Arye Nehorai | Washington University in St. Louis (original) (raw)

Papers by Arye Nehorai

IEEE Transactions on Signal Processing, May 1, 2009

The resolution improvements of time reversal methods through exploiting nonhomogeneous media have... more The resolution improvements of time reversal methods through exploiting nonhomogeneous media have attracted much interest recently with broad applications, including underwater acoustics, radar, detection of defects in metals, communications, and destruction of kidney stones. In this paper, we analyze the effect of inhomogeneity generated by multiple scattering among point scatterers under a multistatic sensing setup. We derive the Cramér-Rao bounds (CRBs) on parameters of the scatterers and compare the CRBs for multiple scattering using the Foldy-Lax model with the reference case without multiple scattering using the Born approximation. We find that multiple scattering could significantly improve the estimation performance of the system and higher order scattering components actually contain much richer information about the scatterers. For the case where multiple scattering is not possible, e.g., where only a single target scatterer exists in the illuminated scenario, we propose the use of artificial scatterers, which could effectively improve the estimation performance of the target despite a decrease in the degrees of freedom of the estimation problem due to the introduced unknown parameters of the artificial scatterers. Numerical examples demonstrate the advantages of the artificial scatterers.

IEEE Transactions on Signal Processing, Sep 1, 2007

Time-reversal methods have attracted increasing interest recently. The so-called computational ti... more Time-reversal methods have attracted increasing interest recently. The so-called computational time-reversal approach creates an image of the illuminated scene by computing the back-propagated field and is useful for detecting and estimating targets in the scene. In Shi and Nehorai ["Maximum Likelihood Estimation of Point Scatterers for Computational Time-Reversal Imaging," Communications in Information and Systems, vol. 5, no. 2, pp. 227-256, 2005], we estimated point scatterers by maximum-likelihood estimate (MLE) using the Born-approximated physical model, as well as the Foldy-Lax model. In this correspondence, we further find an explicit relationship between energy-based basic time-reversal imaging and the MLE approach: the time-reversal imaging function differs by only a scaling factor from the likelihood imaging function using the estimated scattering potential when a single-scatterer model is employed. Furthermore, this scaling factor is a function of the imaging position only. We show that, as a result, time-reversal imaging has a near-far problem that tends to produce a weaker image for areas further away from the imaging arrays, whereas the MLE-based image is more balanced. Experimental results confirm this conclusion.

IEEE Transactions on Signal Processing, 2020

We investigate the one-bit MIMO (1b-MIMO) radar that performs one-bit sampling with a time-varyin... more We investigate the one-bit MIMO (1b-MIMO) radar that performs one-bit sampling with a time-varying threshold in the temporal domain and employs compressive sensing in the spatial and Doppler domains. The goals are to significantly reduce the hardware cost, energy consumption, and amount of stored data. The joint angle and Doppler frequency estimations from noisy one-bit data are studied. By showing that the effect of noise on one-bit sampling is equivalent to that of sparse impulsive perturbations, we formulate the one-bit ℓ1-regularized atomicnorm minimization (1b-ANM-L1) problem to achieve gridless parameter estimation with high accuracy. We also develop an iterative method for solving the 1b-ANM-L1 problem via the alternating direction method of multipliers. The Cramér-Rao bound (CRB) of the 1b-MIMO radar is analyzed, and the analytical performance of one-bit sampling with two different threshold strategies is discussed. Numerical experiments are presented to show that the 1b-MIMO radar can achieve highresolution parameter estimation with a largely reduced amount of data.

