A.E. Yagle | University of Michigan (original) (raw)

Papers by A.E. Yagle

IEEE Transactions on Geoscience and Remote Sensing, 2001

ABSTRACT Motivated by numerous scattering problems where the media is lossy and yet can only be i... more ABSTRACT Motivated by numerous scattering problems where the media is lossy and yet can only be investigated from a single side, the authors discuss algorithms for reconstructing a lossy, stratified dielectric from one-sided plane wave impulse reflection responses. Novel features of these algorithms include: 1) solving the lossy media problem using only one-sided reflection response data; 2) exploiting oblique probing angles; 3) having origins in digital signal processing (DSP) theory; 4) employing fast algorithms that have been modified to solve the forward scattering problem; and 5) solving the scattering problems exactly, including accounting for multiple reflections. A new algorithm is introduced that reconstructs such a media from one-sided transverse electric (TE) and transverse magnetic (TM) impulsive plane wave reflection responses from a single oblique angle. The oblique-probing angle necessitates a bistatic measurement configuration. New probing constraints are developed for a previously presented algorithm based on probing at two angles of incidence. Algorithm stability and data correction are addressed. Numerical examples illustrate the new algorithm in synthesizing the media transient response and reconstructing the media

ABSTRACT This project's focus is on sensor management and associated issues in modeling, ... more ABSTRACT This project's focus is on sensor management and associated issues in modeling, estimation, image reconstruction, and classification, for radar sensing. The central thesis of our original proposal was that intelligent sensor management can provide gains in performance and in operational requirements (energy consumption, deployment time, or exposure to hostile fire). We believe that we have demonstrated this thesis for several key application areas of interest to the army. These areas include minesweeping and detection of UXO, radar multiple target tracking, and energy-aware radar imaging through walls, earth or other attenuating media.

IEEE Transactions on Multimedia, 2013

ABSTRACT Multiframe super-resolution is the problem of reconstructing a single high-resolution (H... more ABSTRACT Multiframe super-resolution is the problem of reconstructing a single high-resolution (HR) image from several low-resolution (LR) versions of it. We assume that the original HR image undergoes different linear transforms, where each transform can be approximated as a set of linear shift-invariant transforms over different subregions of the HR image. The linearly transformed versions of the HR image are then downsampled, resulting in different LR images. Under the assumption of linearity, these LR images can form a basis that spans the set of the polyphase components (PPCs) of the HR image. We propose sampling rate diversity, where a secondary LR image, acquired by a secondary sensor of different (lower) sampling rate, is used as a reference to make known portions (subpolyphase components) of the PPCs of the reconstructed HR image. This setup allows for non-parametric reconstruction of the PPCs, where no knowledge of the underlying transforms is required, by solving for the expansion coefficients of the PPCs, in terms of the LR basis.

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 1992

It is shown that the problem of synthesizing equivalent oscillators and notch filters from the kn... more It is shown that the problem of synthesizing equivalent oscillators and notch filters from the knowledge of a given parent circuit is identical to that of finding the isomorphisms of a noncommutative group. It is also shown that many of the results established by earlier methods can easily be explained using the theory developed. The results derived show that earlier

The so-called split algorithms introduced recently by Delsarte et al. are three-term recurrences ... more The so-called split algorithms introduced recently by Delsarte et al. are three-term recurrences that constitute alternatives to the classical Levinson, Schur, and lattice algorithms. The split algorithms, under some circumstances, require fewer multiplications than the classical algorithms. However, the multichannel split Levinson algorithm for block Hermitian-Toeplitz matrices does not save any multiplications. This note introduces a different multichannel split algorithm that also does not save any multiplications, but does require only one matrix inversion per recursion to propagate, as compared to the two matrix inversions per recursion required by the classical Levinson and Delsarte et al. split algorithms.

