We propose Deep Learning (DL) as a framework for performing simultaneous waveform estimation and image reconstruction in passive synthetic aperture radar (SAR). We interpret image reconstruction as a machine learning task for which a deep recurrent neural network (RNN) can be constructed by unfolding the iterations of a proximal gradient descent algorithm. We formulate the problem by representing the unknown waveform in a basis, and extend the recurrent auto-encoder architecture we proposed in1–3 by modifying the parameterization of the RNN to perform estimation of waveform coefficients, instead of unknown phase components in the forward model. Under a convex prior on the scene reflectivity, the constructed network serves as a convex optimizer in forward propagation, and a non-convex optimizer for the unknown waveform coefficients in backpropagation. With the auto-encoder architecture, the unknowns of the problem are estimated by operations only in the data domain, performed in an unsupervised manner. The highly non-convex problem of backpropagation is guided to a feasible solution over the parameter space by initializing the network with the known components of the SAR forward model. Moreover, prior information regarding the waveform can be incorporated during initialization. We validate the performance of our method with numerical simulations.
The recent success of deep learning has lead to growing interest in applying these methods to signal processing problems. This paper explores the applications of deep learning to synthetic aperture radar (SAR) image formation. We review deep learning from a perspective relevant to SAR image formation. Our objective is to address SAR image formation in the presence of uncertainties in the SAR forward model. We present a recurrent auto-encoder network architecture based on the iterative shrinkage thresholding algorithm (ISTA) that incorporates SAR modeling. We then present an off-line training method using stochastic gradient descent and discuss the challenges and key steps of learning. Lastly, we show experimentally that our method can be used to form focused images in the presence of phase uncertainties. We demonstrate that the resulting algorithm has faster convergence and decreased reconstruction error than that of ISTA.
In this paper we present a method for passive radar detection of ground moving targets using sparsely distributed apertures. We assume the scene is illuminated by a source of opportunity and measure the backscattered signal. We correlate measurements from two different receivers, then form a linear forward model that operates on a rank one, positive semi-definite (PSD) operator, formed by taking the tensor product of the phase-space reflectivity function with its self. Utilizing this structure, image formation and velocity estimation are defined in a constrained optimization framework. Additionally, image formation and velocity estimation are formulated as separate optimization problems, this results in computational savings. Position estimation is posed as a rank one PSD constrained least squares problem. Then, velocity estimation is performed as a cardinality constrained least squares problem, solved using a greedy algorithm. We demonstrate the performance of our method with numerical simulations, demonstrate improvement over back-projection imaging, and evaluate the effect of spatial diversity.
We present an analysis of the positioning errors in Backprojection (BP)-based Synthetic Aperture Radar (SAR) images due to antenna trajectory errors for a monostatic SAR traversing a straight linear trajectory. Our analysis is developed using microlocal analysis, which can provide an explicit quantitative relationship between the trajectory error and the positioning error in BP-based SAR images. The analysis is applicable to arbitrary trajectory errors in the antenna and can be extended to arbitrary imaging geometries. We present numerical simulations to demonstrate our analysis.
Interferometric Synthetic Aperture Radar (IFSAR) uses the phase difference between two SAR images acquired at different positions to infer ground topography. Conventional IFSAR technique is based on wideband transmitted waveforms. As a result, the interferometric phase forms an iso-Doppler surface containing the height information. In this work, we present a novel interferometric SAR technique using ultra-narrowband continuous waveforms to infer ground topography. Due to high Doppler resolution of the transmitted waveforms, we refer to this technique as the Doppler-IFSAR. We form SAR images by backprojecting onto iso-Doppler contours. We present the interferometric phase model for Doppler-IFSAR and outline the relationship between the height and interferometric phase.
We consider a mono-static synthetic aperture radar (SAR) system
ying over a scene of interest, making multiple
visits. During each visit, antenna is traversing a dierent arbitrary, but known trajectory. Therefore, the
dierence in the positions of the antennas, which we refer to as the baseline vector, is arbitrary and changes at
each visit. Our objective is to estimate the displacement in the ground topography and reconstruct the scene
radiance. We perform a spatio-temporal correlation of the received signals measured by each antenna. This results
in a novel model that relates the correlated signal to the displacement. Next, we estimate the displacement in
the ground topography and reconstruct the radiance of the scene by using a ltered-backprojection (FBP) -
type method combined with an entropy minimization technique. Finally, we present numerical experiments to
demonstrate the performance of the proposed method.
In this paper we present a method for imaging ground moving targets using passive synthetic aperture radar.