IEEE Transactions on Signal Processing, Apr 1, 2014

We consider algorithms and recovery guarantees for the analysis sparse model in which the signal ... more We consider algorithms and recovery guarantees for the analysis sparse model in which the signal is sparse with respect to a highly coherent frame. We consider the use of a monotone version of the fast iterative shrinkagethresholding algorithm (MFISTA) to solve the analysis sparse recovery problem. Since the proximal operator in MFISTA does not have a closed-form solution for the analysis model, it cannot be applied directly. Instead, we examine two alternatives based on smoothing and decomposition transformations that relax the original sparse recovery problem, and then implement MFISTA on the relaxed formulation. We refer to these two methods as smoothing-based and decomposition-based MFISTA. We analyze the convergence of both algorithms, and establish that smoothingbased MFISTA converges more rapidly when applied to general nonsmooth optimization problems. We then derive a performance bound on the reconstruction error using these techniques. The bound proves that our methods can recover a signal sparse in a redundant tight frame when the measurement matrix satisfies a properly adapted restricted isometry property. Numerical examples demonstrate the performance of our methods and show that smoothing-based MFISTA converges faster than the decomposition-based alternative in real applications, such as MRI image reconstruction.

IEEE Transactions on Signal Processing, Feb 15, 2017

Sparse linear arrays, such as co-prime arrays and nested arrays, have the attractive capability o... more Sparse linear arrays, such as co-prime arrays and nested arrays, have the attractive capability of providing enhanced degrees of freedom. By exploiting the coarray structure, an augmented sample covariance matrix can be constructed and MUSIC (MUtiple SIgnal Classification) can be applied to identify more sources than the number of sensors. While such a MUSIC algorithm works quite well, its performance has not been theoretically analyzed. In this paper, we derive a simplified asymptotic mean square error (MSE) expression for the MUSIC algorithm applied to the coarray model, which is applicable even if the source number exceeds the sensor number. We show that the directly augmented sample covariance matrix and the spatial smoothed sample covariance matrix yield the same asymptotic MSE for MUSIC. We also show that when there are more sources than the number of sensors, the MSE converges to a positive value instead of zero when the signal-to-noise ratio (SNR) goes to infinity. This finding explains the "saturation" behavior of the coarray-based MUSIC algorithms in the high SNR region observed in previous studies. Finally, we derive the Cramér-Rao bound (CRB) for sparse linear arrays, and conduct a numerical study of the statistical efficiency of the coarray-based estimator. Experimental results verify theoretical derivations and reveal the complex efficiency pattern of coarray-based MUSIC algorithms.

In a recent paper, the authors have explored the use of novel concentration sensors for detecting... more In a recent paper, the authors have explored the use of novel concentration sensors for detecting and localizing vapor-emitting sources. As was shown there, an array of sensors (at least five) is needed for this purpose in general. In the present paper we propose to replace stationary sensors by moving sensors, thus gaining two important advantages: 1) A single moving sensor can accomplish the task of an array of stationary sensors, by exploiting spatial and temporal diversity. 2) The sensor motion can be planned in real time to optimize localization performance, based on past measurements and minimization of the expected localization error as a function of the future sensor's position. The paper describes the details of this approach and illustrates it by an example.