Proceedings of MELECON '94. Mediterranean Electrotechnical Conference, 1994

ABSTRACT

IEEE Transactions on Antennas and Propagation, 2003

ABSTRACT Solving inverse scattering problems using layer stripping algorithms is known to be fast... more ABSTRACT Solving inverse scattering problems using layer stripping algorithms is known to be fast and effective when the data are noise-free. However, layer stripping algorithms have a reputation of being unstable when applied to noisy time-domain reflection response data. The reason is that the noisy data may be infeasible; i.e., could not have been produced by an actual media. In this paper, three feasibility conditions are introduced for data from absorbing (lossy) one-dimensional (1-D) media. Satisfying these conditions is both necessary and sufficient for the data to have been produced by an actual lossy media. That is, layer stripping algorithms applied such noisy but feasible data are stable. A methodology for correcting infeasible data is also proposed. Numerical examples illustrate key points and the correction method.

IEEE Transactions on Geoscience and Remote Sensing, 2001

ABSTRACT Motivated by numerous scattering problems where the media is lossy and yet can only be i... more ABSTRACT Motivated by numerous scattering problems where the media is lossy and yet can only be investigated from a single side, the authors discuss algorithms for reconstructing a lossy, stratified dielectric from one-sided plane wave impulse reflection responses. Novel features of these algorithms include: 1) solving the lossy media problem using only one-sided reflection response data; 2) exploiting oblique probing angles; 3) having origins in digital signal processing (DSP) theory; 4) employing fast algorithms that have been modified to solve the forward scattering problem; and 5) solving the scattering problems exactly, including accounting for multiple reflections. A new algorithm is introduced that reconstructs such a media from one-sided transverse electric (TE) and transverse magnetic (TM) impulsive plane wave reflection responses from a single oblique angle. The oblique-probing angle necessitates a bistatic measurement configuration. New probing constraints are developed for a previously presented algorithm based on probing at two angles of incidence. Algorithm stability and data correction are addressed. Numerical examples illustrate the new algorithm in synthesizing the media transient response and reconstructing the media

IEEE Transactions on Geoscience and Remote Sensing, 2001

ABSTRACT Motivated by numerous scattering problems where the media is lossy and yet can only be i... more ABSTRACT Motivated by numerous scattering problems where the media is lossy and yet can only be investigated from a single side, the authors discuss algorithms for reconstructing a lossy, stratified dielectric from one-sided plane wave impulse reflection responses. Novel features of these algorithms include: 1) solving the lossy media problem using only one-sided reflection response data; 2) exploiting oblique probing angles; 3) having origins in digital signal processing (DSP) theory; 4) employing fast algorithms that have been modified to solve the forward scattering problem; and 5) solving the scattering problems exactly, including accounting for multiple reflections. A new algorithm is introduced that reconstructs such a media from one-sided transverse electric (TE) and transverse magnetic (TM) impulsive plane wave reflection responses from a single oblique angle. The oblique-probing angle necessitates a bistatic measurement configuration. New probing constraints are developed for a previously presented algorithm based on probing at two angles of incidence. Algorithm stability and data correction are addressed. Numerical examples illustrate the new algorithm in synthesizing the media transient response and reconstructing the media

Inverse Problems, 1990

ABSTRACT

Inverse Problems, 1988

The inverse scattering problem for the three-dimensional Schrodinger equation with a non-local po... more The inverse scattering problem for the three-dimensional Schrodinger equation with a non-local potential diagonal in the radius variable is considered. Generalised Gel'fand-Levitan and Marchenko integral equations are derived using Gram-Schmidt orthogonalisations of free-space wave solutions. A generalised miracle equation is then used to recover the non-local potential. This is the first unified presentation of both the generalised Gel'fand-Levitan and Marchenko equations for this problem. New differential fast algorithms for solving these integral equations and recovering the potential are presented. An application to the problem of linear least-squares estimation of a random field is noted.