A passive radar imaging system uses small, mobile receivers that do not radiate any energy. For these reasons,
passive imaging systems result in signicant cost, manufacturing, and stealth advantages. The received signals are
obtained by multiple airborne receivers collecting scattered waves due to illuminating sources of opportunity such
as commercial television, radio, and cell phone towers. We describe a novel forward model and a corresponding
ltered-backprojection type image reconstruction method combined with entropy optimization. Our method
determines the location and velocity of multiple targets moving at dierent velocities. Furthermore, it can
accommodate arbitrary imaging geometries. we present numerical simulations to verify the imaging method.
We present a novel method for ground moving target detection and imaging using a SAR system transmitting
ultra-narrowband continuous waveforms. We develop a new forward model that relates the velocity as well as
reflectivity information at each location to a correlated received signal. We reconstruct moving target images
by a filtered-backprojection method. We use the image contrast as a metric to detect moving targets and
to determine their velocities. The method results in well-focused reflectivity images of moving targets and
their velocity estimates regardless of the target location, speed, and velocity direction. We present numerical
experiments to verify our method.
We present a novel passive radar imaging method for moving targets using distributed apertures. We develop a
passive measurement model that relates measurements at a given receiver to measurements at other receivers.
We formulate the passive imaging problem as a Generalized likelihood ratio test (GLRT) for a hypothetical
target located at an unknown position, moving with an unknown velocity. We design a linear discriminant
functional by maximizing the signal-to-noise ratio (SNR) of the test-statistic, and use the resulting position- and
velocity-resolved test-statistic to form an image of the scene of interest. We present numerical experiments to
demonstrate the performance of our imaging method.
We consider a monostatic synthetic aperture radar system traversing an arbitrary trajectory on a non-flat
topography. We present a novel edge detection method applicable directly to SAR received signal. Our method
first filters the received data, and then backprojects. The filter is designed to detect the edges of the scene in
different directions at each pixel reconstructed. The method is computationally efficient and may be implemented
with the computational complexity of the fast-backprojection algorithms. We present numerical experiments to
demonstrate the performance of our method.
We present a novel passive image formation method for moving targets using distributed apertures capable
of exploiting information about multiple-scattering in the environment. We assume that the environment is
illuminated by non-cooperative transmitters of opportunity with unknown location and unknown transmitted
waveforms. We develop a passive measurement model that relates the scattered field from moving targets at a
given receiver to the scattered field at other receivers. We formulate the passive imaging problem as a generalized
likelihood ratio test for a hypothetical target located at an unknown position, moving with an unknown velocity.
We design a linear discriminant functional by maximizing the Signal-to-Noise Ratio (SNR) of the test-statistic,
and use the resulting position- and velocity-resolved test-statistic to form the image. Our imaging method can
determine the two- or three-dimensional velocity vector as well as the two- or three-dimensional position vector
of a moving target without the knowledge of transmitter locations and transmitted waveforms. We present
numerical experiments to demonstrate the performance of our passive imaging method operating in multiplescattering
environments. The results show that the point spread function of the reconstructed images improves
when the information about multiple scattering is exploited.
We consider synthetic aperture radar system using ultra-narrowband continuous waveforms, which we refer to
as Doppler Synthetic Aperture Radar (DSAR). We present a novel image formation method for bi-static DSAR.
Our method first correlates the received signal with a scaled or frequency-shifted version of the transmitted signal
over a finite time window, and then uses microlocal analysis to reconstruct the scene by a filtered-backprojection
of the correlated signals. Our approach can be used under non-ideal imaging scenarios such as arbitrary flight
trajectories and non-flat topography. Furthermore, it is an analytic reconstruction technique which can be made
computationally efficient. We present numerical experiments to demonstrate the performance of the proposed
method.
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.
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.
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.
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.
In this paper, we analyze the error resulting from the discretization of the forward and inverse problems in simultaneously
reconstructed optical absorption and scattering images. Our analysis indicates the mutual dependence
of the forward and inverse problems, the number of sources and detectors, their configuration and the location
of optical heterogeneities with respect to sources and detectors affect the extent of the error in the reconstructed
optical images resulting from discretization. One important implication of the error analysis is that poor discretization
of one optical coefficient results in error in the other, resulting in inter-parameter "cross-talk" due
entirely to discretization.
In this study, we combine a generalized Tikhonov regularization method with a priori anatomical information
to reconstruct the concentration of fluorophores in mouse with Chronic Obstructive Pulmonary disease (COPD)
from in vivo optical and Magnetic Resonance (MR) measurements. Generalized Tikhonov regularization incorporates
a penalty term in the optimization formulation of the fluorescence molecular tomography (FMT) inverse
problem. Our design involves two penalty terms to make use of a priori anatomical structural information from
segmented MR images. The choice of the penalty terms guide the fluorophores in reconstructed image concentrates
in the region where it is supposed to be and assure smooth flourophore distribution within tissue of same
type and enhances the discontinuities between different tissue types. We compare our results with traditional
Tikhanov regularization techniques in extensive simulations and demonstrate the performance our approach in
vivo mouse data. The results show that the increased fluorophore concentration in the mouse lungs is consistent
with an increased inflammatory response expected from the corresponding animal disease model.