Scientific Reports, Sep 3, 2018

Single-molecule localization microscopy (SMLM) depends on sequential detection and localization o... more Single-molecule localization microscopy (SMLM) depends on sequential detection and localization of individual molecular blinking events. Due to the stochasticity of single-molecule blinking and the desire to improve SMLM's temporal resolution, algorithms capable of analyzing frames with a high density (HD) of active molecules, or molecules whose images overlap, are a prerequisite for accurate location measurements. Thus far, HD algorithms are evaluated using scalar metrics, such as root-mean-square error, that fail to quantify the structure of errors caused by the structure of the sample. Here, we show that the spatial distribution of localization errors within super-resolved images of biological structures are vectorial in nature, leading to systematic structural biases that severely degrade image resolution. We further demonstrate that the shape of the microscope's point-spread function (PSF) fundamentally affects the characteristics of imaging artifacts. We built a Robust Statistical Estimation algorithm (RoSE) to minimize these biases for arbitrary structures and PSFs. RoSE accomplishes this minimization by estimating the likelihood of blinking events to localize molecules more accurately and eliminate false localizations. Using RoSE, we measure the distance between crossing microtubules, quantify the morphology of and separation between vesicles, and obtain robust recovery using diverse 3D PSFs with unmatched accuracy compared to state-of-the-art algorithms. Since its invention, fluorescence imaging has been an indispensable tool for biological studies of cells, tissues, and organisms because of its ability to visualize specific molecules of interest against a dark background in a relatively noninvasive manner. Tagging a biological molecule with a small organic fluorophore or fluorescent protein enables a fluorescence microscope to produce pictures of structures and movies of interactions between molecules within living cells. The optical detection of individual fluorescent molecules in condensed matter 1 is the basis for an entire family of super-resolved fluorescence microscopy techniques 2-5. These methods rely upon the blinking of fluorescent molecules in time to reduce the concentration of active emitters and resolve each molecule in a microscope image 6-8. Repeated cycles of molecular blinking and measurement of molecular positions from their point spread functions (PSFs) by an image analysis algorithm result in reconstructed images of a biological structure with resolution beyond the Abbé diffraction limit (~λ/2NA ≈ 250 nm for visible light, where NA is the numerical aperture of the fluorescence microscope). Here, we refer to these techniques collectively as single-molecule localization microscopy (SMLM). Although the experimenter often chooses imaging conditions to minimize the probability of image overlap between two molecules, the stochasticity of molecular blinking often leads to some overlap in SMLM datasets, especially for complex biological structures with high fluorophore labeling density 9. One may even purposefully increase the density of active fluorescent probes in any given camera acquisition, such that images of neighboring molecules frequently or regularly overlap, in order to improve the temporal resolution of SMLM. Consequently, fewer imaging frames are needed to reconstruct a target structure, thereby leading to decreased phototoxicity as well as a reduction in motion-blur artifacts 10,11. From a statistical perspective, super-resolution imaging in the presence of significant image overlap poses two major problems: (i) identifying the underlying molecules and (ii) estimating their positions and brightnesses. Strategies for resolving overlapping molecules are primarily based on two aspects of prior knowledge: molecules are sparsely distributed in space and they repeatedly and independently blink over time 12. The first strategy recasts the estimation of molecular positions as a sparse recovery optimization problem, where a sparsity prior regulates the solution 13,14. The second approach exploits molecular emission characteristics (e.g., uncorrelated and

IEEE Transactions on Smart Grid, Jul 1, 2014

In an isolated power grid or a micro-grid with a small carbon footprint, the penetration of renew... more In an isolated power grid or a micro-grid with a small carbon footprint, the penetration of renewable energy is usually high. In such power grids, energy storage is important to guarantee an uninterrupted and stable power supply for end users. Different types of energy storage have different characteristics, including their round-trip efficiency, power and energy rating, energy loss over time, and investment and maintenance costs. In addition, the load characteristics and availability of different types of renewable energy sources vary in different geographic regions and at different times of year. Therefore joint capacity optimization for multiple types of energy storage and generation is important when designing this type of power systems. In this paper, we formulate a cost minimization problem for storage and generation planning, considering both the initial investment cost and operational/maintenance cost, and propose a distributed optimization framework to overcome the difficulty brought about by the large size of the optimization problem. The results will help in making decisions on energy storage and generation capacity planning in future decentralized power grids with high renewable penetrations.

IEEE Signal Processing Magazine, Sep 1, 2006

IEEE Transactions on Nanobioscience, Jun 1, 2008

In oligonucleotide microarray experiments, noise is a challenging problem, as biologists now are ... more In oligonucleotide microarray experiments, noise is a challenging problem, as biologists now are studying their organisms not in isolation but in the context of a natural environment. In low photomultiplier tube (PMT) voltage images, weak gene signals and their interactions with the background fluorescence noise are most problematic. In addition, nonspecific sequences bind to array spots intermittently causing inaccurate measurements. Conventional techniques cannot precisely separate the foreground and the background signals. In this paper, we propose analytically based estimation technique. We assume a priori spot-shape information using a circular outer periphery with an elliptical center hole. We assume Gaussian statistics for modeling both the foreground and background signals. The mean of the foreground signal quantifies the weak gene signal corresponding to the spot, and the variance gives the measure of the undesired binding that causes fluctuation in the measurement. We propose a foreground-signal and shapeestimation algorithm using the Gibbs sampling method. We compare our developed algorithm with the existing Mann-Whitney (MW)-and expectation maximization (EM)/iterated conditional modes (ICM)-based methods. Our method outperforms the existing methods with considerably smaller mean-square error (MSE) for all signal-to-noise ratios (SNRs) in computer-generated images and gives better qualitative results in low-SNR real-data images. Our method is computationally relatively slow because of its inherent sampling operation and hence only applicable to very noisy-spot images. In a realistic example using our method, we show that the gene-signal fluctuations on the estimated foreground are better observed for the input noisy images with relatively higher undesired bindings.

