Detection & Estimation

Temperature estimation for a plasma-propelled rocket engine

by Shane Lynn

IEEE Control Systems Magazine (Applications of Control) (Dec. 2009)
Co-authored with John V. Ringwood and J. I. del Valle Gamboa

The VASIMR propulsion system is an ion propulsion system for spacecraft that uses magnetic fields to accelerate plasma... more The VASIMR propulsion system is an ion propulsion system for spacecraft that uses magnetic fields to accelerate plasma to produce thrust. Undesired heat produced in the helicon section of VASIMR must be monitored and removed safely to avoid damage to system components, especially when higher power operating regimes are explored. This article demonstrates a strategy for distributed temperature estimation, based on OES measurement, and a model where the states represent the distributed temperature profile. OES provides a noninvasive measurement technique, which can be used as an output "correction" term for a state-estimation scheme. In this application, it is shown that the 2048 OES channels recorded can be accurately represented by only three principal components for temperature estimation. Use of the principal components as corrector terms in the state-space model dramatically improve model accuracy and the capability of the model to recover from unknown initial conditions and multiple system input changes.

Estimation and Control in Semiconductor Etch: Practice and Possibilities

by Shane Lynn

IEEE Transactions in Semiconductor Manufacturing. Vol. 23, No. 1, Feb 2010.

Semiconductor wafer etching is, to a large extent, an open-loop process with little direct feedback control. Most... more Semiconductor wafer etching is, to a large extent, an open-loop process with little direct feedback control. Most silicon chip manufacturers rely on the rigorous adherence to a “recipe” for the various etch processes, which have been built up based on considerable historical experience. However, residue buildup and difficulties in achieving consistent preventative maintenance operations lead to drifts and step changes in process characteristics. This paper examines the particular technical difficulties encountered in achieving consistency in the etching of semiconductor wafers and documents the range of estimation and control techniques currently available to address these difficulties. An important feature of such an assessment is the range of measurement options available if closed-loop control is to be achieved.

Judgmental Decomposition: When Does It Work?

by J Armstrong

Co-authored with Donald G. MacGregor. Published in International Journal of Forecasting, 10 (1994), 495-906.

We hypothesized that multiplicative decomposition would improve accuracy only in certain conditions. In particular, we... more We hypothesized that multiplicative decomposition would improve accuracy only in certain conditions. In particular, we expected it to help for problems involving extreme and uncertain
values. We first reanalyzed results from two published studies. Decomposition improved accuracy for nine problems that involved extreme and uncertain values, but for six problems with target values that were not extreme and uncertain, decomposition was not more accurate. Next,we conducted experiments involving 10 problems with 280 subjects making 1078 estimates. As hypothesized, decomposition improved accuracy when the problem involved the estimation of extreme and uncertain values. Otherwise, decomposition often produced  ess accurate predictions.

Random observations on random observations: Sparse signal acquisition and processing

by Mark Davenport

Ph.D. Thesis, Rice University, August 2010. (Winner of 2011 Ralph Budd Award from Rice University for best thesis in the School of Engineering.)

In recent years, signal processing has come under mounting pressure to accommodate the increasingly high-dimensional... more In recent years, signal processing has come under mounting pressure to accommodate the increasingly high-dimensional raw data generated by modern sensing systems. Despite extraordinary advances in computational power, processing the
signals produced in application areas such as imaging, video, remote surveillance, spectroscopy, and genomic data analysis continues to pose a tremendous challenge. Fortunately, in many cases these high-dimensional signals contain relatively little information compared to their ambient dimensionality. For example, signals can often be well-approximated as a sparse linear combination of elements from a known basis or dictionary.

Traditionally, sparse models have been exploited only after acquisition, typically for tasks such as compression. Recently, however, the applications of sparsity have greatly expanded with the emergence of compressive sensing, a new approach to data acquisition that directly exploits sparsity in order to acquire analog signals more efficiently via a small set of more general, often randomized, linear measurements. If properly chosen, the number of measurements can be much smaller than the number of Nyquist-rate samples. A common theme in this research is the use of randomness in signal acquisition, inspiring the design of hardware systems that directly implement random measurement protocols.