In fluorescence diffuse optical tomography, the error due to
discretization of the forward and inverse problems leads to an error
in the reconstructed image. Using a Galerkin formulation, we
consider zeroth and first order Tikhonov regularization terms and
analyze the forward and inverse problems under an optimization
formulation which incorporates a priori information. We
derive error estimates to describe the impact that discretization of
the forward and inverse problems due to finite element method has on
the accuracy of the reconstructed optical absorbtion image.
A hitchhiker is a passive radar receiver that relies on sources of opportunity to perform radar tasks.1-4 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 synthetic aperture hitchhiker (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 SAR5. 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.
Reconstruction algorithms for monostatic synthetic aperture radar (SAR) with poor antenna directivity
traversing straight and arbitrary flight trajectories have been developed by various authors1-5, 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 (straight6,7 or circular8,9 flight
trajectories) over flat topography.
In this paper, we present an approximate analytic inversion method for bistatic SAR (Bi-SAR).10 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
simulations.
The idea of preconditioning 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
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.
In this work, we discuss the incorporation of a priori information into the inverse problem formulation for
fluorescence optical tomography. In this respect, we first formulate the inverse problem in the optimization
framework which allows the incorporation of a priori information about the solution and its gradient. Then, we
consider the variational problem, which is equivalent to the optimization problem and prove the existence and
uniqueness of the solution. Finally, we discuss the design of the functions that incorporate the a priori information
into the inverse problem formulation and present a model problem to illustrate the design procedure.
KEYWORDS: Sensors, Fourier transforms, Algorithm development, Reconstruction algorithms, X-rays, Data processing, Signal attenuation, Medical imaging, Detector arrays, Computing systems
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 work investigates the design of optimum distribution of photon density power among the source positions, and optimum modulation frequencies to maximize the detectability of heterogeneities embedded in turbid medium using near infrared light. The optimum waveforms are designed for the sources in near-infrared diffuse optical tomography which involves reconstruction of spatially varying optical properties of turbid medium as well as fluorophore lifetime and yield from boundary measurements. We start our analysis by first deriving the discrete source-to-detector map based on the finite-element formulation of the diffuse photon density wave equation and Robin boundary conditions. We determine statistical figures of merit to maximize the contrast of heterogeneities with respect to a given background. Next, we design optical waveforms that will maximize the figure of merit for the detectability of heterogeneities. When the figure of merit is derived based on optimal linear detection under the assumption of Gaussianity, the optimal source vector is given by the eigenvector corresponding to the maximum eigenvalue of the norm of the differences between the source-to-detector maps of homogeneous and heterogeneous domains. We extended our approach to investigate the optimum spatial positions and intensities of point sources to maximize the detectability of the heterogeneities. We explored the effect of tumor location with respect to the sources, tumor size, and the number of sources on detectability.
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.
In this work, we present spatially resolved pharmacokinetic rate images of indocyanine green (ICG) obtained from three breast cancer patients using near infrared imaging methods. We used a two-compartment model, namely, plasma and extracellular extravascular (EES), to model ICG kinetics around the tumor region. We introduced extended Kalman filtering (EKF) framework to estimate the ICG pharmacokinetic rate images. The EKF framework allows simultaneous estimation of pharmacokinetic rates and the ICG concentrations in each
compartment. Based on the pharmacokinetic rate images, we observed that the rates from inside and outside the tumor region are statistically different with a p-value of 0.0001 for each patient. Additionally, we observed that the ICG concentrations in plasma and the EES compartments are higher around the tumors agreeing with the hypothesis that ICG may act as a diffusible extravascular flow in leaky capillary of cancer vessels. Our study shows that spatially resolved pharmacokinetic rate images can be potentially useful for breast cancer screening and diagnosis.
We explore the utility of functional Near Infra Red (fNIR) technology in providing both empirical support and a basis for assessing and predicting dynamic changes in cognitive workload within the theoretical context of computational cognitive modeling (CCM). CCM has had many successes and in recent years has expanded from a tool for basic research to one that can tackle more complex real-world tasks. As a tool for basic research it seeks to provide a model of cognitive functionality; as a tool for cognitive engineering it seeks applications in monitoring and predicting real-time performance. With this powerful theoretical tool we combine the empirical power of fNIR technology. The fNIR technology is used to
non-invasively monitor regional hemodynamic activities, namely blood volume changes and oxygenation dynamics. We examined a simple auditory classification task in four different workload conditions. We monitored the blood activity in the prefrontal cortex region of the frontal lobe during the performance of the task to assess the patterns of activity as workload changes. We associated patterns of model activity with patterns of the hemodynamic data. We used
ACT-R for creating the computational cognitive model. For the fNIR analysis, we used a generalized linear regression model along with time series clustering. We found that in the highest workload condition the model predicts a cognitive 'overload', which correlated well with the fNIR cluster and classification analysis, as this condition differs significantly from the other three conditions. Linear regression on a subset of the data where workload increases monotonically shows that apart from the overload condition, there was a positive relationship between increase in workload and increase in blood volume activation. In addition, individual variations in hemodynamic response suggest that individuals differ in how they process different workload levels.