IEEE Transactions on Signal Processing, May 1, 2006

Registration is a fundamental step in image processing systems where there is a need to match two... more Registration is a fundamental step in image processing systems where there is a need to match two or more images. Applications include motion detection, target recognition, video processing, and medical imaging. Although a vast number of publications have appeared on image registration, performance analysis is usually performed visually, and little attention has been given to statistical performance bounds. Such bounds can be useful in evaluating image registration techniques, determining parameter regions where accurate registration is possible, and choosing features to be used for the registration. In this paper, Cramér-Rao bounds on a wide variety of geometric deformation models, including translation, rotation, shearing, rigid, more general affine and nonlinear transformations, are derived. For some of the cases, closed-form expressions are given for the maximum-likelihood (ML) estimates, as well as their variances, as space permits. The bounds are also extended to unknown original objects. Numerical examples illustrating the analytical performance bounds are presented.

Neural Information Processing Systems, Dec 8, 2014

The ability to automatically discover patterns and perform extrapolation is an essential quality ... more The ability to automatically discover patterns and perform extrapolation is an essential quality of intelligent systems. Kernel methods, such as Gaussian processes, have great potential for pattern extrapolation, since the kernel flexibly and interpretably controls the generalisation properties of these methods. However, automatically extrapolating large scale multidimensional patterns is in general difficult, and developing Gaussian process models for this purpose involves several challenges. A vast majority of kernels, and kernel learning methods, currently only succeed in smoothing and interpolation. This difficulty is compounded by the fact that Gaussian processes are typically only tractable for small datasets, and scaling an expressive kernel learning approach poses different challenges than scaling a standard Gaussian process model. One faces additional computational constraints, and the need to retain significant model structure for expressing the rich information available in a large dataset. In this paper, we propose a Gaussian process approach for large scale multidimensional pattern extrapolation. We recover sophisticated out of class kernels, perform texture extrapolation, inpainting, and video extrapolation, and long range forecasting of land surface temperatures, all on large multidimensional datasets, including a problem with 383,400 training points. The proposed method significantly outperforms alternative scalable and flexible Gaussian process methods, in speed and accuracy. Moreover, we show that a distinct combination of expressive kernels, a fully non-parametric representation, and scalable inference which exploits existing model structure, are critical for large scale multidimensional pattern extrapolation.

IEEE Transactions on Signal Processing, Nov 1, 2014

IEEE Transactions on Signal Processing, Oct 1, 2008

IEEE Transactions on Signal Processing, Feb 1, 2009

We propose a simple three-dimensional (3-D) direction-finding system that exploits multipath refl... more We propose a simple three-dimensional (3-D) direction-finding system that exploits multipath reflections close to the sensors to improve performance by increasing the effective array aperture. Such close-range multipath reflections can originate, for example, from parts of the platform on which the sensor is mounted. Our system is inspired by the human auditory system where multipath reflections from the external ear (pinna) enable 3-D direction finding. To demonstrate the advantage of exploiting multipath reflections, we consider a simple example of a passive system with only one sensor and two nearby reflectors. First, we present a parametric measurement model and then compute the asymptotic Cramér-Rao bound on the 3-D direction estimates for a stochastic source signal of unknown parametrized spectrum. We provide a few numerical examples to illustrate our analytical results. We find that for this example additional reflectors and a wider source spectrum can achieve better direction estimates.

