Can Evren Yarman

Bistatic Synthetic Aperture Radar Imaging for Arbitrary Flight Trajectories

This paper presents an approximate analytic inversion method for bistatic synthetic aperture radar. A scene of interest is illuminated by electromagnetic waves that are transmitted from positions along an arbitrary, but known, flight trajectory and the scattered waves are measured from positions along a different flight trajectory which is also arbitrary, but known. We assume a single-scattering model for the radar data, and we assume that the ground topography is known but not necessarily flat. We use microlocal analysis to develop a filtered-backprojection-type reconstruction method.

Synthetic-aperture inversion in the presence of noise and clutter

This paper presents an analytic method for synthetic-aperture inversion when the measurements are corrupted with noise and clutter. We use microlocal analysis in a statistical setting to develop filtered-backprojection-type reconstruction methods. The inversion method is applicable in non-ideal scenarios, such as those involving arbitrary source trajectories or variable antenna beam patterns. We show that the backprojection preserves the location and orientation of the singularities of the first- and second-order statistics of the target scene. We derive backprojection filters with respect to different statistical criteria. In particular, if we use a criterion based on first-order statistics, the resulting image can be interpreted as approximately unbiased. Alternatively, if we use a criterion based on second-order statistics to design the backprojection filter, such as a minimum-mean-square error criterion, the strength of the singularities due to noise and clutter is suppressed in the resulting image. Although we have developed our approach specifically for synthetic-aperture radar application, the method is also applicable to other inversion problems in which microlocal techniques are relevant, such as geophysics and x-ray tomography.

Synthetic Aperture Hitchhiker Imaging

We introduce a novel synthetic-aperture imaging method for radar systems that relies on sources of opportunity. We consider receivers that fly along arbitrary, but known, flight trajectories and develop a spatio-temporal correlation-based filtered-backprojection-type image reconstruction method. The method involves first correlating the measurements from two different receiver locations. This leads to a forward model where the radiance of the target scene is projected onto the intersection of certain hyperboloids with the surface topography. We next use microlocal techniques to develop a filtered-backprojection-type inversion method to recover the scene radiance. The method is applicable to both stationary and mobile, and cooperative and noncooperative sources of opportunity. Additionally, it is applicable to nonideal imaging scenarios such as those involving arbitrary flight trajectories, and has the desirable property of preserving the visible edges of the scene radiance. We present an analysis of the computational complexity of the image reconstruction method and demonstrate its performance in numerical simulations for single and multiple transmitters of opportunity.

Doppler synthetic aperture hitchhiker imaging

In this paper we consider passive airborne receivers that use backscattered signals from sources of opportunity transmitting single-frequency or ultra-narrowband waveforms. Because of its combined passive synthetic aperture and the single-frequency nature of the transmitted waveforms, we refer to the system under consideration 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. This processing removes the transmitter-related variables from the phase of the Fourier integral operator that maps the radiance of the scene to the correlated signal. Next, we use microlocal analysis to reconstruct the scene radiance by the weighted backprojection of the correlated signal. The image reconstruction method is applicable to both cooperative and non-cooperative sources of opportunity using one or more airborne receivers. It has the desirable property of preserving the visible edges of the scene radiance. Additionally, it is an analytic reconstruction technique that can be made computationally efficient. We present numerical simulations to demonstrate the performance of the image reconstruction method and to verify the theoretical results.

Multistatic Synthetic Aperture Radar Image Formation

In this paper, we consider a multistatic synthetic aperture radar (SAR) imaging scenario where a swarm of airborne antennas, some of which are transmitting, receiving or both, are traversing arbitrary flight trajectories and transmitting arbitrary waveforms without any form of multiplexing. The received signal at each receiving antenna may be interfered by the scattered signal due to multiple transmitters and additive thermal noise at the receiver. In this scenario, standard bistatic SAR image reconstruction algorithms result in artifacts in reconstructed images due to these interferences. In this paper, we use microlocal analysis in a statistical setting to develop a filtered-backprojection (FBP) type analytic image formation method that suppresses artifacts due to interference while preserving the location and orientation of edges of the scene in the reconstructed image. Our FBP-type algorithm exploits the second-order statistics of the target and noise to suppress the artifacts due to interference in a mean-square sense. We present numerical simulations to demonstrate the performance of our multistatic SAR image formation algorithm with the FBP-type bistatic SAR image reconstruction algorithm. While we mainly focus on radar applications, our image formation method is also applicable to other problems arising in fields such as acoustic, geophysical and medical imaging.