This thesis builds on the field of compressive sensing and illustrates how sparsity can be exploited to design efficient signal processing algorithms at all stages of the information processing pipeline, with a particular focus on the manner in which randomness can be exploited to design new kinds of acquisition systems for sparse signals. Our key contributions include: (i) exploration and analysis of the appropriate properties for a sparse signal acquisition system; (ii) insight into the useful properties of random measurement schemes; (iii) analysis of an important family of algorithms for recovering sparse signals from random measurements; (iv) exploration of the impact of noise, both structured and unstructured, in the context of random measurements; and (v) algorithms that process random measurements to directly extract higher-level information or solve inference problems without resorting to full-scale signal recovery, reducing both the cost of signal acquisition and the complexity of the post-acquisition processing.

Signal processing with compressive measurements

by Mark Davenport

Co-authored with P.T. Boufounos, M.B. Wakin, and R.G. Baraniuk. (IEEE J. of Selected Topics in Signal Processing, 4(2) pp. 445-460, April 2010.)

The recently introduced theory of compressive sensing enables the recovery of sparse or compressible signals from a... more The recently introduced theory of compressive sensing enables the recovery of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be much smaller than the number of Nyquist-rate samples. Interestingly, it has been shown that random projections are a near-optimal measurement scheme. This has inspired the design of hardware systems that directly implement random measurement protocols. However, despite the intense focus of the community on signal recovery, many (if not most) signal processing problems do not require full signal recovery. In this paper, we take some first steps in the direction of solving inference problems-such as detection, classification, or estimation-and filtering problems using only compressive measurements and without ever reconstructing the signals involved. We provide theoretical bounds along with experimental results.

Manifold-based approaches for improved classification

by Mark Davenport

Co-authored with C. Hegde, M.B. Wakin, and R.G. Baraniuk. (NIPS Workshop on Topology Learning, Whistler, Canada, December 2007.)

While manifold structure is often exploited for dimensionality reduction or feature extraction, this structure is... more While manifold structure is often exploited for dimensionality reduction or feature extraction, this structure is rarely used by classification algorithms. We present a class of algorithms that utilize the low-dimensional manifold nature of signal ensembles and result in improved classification performance. The algorithms are built within theoretical frameworks that take into consideration prior knowledge of geometric structure in both labeled and unlabeled data points. Additionally, these frameworks can exploit recent results on random projections of smooth manifolds to ensure computational feasibility on extremely high-dimensional problems.

Efficient machine learning using random projections

by Mark Davenport

Co-authored with C. Hegde, M.B. Wakin, and R.G. Baraniuk. (NIPS Workshop on Efficient Machine Learning, Whistler, Canada, December 2007.)

As an alternative to cumbersome nonlinear schemes for dimensionality reduction, the technique of random linear... more As an alternative to cumbersome nonlinear schemes for dimensionality reduction, the technique of random linear projection has recently emerged as a viable alternative for storage and rudimentary processing of high-dimensional data. We invoke new theory to motivate the following claim: the random projection method may be used in conjunction with standard algorithms for a multitude of machine learning tasks, with virtually no degradation in performance. Thus, random projections can been shown to result in both significant computational savings and provably good performance.

Multiscale random projections for compressive classification

by Mark Davenport

Co-authored with M.F. Duarte, M.B. Wakin, J.N. Laska, D. Takhar, K.F. Kelly, and R.G. Baraniuk. (Proc. IEEE International Conference on Image Processing (ICIP), San Antonio, Texas, September 2007.)

We propose a framework for exploiting dimension-reducing random projections in detection and classification problems.... more We propose a framework for exploiting dimension-reducing random projections in detection and classification problems. Our approach is based on the generalized likelihood ratio test; in the case of image classification, it exploits the fact that a set of images of a fixed scene under varying articulation parameters forms a low-dimensional, nonlinear manifold. Exploiting recent results showing that random projections stably embed a smooth manifold in a lower-dimensional space, we develop the multiscale smashed filter as a compressive analog of the familiar matched filter classifier. In a practical target classification problem using a single-pixel camera that directly acquires compressive image projections, we achieve high classification rates using many fewer measurements than the dimensionality of the images.