IEEE Transactions on Signal Processing, Feb 1, 2009

IEEE Transactions on Signal Processing, May 1, 2009

The resolution improvements of time reversal methods through exploiting nonhomogeneous media have... more The resolution improvements of time reversal methods through exploiting nonhomogeneous media have attracted much interest recently with broad applications, including underwater acoustics, radar, detection of defects in metals, communications, and destruction of kidney stones. In this paper, we analyze the effect of inhomogeneity generated by multiple scattering among point scatterers under a multistatic sensing setup. We derive the Cramér-Rao bounds (CRBs) on parameters of the scatterers and compare the CRBs for multiple scattering using the Foldy-Lax model with the reference case without multiple scattering using the Born approximation. We find that multiple scattering could significantly improve the estimation performance of the system and higher order scattering components actually contain much richer information about the scatterers. For the case where multiple scattering is not possible, e.g., where only a single target scatterer exists in the illuminated scenario, we propose the use of artificial scatterers, which could effectively improve the estimation performance of the target despite a decrease in the degrees of freedom of the estimation problem due to the introduced unknown parameters of the artificial scatterers. Numerical examples demonstrate the advantages of the artificial scatterers.

IEEE Transactions on Signal Processing, Sep 1, 2007

Time-reversal methods have attracted increasing interest recently. The so-called computational ti... more Time-reversal methods have attracted increasing interest recently. The so-called computational time-reversal approach creates an image of the illuminated scene by computing the back-propagated field and is useful for detecting and estimating targets in the scene. In Shi and Nehorai ["Maximum Likelihood Estimation of Point Scatterers for Computational Time-Reversal Imaging," Communications in Information and Systems, vol. 5, no. 2, pp. 227-256, 2005], we estimated point scatterers by maximum-likelihood estimate (MLE) using the Born-approximated physical model, as well as the Foldy-Lax model. In this correspondence, we further find an explicit relationship between energy-based basic time-reversal imaging and the MLE approach: the time-reversal imaging function differs by only a scaling factor from the likelihood imaging function using the estimated scattering potential when a single-scatterer model is employed. Furthermore, this scaling factor is a function of the imaging position only. We show that, as a result, time-reversal imaging has a near-far problem that tends to produce a weaker image for areas further away from the imaging arrays, whereas the MLE-based image is more balanced. Experimental results confirm this conclusion.

IEEE Transactions on Signal Processing, 2020

We investigate the one-bit MIMO (1b-MIMO) radar that performs one-bit sampling with a time-varyin... more We investigate the one-bit MIMO (1b-MIMO) radar that performs one-bit sampling with a time-varying threshold in the temporal domain and employs compressive sensing in the spatial and Doppler domains. The goals are to significantly reduce the hardware cost, energy consumption, and amount of stored data. The joint angle and Doppler frequency estimations from noisy one-bit data are studied. By showing that the effect of noise on one-bit sampling is equivalent to that of sparse impulsive perturbations, we formulate the one-bit ℓ1-regularized atomicnorm minimization (1b-ANM-L1) problem to achieve gridless parameter estimation with high accuracy. We also develop an iterative method for solving the 1b-ANM-L1 problem via the alternating direction method of multipliers. The Cramér-Rao bound (CRB) of the 1b-MIMO radar is analyzed, and the analytical performance of one-bit sampling with two different threshold strategies is discussed. Numerical experiments are presented to show that the 1b-MIMO radar can achieve highresolution parameter estimation with a largely reduced amount of data.