International Conference on Acoustics, Speech, and Signal Processing, 1998

The phase retrieval problem arises when a signal must be reconstructed from only the magnitude of... more The phase retrieval problem arises when a signal must be reconstructed from only the magnitude of its Fourier transform; if the phase information were also available, the signal could simply be synthesized using the inverse Fourier transform. In continuous phase retrieval, most previous solutions rely on discretizing the problem and then employing an iterative algorithm. We avoid this approximation by

ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing, 1987

ABSTRACT

Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269), 1998

Discrete tomography is the problem of reconstructing a binary image defined on a discrete lattice... more Discrete tomography is the problem of reconstructing a binary image defined on a discrete lattice of points from its projections at only a few angles. It has applications in X-ray crystallography, in which the projections are the number of atoms in the crystal along a given line, and nondestructive testing. The 2-D version of this problem is fairly well understood, and several algorithms for solving it are known, most of which involve discrete mathematics or network theory. However, the 3-D problem is much harder to solve. This paper shows how the problem can be recast in a purely algebraic form. This results in: (1) new insight into the number of projection angles needed for an almost surely unique solution; (2) non-obvious dependencies in projection data; and (3) new algorithms for solving.

IIEEE International Conference on Acoustics Speech and Signal Processing, 2002

ABSTRACT The problem of reconstructing an image from irregular samples of its 2-D DTFT arises in ... more ABSTRACT The problem of reconstructing an image from irregular samples of its 2-D DTFT arises in synthetic aperture radar (SAR), magnetic resonance imaging (MRI), limited angle tomography, and 2-D filter design. Since there is no 2-D Lagrange interpolation, sufficient conditions for the uniqueness and conditioning of the reconstruction problem are both not apparent. The Good-Thomas FFT is used to unwrap the 2-D problem into a 1-D problem, from which uniqueness results and, more importantly, insights into the problem conditioning are available. We propose the variance of distances between adjacent frequency locations as a sensitivity measure, which aids in determining a well-conditioned configuration of frequency values. The sensitivity measure is analyzed on its accuracy of estimating the conditioning and on its computational speed. The image is then reconstructed by solving the problem using the conjugate gradient method.

IEEE Transactions on Geoscience and Remote Sensing, 2001

ABSTRACT Motivated by numerous scattering problems where the media is lossy and yet can only be i... more ABSTRACT Motivated by numerous scattering problems where the media is lossy and yet can only be investigated from a single side, the authors discuss algorithms for reconstructing a lossy, stratified dielectric from one-sided plane wave impulse reflection responses. Novel features of these algorithms include: 1) solving the lossy media problem using only one-sided reflection response data; 2) exploiting oblique probing angles; 3) having origins in digital signal processing (DSP) theory; 4) employing fast algorithms that have been modified to solve the forward scattering problem; and 5) solving the scattering problems exactly, including accounting for multiple reflections. A new algorithm is introduced that reconstructs such a media from one-sided transverse electric (TE) and transverse magnetic (TM) impulsive plane wave reflection responses from a single oblique angle. The oblique-probing angle necessitates a bistatic measurement configuration. New probing constraints are developed for a previously presented algorithm based on probing at two angles of incidence. Algorithm stability and data correction are addressed. Numerical examples illustrate the new algorithm in synthesizing the media transient response and reconstructing the media

ABSTRACT This project's focus is on sensor management and associated issues in modeling, ... more ABSTRACT This project's focus is on sensor management and associated issues in modeling, estimation, image reconstruction, and classification, for radar sensing. The central thesis of our original proposal was that intelligent sensor management can provide gains in performance and in operational requirements (energy consumption, deployment time, or exposure to hostile fire). We believe that we have demonstrated this thesis for several key application areas of interest to the army. These areas include minesweeping and detection of UXO, radar multiple target tracking, and energy-aware radar imaging through walls, earth or other attenuating media.