The smashed filter for compressive classification and target recognition

by Mark Davenport

Co-authored with M.F. Duarte, M.B. Wakin, J.N. Laska, D. Takhar, K.F. Kelly, and R.G. Baraniuk. (Proc. Computational Imaging V at SPIE Electronic Imaging, San Jose, California, January 2007.)

The theory of compressive sensing (CS) enables the reconstruction of a sparse or compressible image or signal from a... more The theory of compressive sensing (CS) enables the reconstruction of a sparse or compressible image or signal from a small set of linear, non-adaptive (even random) projections. However, in many applications, including object and target recognition, we are ultimately interested in making a decision about an image rather than computing a reconstruction. We propose here a framework for compressive classification that operates directly on the compressive measurements without first reconstructing the image. We dub the resulting dimensionally reduced matched filter the smashed filter. The first part of the theory maps traditional maximum likelihood hypothesis testing into the compressive domain; we find that the number of measurements required for a given classification performance level does not depend on the sparsity or compressibility of the images but only on the noise level. The second part of the theory applies the generalized maximum likelihood method to deal with unknown transformations such as the translation, scale, or viewing angle of a target object. We exploit the fact the set of transformed images forms a low-dimensional, nonlinear manifold in the high-dimensional image space. We find that the number of measurements required for a given classification performance level grows linearly in the dimensionality of the manifold but only logarithmically in the number of pixels/samples and image classes. Using both simulations and measurements from a new single-pixel compressive camera, we demonstrate the effectiveness of the smashed filter for target classification using very few measurements.

Scalable inference and recovery from compressive measurements

by Mark Davenport

Co-authored with R.G. Baraniuk and M.B. Wakin. (NIPS Workshop on Novel Applications of Dimensionality Reduction, Whistler, Canada, December 2006.)

Despite the apparent need for adaptive, nonlinear techniques for dimensionality reduction, random linear projections... more Despite the apparent need for adaptive, nonlinear techniques for dimensionality reduction, random linear projections have proven to be extremely effective at capturing signal structure in cases where the signal obeys a low-dimensional model. Similarly, random projections are a useful tool for solving problems where the ultimate question of interest about the data requires a small amount of information compared to the dimensionality of the data itself. The success of random projections in both of these arenas can be traced to an elementary concentration of measure property, which allows us to extend the utility of random projections to a variety of new signal models and applications.

Detection and estimation with compressive measurements

by Mark Davenport

Co-authored with M.B. Wakin and R.G. Baraniuk. (Rice University ECE Technical Report TREE 0610, November 2006. Originally titled "The Compressive Matched Filter".)

The recently introduced theory of compressed sensing enables the reconstruction of sparse or compressible signals from... more The recently introduced theory of compressed sensing enables the reconstruction of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be much smaller than the number of Nyquist rate samples. Interestingly, it has been shown that random projections are a satisfactory measurement scheme. This has inspired the design of physical systems that directly implement similar measurement schemes. However, despite the intense focus on the reconstruction of signals, many (if not most) signal processing problems do not require a full reconstruction of the signal—we are often interested only in solving some sort of detection problem or in the estimation of some function of the data. In this report, we show that the compressed sensing framework is useful for a wide range of statistical inference tasks. In particular, we demonstrate how to solve a variety of signal detection and estimation problems given the measurements without ever reconstructing the signals themselves. We provide theoretical bounds along with experimental results.

Sparse signal detection from incoherent projections

by Mark Davenport

Co-authored with M.F. Duarte, M.W. Wakin, and R.G. Baraniuk. (Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Toulouse, France, May 2006.)