IEEE Transactions on Signal Processing, Apr 1, 2014

We consider algorithms and recovery guarantees for the analysis sparse model in which the signal ... more We consider algorithms and recovery guarantees for the analysis sparse model in which the signal is sparse with respect to a highly coherent frame. We consider the use of a monotone version of the fast iterative shrinkagethresholding algorithm (MFISTA) to solve the analysis sparse recovery problem. Since the proximal operator in MFISTA does not have a closed-form solution for the analysis model, it cannot be applied directly. Instead, we examine two alternatives based on smoothing and decomposition transformations that relax the original sparse recovery problem, and then implement MFISTA on the relaxed formulation. We refer to these two methods as smoothing-based and decomposition-based MFISTA. We analyze the convergence of both algorithms, and establish that smoothingbased MFISTA converges more rapidly when applied to general nonsmooth optimization problems. We then derive a performance bound on the reconstruction error using these techniques. The bound proves that our methods can recover a signal sparse in a redundant tight frame when the measurement matrix satisfies a properly adapted restricted isometry property. Numerical examples demonstrate the performance of our methods and show that smoothing-based MFISTA converges faster than the decomposition-based alternative in real applications, such as MRI image reconstruction.

IEEE Transactions on Signal Processing, Feb 15, 2017

Sparse linear arrays, such as co-prime arrays and nested arrays, have the attractive capability o... more Sparse linear arrays, such as co-prime arrays and nested arrays, have the attractive capability of providing enhanced degrees of freedom. By exploiting the coarray structure, an augmented sample covariance matrix can be constructed and MUSIC (MUtiple SIgnal Classification) can be applied to identify more sources than the number of sensors. While such a MUSIC algorithm works quite well, its performance has not been theoretically analyzed. In this paper, we derive a simplified asymptotic mean square error (MSE) expression for the MUSIC algorithm applied to the coarray model, which is applicable even if the source number exceeds the sensor number. We show that the directly augmented sample covariance matrix and the spatial smoothed sample covariance matrix yield the same asymptotic MSE for MUSIC. We also show that when there are more sources than the number of sensors, the MSE converges to a positive value instead of zero when the signal-to-noise ratio (SNR) goes to infinity. This finding explains the "saturation" behavior of the coarray-based MUSIC algorithms in the high SNR region observed in previous studies. Finally, we derive the Cramér-Rao bound (CRB) for sparse linear arrays, and conduct a numerical study of the statistical efficiency of the coarray-based estimator. Experimental results verify theoretical derivations and reveal the complex efficiency pattern of coarray-based MUSIC algorithms.

In a recent paper, the authors have explored the use of novel concentration sensors for detecting... more In a recent paper, the authors have explored the use of novel concentration sensors for detecting and localizing vapor-emitting sources. As was shown there, an array of sensors (at least five) is needed for this purpose in general. In the present paper we propose to replace stationary sensors by moving sensors, thus gaining two important advantages: 1) A single moving sensor can accomplish the task of an array of stationary sensors, by exploiting spatial and temporal diversity. 2) The sensor motion can be planned in real time to optimize localization performance, based on past measurements and minimization of the expected localization error as a function of the future sensor's position. The paper describes the details of this approach and illustrates it by an example.