IEEE Transactions on Multimedia, 2013

ABSTRACT Multiframe super-resolution is the problem of reconstructing a single high-resolution (H... more ABSTRACT Multiframe super-resolution is the problem of reconstructing a single high-resolution (HR) image from several low-resolution (LR) versions of it. We assume that the original HR image undergoes different linear transforms, where each transform can be approximated as a set of linear shift-invariant transforms over different subregions of the HR image. The linearly transformed versions of the HR image are then downsampled, resulting in different LR images. Under the assumption of linearity, these LR images can form a basis that spans the set of the polyphase components (PPCs) of the HR image. We propose sampling rate diversity, where a secondary LR image, acquired by a secondary sensor of different (lower) sampling rate, is used as a reference to make known portions (subpolyphase components) of the PPCs of the reconstructed HR image. This setup allows for non-parametric reconstruction of the PPCs, where no knowledge of the underlying transforms is required, by solving for the expansion coefficients of the PPCs, in terms of the LR basis.

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 1992

It is shown that the problem of synthesizing equivalent oscillators and notch filters from the kn... more It is shown that the problem of synthesizing equivalent oscillators and notch filters from the knowledge of a given parent circuit is identical to that of finding the isomorphisms of a noncommutative group. It is also shown that many of the results established by earlier methods can easily be explained using the theory developed. The results derived show that earlier

The so-called split algorithms introduced recently by Delsarte et al. are three-term recurrences ... more The so-called split algorithms introduced recently by Delsarte et al. are three-term recurrences that constitute alternatives to the classical Levinson, Schur, and lattice algorithms. The split algorithms, under some circumstances, require fewer multiplications than the classical algorithms. However, the multichannel split Levinson algorithm for block Hermitian-Toeplitz matrices does not save any multiplications. This note introduces a different multichannel split algorithm that also does not save any multiplications, but does require only one matrix inversion per recursion to propagate, as compared to the two matrix inversions per recursion required by the classical Levinson and Delsarte et al. split algorithms.

Proceedings of MELECON '94. Mediterranean Electrotechnical Conference, 1994

ABSTRACT

IEEE Transactions on Antennas and Propagation, 2003

ABSTRACT Solving inverse scattering problems using layer stripping algorithms is known to be fast... more ABSTRACT Solving inverse scattering problems using layer stripping algorithms is known to be fast and effective when the data are noise-free. However, layer stripping algorithms have a reputation of being unstable when applied to noisy time-domain reflection response data. The reason is that the noisy data may be infeasible; i.e., could not have been produced by an actual media. In this paper, three feasibility conditions are introduced for data from absorbing (lossy) one-dimensional (1-D) media. Satisfying these conditions is both necessary and sufficient for the data to have been produced by an actual lossy media. That is, layer stripping algorithms applied such noisy but feasible data are stable. A methodology for correcting infeasible data is also proposed. Numerical examples illustrate key points and the correction method.

IEEE Transactions on Geoscience and Remote Sensing, 2001

ABSTRACT Motivated by numerous scattering problems where the media is lossy and yet can only be i... more ABSTRACT Motivated by numerous scattering problems where the media is lossy and yet can only be investigated from a single side, the authors discuss algorithms for reconstructing a lossy, stratified dielectric from one-sided plane wave impulse reflection responses. Novel features of these algorithms include: 1) solving the lossy media problem using only one-sided reflection response data; 2) exploiting oblique probing angles; 3) having origins in digital signal processing (DSP) theory; 4) employing fast algorithms that have been modified to solve the forward scattering problem; and 5) solving the scattering problems exactly, including accounting for multiple reflections. A new algorithm is introduced that reconstructs such a media from one-sided transverse electric (TE) and transverse magnetic (TM) impulsive plane wave reflection responses from a single oblique angle. The oblique-probing angle necessitates a bistatic measurement configuration. New probing constraints are developed for a previously presented algorithm based on probing at two angles of incidence. Algorithm stability and data correction are addressed. Numerical examples illustrate the new algorithm in synthesizing the media transient response and reconstructing the media

