Il-Young Son

Passive imaging using distributed apertures in multiple-scattering environments

We develop a new passive image formation method capable of exploiting information about multiple scattering in the environment, as well as statistics of the objects to be imaged, additive noise and clutter, using measurements from a sparse array of receivers that rely on illumination sources of opportunity. The array of receivers can be distributed spatially in an arbitrary fashion with several hundred wavelengths apart. We use a physics-based approach to model a multiple-scattering environment and develop a statistical model that relates measurements in a given receiver to measurements in other receivers. The model is based on back-propagating measurements in a given receiver to a hypothetical target location and then forward propagating to another receiver location based on the Green’s function of the background environment. We next address the imaging problem as a generalized likelihood ratio test (GLRT) for an unknown target location. The GLRT framework allowsaprioriscene, clutter and noise information to be incorporated into the problem formulation, as well as non-Gaussian data likelihood and ap riorimodels. We address the spatially resolved hypothesis testing problem by constraining the associated discriminant functional to be linear and by maximizing the signal-to-noise ratio of the test statistics. We use the resulting spatially resolved test statistic to form the image. We present the resolution analysis of our imaging algorithms for free-space and a multiple-scattering environment model. Our analysis demonstrates the improvements in the point spread function and the signal-to-noise ratio of the reconstructed images when multiple scattering is exploited, as well as the potential artifacts and limitations. We present numerical experiments to demonstrate the performance of the resulting algorithms and to validate the theoretical findings. (Some figures in this article are in colour only in the electronic version)

NEAR INFRARED IMAGING AND SPECTROSCOPY FOR BRAIN ACTIVITY MONITORING

The first demonstration that near infrared (NIR) light can be used to monitor the state of cortical tissues noninvasively through the skull was presented by Jobsis in 1977 [53]. About a decade later, researchers started looking at the potential use of NIR spectroscopy for functional brain activity monitoring. Early studies began with simple motor and sensory tasks demonstrating the feasibility of the technology for noninvasively assessing the state of cerebral activity in a localized area. More recent studies have attempted to monitor more complex cognitive tasks such as warfare management [48] and aircraft landing simulations [102]. In this chapter, the research surrounding the application of NIR imaging and spectroscopy to noninvasive monitoring of functional brain activity is reviewed. A comprehensive review of equipment technologies, mathematical models, and past studies is given with some emphasis on the techology’s potential in security and defense applications.

Passive Synthetic Aperture Radar Imaging Using Low-Rank Matrix Recovery Methods

We present a novel image formation method for passive synthetic aperture radar (SAR) imaging. The method is an alternative to widely used time difference of arrival (TDOA) or correlation-based backprojection method. These methods work under the assumption that the scene is composed of a single or a few widely separated point targets. The new method overcomes this limitation and can reconstruct heterogeneous scenes with extended targets. We assume that the scene of interest is illuminated by a stationary transmitter of opportunity with known illumination direction, but unknown location. We consider two airborne receivers and correlate the fast-time bistatic measurements at each slow-time. This correlation process maps the tensor product of the scene reflectivity with itself to the correlated measurements. Since this tensor product is a rank-one positive semi-definite operator, the image formation lends itself to low-rank matrix recovery techniques. Taking into account additive noise in bistatic measurements, we formulate the estimation of the rank-one operator as a convex optimization with rank constrain. We present a gradient-descent based iterative reconstruction algorithm and analyze its computational complexity. Extensive numerical simulations show that the new method is superior to correlation-based backprojection in reconstructing extended and distributed targets with better geometric fidelity, sharper edges, and better noise suppression.

Radar detection using sparsely distributed apertures in urban environment

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 first 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 filtering.

Passive imaging with multistatic polarimetric radar

In this work we present a study applying polarimetric principles to passive radar imaging. We assume a stationary scene illuminated by spatially distributed transmitters with unknown location and polarization. The scattered waves are captured by spatially distributed stationary receivers equipped with a pair of orthogonally polarized antennas. We model the target as a set of dipoles. Using this model, we derive a set of templates for spatially resolved detection. Our aim is to show that one can recover valuable information about the target through polarimetric consideration in a passive detection setting that exhibits both polarization and spatial diversity.