Scientific Reports, Sep 3, 2018

Single-molecule localization microscopy (SMLM) depends on sequential detection and localization o... more Single-molecule localization microscopy (SMLM) depends on sequential detection and localization of individual molecular blinking events. Due to the stochasticity of single-molecule blinking and the desire to improve SMLM's temporal resolution, algorithms capable of analyzing frames with a high density (HD) of active molecules, or molecules whose images overlap, are a prerequisite for accurate location measurements. Thus far, HD algorithms are evaluated using scalar metrics, such as root-mean-square error, that fail to quantify the structure of errors caused by the structure of the sample. Here, we show that the spatial distribution of localization errors within super-resolved images of biological structures are vectorial in nature, leading to systematic structural biases that severely degrade image resolution. We further demonstrate that the shape of the microscope's point-spread function (PSF) fundamentally affects the characteristics of imaging artifacts. We built a Robust Statistical Estimation algorithm (RoSE) to minimize these biases for arbitrary structures and PSFs. RoSE accomplishes this minimization by estimating the likelihood of blinking events to localize molecules more accurately and eliminate false localizations. Using RoSE, we measure the distance between crossing microtubules, quantify the morphology of and separation between vesicles, and obtain robust recovery using diverse 3D PSFs with unmatched accuracy compared to state-of-the-art algorithms. Since its invention, fluorescence imaging has been an indispensable tool for biological studies of cells, tissues, and organisms because of its ability to visualize specific molecules of interest against a dark background in a relatively noninvasive manner. Tagging a biological molecule with a small organic fluorophore or fluorescent protein enables a fluorescence microscope to produce pictures of structures and movies of interactions between molecules within living cells. The optical detection of individual fluorescent molecules in condensed matter 1 is the basis for an entire family of super-resolved fluorescence microscopy techniques 2-5. These methods rely upon the blinking of fluorescent molecules in time to reduce the concentration of active emitters and resolve each molecule in a microscope image 6-8. Repeated cycles of molecular blinking and measurement of molecular positions from their point spread functions (PSFs) by an image analysis algorithm result in reconstructed images of a biological structure with resolution beyond the Abbé diffraction limit (~λ/2NA ≈ 250 nm for visible light, where NA is the numerical aperture of the fluorescence microscope). Here, we refer to these techniques collectively as single-molecule localization microscopy (SMLM). Although the experimenter often chooses imaging conditions to minimize the probability of image overlap between two molecules, the stochasticity of molecular blinking often leads to some overlap in SMLM datasets, especially for complex biological structures with high fluorophore labeling density 9. One may even purposefully increase the density of active fluorescent probes in any given camera acquisition, such that images of neighboring molecules frequently or regularly overlap, in order to improve the temporal resolution of SMLM. Consequently, fewer imaging frames are needed to reconstruct a target structure, thereby leading to decreased phototoxicity as well as a reduction in motion-blur artifacts 10,11. From a statistical perspective, super-resolution imaging in the presence of significant image overlap poses two major problems: (i) identifying the underlying molecules and (ii) estimating their positions and brightnesses. Strategies for resolving overlapping molecules are primarily based on two aspects of prior knowledge: molecules are sparsely distributed in space and they repeatedly and independently blink over time 12. The first strategy recasts the estimation of molecular positions as a sparse recovery optimization problem, where a sparsity prior regulates the solution 13,14. The second approach exploits molecular emission characteristics (e.g., uncorrelated and

IEEE Transactions on Smart Grid, Jul 1, 2014

In an isolated power grid or a micro-grid with a small carbon footprint, the penetration of renew... more In an isolated power grid or a micro-grid with a small carbon footprint, the penetration of renewable energy is usually high. In such power grids, energy storage is important to guarantee an uninterrupted and stable power supply for end users. Different types of energy storage have different characteristics, including their round-trip efficiency, power and energy rating, energy loss over time, and investment and maintenance costs. In addition, the load characteristics and availability of different types of renewable energy sources vary in different geographic regions and at different times of year. Therefore joint capacity optimization for multiple types of energy storage and generation is important when designing this type of power systems. In this paper, we formulate a cost minimization problem for storage and generation planning, considering both the initial investment cost and operational/maintenance cost, and propose a distributed optimization framework to overcome the difficulty brought about by the large size of the optimization problem. The results will help in making decisions on energy storage and generation capacity planning in future decentralized power grids with high renewable penetrations.

IEEE Signal Processing Magazine, Sep 1, 2006

IEEE Transactions on Nanobioscience, Jun 1, 2008

In oligonucleotide microarray experiments, noise is a challenging problem, as biologists now are ... more In oligonucleotide microarray experiments, noise is a challenging problem, as biologists now are studying their organisms not in isolation but in the context of a natural environment. In low photomultiplier tube (PMT) voltage images, weak gene signals and their interactions with the background fluorescence noise are most problematic. In addition, nonspecific sequences bind to array spots intermittently causing inaccurate measurements. Conventional techniques cannot precisely separate the foreground and the background signals. In this paper, we propose analytically based estimation technique. We assume a priori spot-shape information using a circular outer periphery with an elliptical center hole. We assume Gaussian statistics for modeling both the foreground and background signals. The mean of the foreground signal quantifies the weak gene signal corresponding to the spot, and the variance gives the measure of the undesired binding that causes fluctuation in the measurement. We propose a foreground-signal and shapeestimation algorithm using the Gibbs sampling method. We compare our developed algorithm with the existing Mann-Whitney (MW)-and expectation maximization (EM)/iterated conditional modes (ICM)-based methods. Our method outperforms the existing methods with considerably smaller mean-square error (MSE) for all signal-to-noise ratios (SNRs) in computer-generated images and gives better qualitative results in low-SNR real-data images. Our method is computationally relatively slow because of its inherent sampling operation and hence only applicable to very noisy-spot images. In a realistic example using our method, we show that the gene-signal fluctuations on the estimated foreground are better observed for the input noisy images with relatively higher undesired bindings.