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.
A number of studies indicate that compartmental modeling of
indocyanine green (ICG) pharmacokinetics, as measured by near
infrared (NIR) techniques, may provide diagnostic information for
tumor differentiation. However, compartmental parameter estimation
is a highly non-linear problem with limited data available in a
clinical setting. Furthermore, pharmacokinetic parameter estimates
show statistical variation from one data set to another. Thus, a
systematic and robust approach is needed to model, estimate and
quantify ICG pharmacokinetic parameters. In this paper, we propose
to model ICG pharmacokinetics in extended Kalman filtering (EKF)
framework. EKF effectively models multiple-compartment and
multiple-measurement systems in the presence of measurement noise
and uncertainties in model dynamics. It provides simultaneous
estimation of pharmacokinetic parameters and ICG concentrations in
each compartment. Moreover, recursive nature of the Kalman filter
estimator potentially allows real time monitoring of time varying
pharmacokinetic rates and concentration changes in different
compartments. We tested our approach using the ICG concentration
data acquired from four Fischer rats carrying adenocarcinoma tumor
cells. Our study indicates that EKF model may provide additional
parameters that may be useful for tumor differentiation.
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.
Diffuse Optical Tomography (DOT) image reconstruction is a
challenging 3D problem with a relatively large number of unknowns.
DOT poses a typical ill-posed problem usually plagued by
under-determination, which complicates the inverse problem.
Conventional image reconstruction algorithms can not provide high
spatial resolution and may become computationally expensive and
unreliable especially in the presence of noise.
In this work, we extend our previous formulation for the 3D
inverse DOT problem, where we focus to improve the spatial
resolution and quantitative accuracy of 3D DOT images by using
anatomical a priori information, which is specific to the medium
of interest. Maximum A Posteriori (MAP) estimate of the image is
formed based on the formulation of the image's probability density
function, which is extracted from the available a priori
anatomical information. An ``alternating minimization'' algorithm,
which sequentially updates the unknown parameters, is used to
solve the resulting optimization problem. Proposed method is
evaluated in a 3D simulation experiment. Results demonstrate
that the proposed method leads to significantly improved spatial
resolution, quantitative accuracy and faster convergence than
standard and regularized least squares solutions even in the
presence of noise. As a result, the approach demonstrated in this
paper both addresses the ill-posedness and balances the
computation complexity vs. image quality trade-off in the 3D DOT
inverse problem.
Diffuse optical imaging is an emerging modality that uses Near Infrared (NIR) light to reveal structural and functional information of deep biological tissue. It provides contrast mechanisms for molecular, chemical, and anatomical imaging that is not available from other imaging modalities. Diffuse Optical Tomography (DOT) deals with 3D reconstruction of optical properties of tissue given the measurements and a forward model of photon propagation. DOT has inherently low spatial resolution due to diffuse nature of photons. In this work, we focus to improve the spatial resolution and the quantitative accuracy of DOT by using a priori anatomical information specific to unknown image. Such specific a priori information can be obtained from a secondary high-resolution imaging modality such as Magnetic Resonance (MR) or X-ray. Image reconstruction is formulated within a Bayesian framework to determine the spatial distribution of the absorption coefficients of the medium. A spatially varying a priori probability density function is designed based on the segmented anatomical information. Conjugate gradient method is utilized to solve the resulting optimization problem. Proposed method is evaluated using simulation and phantom measurements collected with a novel time-resolved optical imaging system. Results demonstrate that the proposed method leads to improved spatial resolution, quantitative accuracy and faster convergence than standard least squares approach.
A number of researchers have previously shown that the ultrasound RF echo of tissue exhibits (1/f)-β characteristics and developed tissue characterization methods based on the fractal parameter β. In this paper we propose Fractional Differencing Autoregressive Moving Average (FARMA) process for modeling RF ultrasound echo and develop breast tissue characterization method based on the FARMA model parameters. This model has been used to capture statistical self-similarity and long-range correlations in image textures, in wide ranging engineering and science applications, including communication network traffic. Here, we present estimation techniques to extract the model parameters, namely features, for classification purposes and tissue characterization. We show the performance of our tissue characterization procedure on several in vivo ultrasound breast images including benign and malignant tumors. The area of the receiver operator characteristics (ROC) based on 60 in vivo images yields a value of 0.79, which indicates that proposed tissue characterization method is comparable in performance with other successful methods reported in the literature.
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.
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