Passive synthetic aperture radar imaging based on low-rank matrix recovery

We present a novel image formation method for passive synthetic aperture radar (SAR) imaging. The method is an alternative to Time Difference of Arrival (TDOA) based backprojection method. The TDOA based backprojection works under the assumption that the scene is composed of a single or a few widely separated point targets. The new method overcomes this limitation and can reconstruct heterogenous scenes with extended targets. We assume that a scene of interest is illuminated by a stationary transmitter of opportunity with known illumination direction, but unknown location. We consider two airborne receivers collecting back-scattered data from the scene. We correlate the fast-time measurements from both receivers at each slow-time. The correlation process removes the transmitter dependency from the phase of the forward model under the small scene and far-field assumptions. We then define a linear model that maps the tensor product of the scene reflectivity with itself to the correlated measurements. The resulting inverse problem involves recovering a rank-one matrix from correlated measurements. We reconstruct the scene reflectivity by low-rank matrix recovery techniques. Numerical simulations show that the new method is superior to TDOA based backprojection for realistic SAR scenes.

A 2-level domain decomposition algorithm for inverse diffuse optical tomography

In this paper, we explore domain decomposition algorithms for the inverse DOT problem in order to reduce the computational complexity and accelerate the convergence of the optical image reconstruction. We propose a combination of a two-level multigrid algorithm with a modified multiplicative Schwarz algorithm, where a conjugate gradient is used as an accelerator to solve each sub-problem formulated on each of the partitioned sub-domains. For our experiments, simulated phantom configuration with two rectangular inclusions is used as a testbed to measure the computational efficiency of our algorithms. No a priori information about the configuration is assumed except for the source and detector locations. For the application of our modified Schwarz algorithm alone, we observe an increase in efficiency of 100% as compared to the conjugate gradient solution obtained for the full domain. With the addition of the coarse grid, this efficiency rises to 400%. The coarse grid also serves to improve the overall appearance of the reconstructed image at the boundaries of the inclusions.

Passive polarimetrie multistatic radar for ground moving target

We consider a scene illuminated by a single stationary transmitter with unknown polarization and a set of spatially distributed receivers exhibiting polarization diversity. We present a model and detection framework to detect moving targets using a multistatic passive receivers with polarimetric diversity. We model the targets as a set of dipole antennas. The model captures the anisotropic nature of targets exhibited in multistatic configurations. We address the moving target detection problem in a generalized likelihood ratio test (GLRT) framework. In addition, we introduce a method for estimating the dipole moments of the target derived from the GLRT formulation. We show, through a set of simulations, the efficacy of polarization diversity in both target detection and dipole estimation.

Domain decomposition method for diffuse optical tomography

Diffuse optical tomography is modelled as an optimization problem to find the absorption and scattering coefficients that minimize the error between the measured photon density function and the approximated one computed using the coefficients. The problem is composed of two steps: the forward solver to compute the photon density function and its Jacobian (with respect to the coefficients), and the inverse solver to update the coefficients based on the photon density function and its Jacobian attained in the forward solver. The resulting problem is nonlinear and highly ill-posed. Thus, it requires large amount of computation for high quality image. As such, for real time application, it is highly desirable to reduce the amount of computation needed. In this paper, domain decomposition method is adopted to decrease the computation complexity of the problem. Two level multiplicative overlapping domain decomposition method is used to compute the photon density function and its Jacobian at the inner loop and extended to compute the estimated changes in the coefficients in the outer loop. Local convergence for the two-level space decomposition for the outer loop is shown for the case when the variance of the coefficients is small.

Two-level domain decomposition algorithm for a nonlinear inverse DOT problem

Diffuse optical tomography (DOT) in the near infrared involves reconstruction of spatially varying optical properties of turbid medium from boundary measurements based on a forward model of photon propagation. Due to highly non-linear nature of the DOT, high quality image reconstruction is a computationally demanding problem that requires repeated solutions of both the forward and the inverse problems. Therefore, it is highly desirable to develop methods and algorithms that are computationally efficient. In this paper, we propose a domain decomposition approach to address the computational complexity of the DOT problem. We propose a two-level multiplicative overlapping domain decomposition method for the forward problem and a two-level space decomposition method for the inverse problem. We showed the convergence of the inverse solver and derived the computational complexity of each method. We demonstrate the performance of the proposed approach in numerical simulations.