IEEE Transactions on Signal Processing, May 1, 2006

Registration is a fundamental step in image processing systems where there is a need to match two... more Registration is a fundamental step in image processing systems where there is a need to match two or more images. Applications include motion detection, target recognition, video processing, and medical imaging. Although a vast number of publications have appeared on image registration, performance analysis is usually performed visually, and little attention has been given to statistical performance bounds. Such bounds can be useful in evaluating image registration techniques, determining parameter regions where accurate registration is possible, and choosing features to be used for the registration. In this paper, Cramér-Rao bounds on a wide variety of geometric deformation models, including translation, rotation, shearing, rigid, more general affine and nonlinear transformations, are derived. For some of the cases, closed-form expressions are given for the maximum-likelihood (ML) estimates, as well as their variances, as space permits. The bounds are also extended to unknown original objects. Numerical examples illustrating the analytical performance bounds are presented.

Neural Information Processing Systems, Dec 8, 2014

The ability to automatically discover patterns and perform extrapolation is an essential quality ... more The ability to automatically discover patterns and perform extrapolation is an essential quality of intelligent systems. Kernel methods, such as Gaussian processes, have great potential for pattern extrapolation, since the kernel flexibly and interpretably controls the generalisation properties of these methods. However, automatically extrapolating large scale multidimensional patterns is in general difficult, and developing Gaussian process models for this purpose involves several challenges. A vast majority of kernels, and kernel learning methods, currently only succeed in smoothing and interpolation. This difficulty is compounded by the fact that Gaussian processes are typically only tractable for small datasets, and scaling an expressive kernel learning approach poses different challenges than scaling a standard Gaussian process model. One faces additional computational constraints, and the need to retain significant model structure for expressing the rich information available in a large dataset. In this paper, we propose a Gaussian process approach for large scale multidimensional pattern extrapolation. We recover sophisticated out of class kernels, perform texture extrapolation, inpainting, and video extrapolation, and long range forecasting of land surface temperatures, all on large multidimensional datasets, including a problem with 383,400 training points. The proposed method significantly outperforms alternative scalable and flexible Gaussian process methods, in speed and accuracy. Moreover, we show that a distinct combination of expressive kernels, a fully non-parametric representation, and scalable inference which exploits existing model structure, are critical for large scale multidimensional pattern extrapolation.

IEEE Transactions on Signal Processing, Nov 1, 2014

IEEE Transactions on Signal Processing, Oct 1, 2008

IEEE Transactions on Signal Processing, Feb 1, 2009

We propose a simple three-dimensional (3-D) direction-finding system that exploits multipath refl... more We propose a simple three-dimensional (3-D) direction-finding system that exploits multipath reflections close to the sensors to improve performance by increasing the effective array aperture. Such close-range multipath reflections can originate, for example, from parts of the platform on which the sensor is mounted. Our system is inspired by the human auditory system where multipath reflections from the external ear (pinna) enable 3-D direction finding. To demonstrate the advantage of exploiting multipath reflections, we consider a simple example of a passive system with only one sensor and two nearby reflectors. First, we present a parametric measurement model and then compute the asymptotic Cramér-Rao bound on the 3-D direction estimates for a stochastic source signal of unknown parametrized spectrum. We provide a few numerical examples to illustrate our analytical results. We find that for this example additional reflectors and a wider source spectrum can achieve better direction estimates.

IEEE Transactions on Signal Processing, Feb 1, 2009