IEEE Transactions on Geoscience and Remote Sensing, 2001

ABSTRACT Motivated by numerous scattering problems where the media is lossy and yet can only be i... more ABSTRACT Motivated by numerous scattering problems where the media is lossy and yet can only be investigated from a single side, the authors discuss algorithms for reconstructing a lossy, stratified dielectric from one-sided plane wave impulse reflection responses. Novel features of these algorithms include: 1) solving the lossy media problem using only one-sided reflection response data; 2) exploiting oblique probing angles; 3) having origins in digital signal processing (DSP) theory; 4) employing fast algorithms that have been modified to solve the forward scattering problem; and 5) solving the scattering problems exactly, including accounting for multiple reflections. A new algorithm is introduced that reconstructs such a media from one-sided transverse electric (TE) and transverse magnetic (TM) impulsive plane wave reflection responses from a single oblique angle. The oblique-probing angle necessitates a bistatic measurement configuration. New probing constraints are developed for a previously presented algorithm based on probing at two angles of incidence. Algorithm stability and data correction are addressed. Numerical examples illustrate the new algorithm in synthesizing the media transient response and reconstructing the media

Inverse Problems, 1990

ABSTRACT

Inverse Problems, 1988

The inverse scattering problem for the three-dimensional Schrodinger equation with a non-local po... more The inverse scattering problem for the three-dimensional Schrodinger equation with a non-local potential diagonal in the radius variable is considered. Generalised Gel'fand-Levitan and Marchenko integral equations are derived using Gram-Schmidt orthogonalisations of free-space wave solutions. A generalised miracle equation is then used to recover the non-local potential. This is the first unified presentation of both the generalised Gel'fand-Levitan and Marchenko equations for this problem. New differential fast algorithms for solving these integral equations and recovering the potential are presented. An application to the problem of linear least-squares estimation of a random field is noted.

International Conference on Acoustics, Speech, and Signal Processing, 1998

The phase retrieval problem arises when a signal must be reconstructed from only the magnitude of... more The phase retrieval problem arises when a signal must be reconstructed from only the magnitude of its Fourier transform; if the phase information were also available, the signal could simply be synthesized using the inverse Fourier transform. In continuous phase retrieval, most previous solutions rely on discretizing the problem and then employing an iterative algorithm. We avoid this approximation by

ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing, 1987

ABSTRACT

Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269), 1998

Discrete tomography is the problem of reconstructing a binary image defined on a discrete lattice... more Discrete tomography is the problem of reconstructing a binary image defined on a discrete lattice of points from its projections at only a few angles. It has applications in X-ray crystallography, in which the projections are the number of atoms in the crystal along a given line, and nondestructive testing. The 2-D version of this problem is fairly well understood, and several algorithms for solving it are known, most of which involve discrete mathematics or network theory. However, the 3-D problem is much harder to solve. This paper shows how the problem can be recast in a purely algebraic form. This results in: (1) new insight into the number of projection angles needed for an almost surely unique solution; (2) non-obvious dependencies in projection data; and (3) new algorithms for solving.

IIEEE International Conference on Acoustics Speech and Signal Processing, 2002

ABSTRACT The problem of reconstructing an image from irregular samples of its 2-D DTFT arises in ... more ABSTRACT The problem of reconstructing an image from irregular samples of its 2-D DTFT arises in synthetic aperture radar (SAR), magnetic resonance imaging (MRI), limited angle tomography, and 2-D filter design. Since there is no 2-D Lagrange interpolation, sufficient conditions for the uniqueness and conditioning of the reconstruction problem are both not apparent. The Good-Thomas FFT is used to unwrap the 2-D problem into a 1-D problem, from which uniqueness results and, more importantly, insights into the problem conditioning are available. We propose the variance of distances between adjacent frequency locations as a sensitivity measure, which aids in determining a well-conditioned configuration of frequency values. The sensitivity measure is analyzed on its accuracy of estimating the conditioning and on its computational speed. The image is then reconstructed by solving the problem using the conjugate gradient method.