Doppler-Hitchhiker: A Novel Passive Synthetic Aperture Radar Using Ultranarrowband Sources of Opportunity

In this paper, we present a novel synthetic aperture radar imaging modality that uses ultranarrowband sources of opportunity and passive airborne receivers to form an image of the ground. Due to its combined passive synthetic aperture and high Doppler resolution of the transmitted waveforms, we refer to this modality as the Doppler Synthetic Aperture Hitchhiker or Doppler-hitchhiker for short. Our imaging method first correlates the windowed signal obtained from one receiver with the scaled and translated version of the received signal in another window from the same or another receiver. We show that this correlation processing removes the transmitter-related variables from the phase of the resulting operator that maps the radiance of the scene to the correlated signals. We define a concept of passive Doppler scale factor using the radial velocities of the receivers. Next, we show that the scaled, translated, and correlated signal is the projection of the scene radiance onto the contours that are formed by the intersection of the surfaces of constant passive Doppler scale factor and ground topography. We use microlocal analysis to design a generalized filtered-backprojection operator to reconstruct the scene radiance from its projections. Our analysis shows that the resolution of the reconstructed images improves with the increased time duration and center frequency of the transmitted ultranarrowband signals. Our reconstruction method is analytic and therefore can be made computationally efficient. Furthermore, it easily accommodates arbitrary flight trajectories, nonflat topography, and system-related parameters. We present numerical simulations to demonstrate the performance of our imaging method.

Uncertainty And Resolution Analysis For Anisotropic Tomography Using Iterative Eigendecomposition

Tomographic velocity model building has become an industry standard for depth migration. Anisotropy of the Earth challenges tomography because the inverse problem becomes severely ill-posed. Singular value decomposition (SVD) of tomographic operators or, similarly, eigendecomposition of the corresponding normal equations, are well known as a useful framework for analysis of the most significant dependencies between model and data. However, application of this approach in velocity model building has been limited, primarily because of the perception that it is computationally prohibitively expensive, especially for the anisotropic case. In this paper, we extend our prior work (Osypov et al., 2008) to VTI tomography, modify the process of regularization optimization, and propose an updated way for uncertainty and resolution quantification using the apparatus of eigendecomposition. We demonstrate the simultaneous tomographic estimation of VTI parameters on a real dataset. Our approach provides extra capabilities for regularization optimization and uncertainty analysis in anisotropic model parameter space which can be further translated into the structural uncertainty within the image.

Model‐uncertainty quantification in seismic tomography: method and applications

Uncertainty is inherent in every stage of the oil and gas exploration and production (E&P) business and understanding uncertainty enables mitigation of E&P risks. Therefore, quantification of uncertainty is beneficial for decision making and uncertainty should be managed along with other aspects of business. For example, decisions on well positioning should take into account the structural uncertainty related to the non-uniqueness of a velocity model used to create a seismic depth image. Moreover, recent advances in seismic acquisition technology, such as full-azimuth, long-offset techniques, combined with high-accuracy migration algorithms such as reverse-time migration, can greatly enhance images even in highly complex structural settings, provided that an Earth velocity model with sufficient resolution is available. Modern practices often use non-seismic observation to better constrain velocity model building. However, even with additional information, there is still ambiguity in our velocity models caused by the inherent non-uniqueness of the seismic experiment. Many different Earth velocity models exist that match the observed seismic (and well) data and this ambiguity grows rapidly away from well controls. The result is uncertainty in the seismic velocity model and the true positions of events in our images. Tracking these uncertainties can lead to significant improvement in the quantification of exploration risk (e.g., trap failure when well-logging data are not representative), drilling risk (e.g., dry wells and abnormal pore pressure) and volumetric uncertainties. Whilst the underlying ambiguity can never be fully eradicated, a quantified measure of these uncertainties provides a valuable tool for understanding and evaluating the risks and for development of better risk-mitigation plans and decision-making strategies

Radon transform inversion via Wiener filtering over the Euclidean motion group

In this paper we formulate the Radon transform as a convolution integral over the Euclidean motion group (SE(2)) and provide a minimum mean square error (MMSE) stochastic deconvolution method for the Radon transform inversion. Proposed approach provides a fundamentally new formulation that can model nonstationary signal and noise fields. Key components of our development are the Fourier transform over SE(2), stochastic processes indexed by groups and fast implementation of the SE(2) Fourier transform. Numerical studies presented here demonstrate that the method yields image quality that is comparable or better than the filtered backprojection algorithm. Apart from X-ray tomographic image reconstruction, the proposed deconvolution method is directly applicable to inverse radiotherapy, and broad range of science and engineering problems in computer vision, pattern recognition, robotics as well as protein science.

Bistatic Synthetic Aperture Hitchhiker Imaging

We introduce a new bistatic synthetic-aperture imaging method for a radar system consisting of two receivers, which will be referred to as hitchhikers, and a source of opportunity. We assume the receivers fly along arbitrary, but known, flight trajectories. We develop a correlation-based filtered-backprojection reconstruction method that preserves the visible edges of the target scene in the reconstructed image. We present an analysis of the computational complexity of the introduced method and demonstrate its applicability in numerical simulations. Potential applications of the proposed method include image formation using low earth orbiting and space-borne satellites as sources of opportunity.