image
reconstruction method. However, its applicability is limited to straight flight trajectories and monostatic SAR.
We present a new mathematical treatment of the CSA from the perspective of Fourier Integral Operators theory.
Our treatment leads to a chirp-scaling-based true amplitude imaging algorithm, which places the visible edges of
the scene at the correct locations and directions with the correct strength. Furthermore, it provides a framework
for the extension of the chirp-scaling based approach to non-ideal imaging scenarios as well as other SAR imaging
modalities such as bistatic-SAR and hitchhiker-SAR.
We consider a bistatic synthetic aperture radar (BiSAR) system operating in non-ideal imaging conditions with
receive and transmit antennas traversing arbitrary flight trajectories over a non-flat topography; transmitting
arbitrary waveforms along flight trajectories etc. In1 we developed a generalized filtered-backprojection (GFBP)
method for BiSAR image formation applicable to such non-ideal imaging scenarios. The method puts edges not
only at the right location and orientation, but also at the right strength resulting in true amplitude images. The
main computational complexity of the GFBP method comes from the spatially dependent filtering step. In this
work, we present an alternative, novel FBP method applicable to non-ideal imaging scenarios resulting in true
amplitude images. The method involves ramp filtering in data domain and image domain scaling. Additionally,
the method results in fast, computationally efficient implementation than that of GFBP methods.
We present an analytic, filtered-backprojection (FBP) type inversion method for bistatic synthetic aperture
radar (BISAR) when the measurements have been corrupted by noise and clutter. The inversion method uses
microlocal analysis in a statistical setting to design a backprojection filter that reduces the impact of noise and
clutter while preserving the fidelity of the target image. We assume an isotropic single scattering model for the
electromagnetic radiation that illuminates the scene of interest. We assume a priori statistical information on
the target, clutter and noise. We demonstrate the performance of the algorithm and its ability to better resolve
targets through numerical simulations.
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
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.
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
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 presents an alternative formulation for the cone-beam projections given an arbitrary source trajectory and detector orientation. This formulation leads to a new inversion formula. As a special case, the inversion formula for the spiral source trajectory is derived.
This paper presents a new method for exponential Radon transform inversion based on the harmonic analysis of the Euclidean motion group of the plane. The proposed inversion method is based on the observation that the exponential Radon transform can be modified to obtain a new transform, defined as the modified exponential Radon transform, that can be expressed as a convolution on the Euclidean motion group. The convolution representation of the modified exponential Radon transform is block diagonalized in the Euclidean motion group Fourier domain. Further analysis of the block diagonal representation provides a class of relationships between the spherical harmonic decompositions of the Fourier transforms of the function and its exponential Radon trans-form. The block diagonal representation provides a method to simultaneously compute all these relationships. The proposed algorithm is implemented using the fast implementation of the Euclidean motion group Fourier transform and its performances is demonstrated in numerical simulations.
The problem of Radon transform inversion arises in field as diverse as medical imaging, synthetic aperture radar, and radio astronomy. In this paper, we model the Radon transform as a convolution integral over the Euclidean motion group and provide a novel deconvolution method for its inversion. The deconvolution method presesnted here is a special case of the Wiener filtering framework in abstract harmonic analysis that was recently developed by the author. The proposed deconvolution method provides a fundamentally new statistical formulation for the inversion of the Radon transform that can operate in nonstationary noise and signal fields. It can be utilized for radiation treatment planning, inverse source problems, and 3D and 4D computed tomography. Furthermore it is directly applicable to many computer vision and pattern recognition problems, as well as to problems in robotics and polymer science. Here, we present an algorithm for the discrete implementation of the Wiener filter and provide a comparison of the proposed image reconstruction method with the filtered back projection algorithms.