The recently introduced theory of Compressed Sensing (CS) enables the reconstruction or approximation of sparse or... more The recently introduced theory of Compressed Sensing (CS) enables the reconstruction or approximation of sparse or compressible signals from a small set of incoherent projections; often the number of projections can be much smaller than the number of Nyquist rate samples. In this paper, we show that the CS framework is information scalable to a wide range of statistical inference tasks. In particular, we demonstrate how CS principles can solve signal detection problems given incoherent measurements without ever reconstructing the signals involved. We specifically study the case of signal detection in strong inference and noise and propose an Incoherent Detection and Estimation Algorithm (IDEA) based on Matching Pursuit. The number of measurements and computations necessary for successful detection using IDEA is significantly lower than that necessary for successful reconstruction. Simulations show that IDEA is very resilient to strong interference, additive noise, and measurement quantization. When combined with random measurements, IDEA is applicable to a wide range of different signal classes.

Finding the closest lattice point by iterative slicing

by ofir shalvi

published on: SIAM Journal of Discrete Math, vol. 29(2), 2009

Accurate and efficient implementation of the time-frequency matched filter

by John M. O' Toole

J. M. O’ Toole, M. Mesbah, and B. Boashash, “Accurate and efficient implementation of the time-frequency matched filter,” IET Signal Processing, vol. 4, no. 4, pp. 428-437, 2010.

The discrete time–frequency matched filter should replicate the continuous time–frequency matched filter, but the... more The discrete time–frequency matched filter should replicate the continuous time–frequency matched filter, but the methods differ. To avoid aliasing, the discrete method transforms the real-valued signal to the complex-valued analytic signal. The theory for the time–frequency matched filter does not consider the discrete case using the analytic signal. The authors find that the performance of the matched filter degrades when using the analytic, rather than real-valued, signal. This performance degradation is dependent on the signal-to-noise ratio and the signal type. In addition, the authors present a simple algorithm to efficiently compute the time–frequency matched filter. The algorithm with the real-valued signal, comparative to using the analytic signal, requires one-quarter of the computational load. Hence the real-valued signal – and not the analytic signal – enables an accurate and efficient implementation of the time–frequency matched filter.

Time-frequency detection of slowly varying periodic signals with harmonics: methods and performance evaluation

by John M. O' Toole

J. M. O’Toole and B. Boashash, “Time-frequency detection of slowly varying periodic signals with harmonics: methods and performance evaluation,” EURASIP Journal on Advances in Signal Processing, vol. 2011, no. 193797, pp. 1-16, 2011

We consider the problem of detecting an unknown signal from an unknown noise type. We restrict the signal type to a... more We consider the problem of detecting an unknown signal from an unknown noise type. We restrict the signal type to a class of slowly varying periodic signalswith harmonic components, a classwhich includes real signals such as the electroencephalogramor speech signals. This paper presents twomethods designed to detect these signal types: the ambiguity filter and the time-frequency correlator. Bothmethods are based on different modifications of the time-frequency-matched filter and bothmethods attempt to overcome the problem of predefining the template set for the matched filter. The ambiguity filter method reduces the number of required templates by one half; the time-frequency correlator method does not require a predefined template set at all. To evaluate their detection performance, we test themethods using simulated and real data sets. Experiential results showthat the two proposed methods, relative to the time-frequency-matched filter, can more accurately detect speech signals and other simulated signals in the presence of colouredGaussian noise. Results also showthat all time-frequency methods outperformthe classical time-domain- matched filter for both simulated and real signals, thus demonstrating the utility of the time-frequency detection approach.

Noise Estimation in Long-Range Matched-Filter Envelope Sonar Data

by Robert Bareš

Co-authored with Dafydd Evans and Stephen Long
published in the IEEE Journal of Oceanic Engineering, April 2010

In sonar signal processing when selecting a threshold for detection, it is necessary to consider the noise in the... more In sonar signal processing when selecting a threshold for detection, it is necessary to consider the noise in the signal to achieve the desired rates of detection and false alarm. The clutter component of this noise, caused by scattering from environmental features, is often a limiting factor. This is particularly the case when active sonar systems operate in shallow water. Therefore, suitable modeling of clutter-limited data is vital for accurate detection in such environments. This paper investigates the K-distribution, the Weibull distribution, and the log-normal distribution as models for clutter-limited matched-filter envelope sonar data, obtained using FM chirp pulses in a shallow-water environment. The models are evaluated using modified Kolmogorov-Smirnov (KS) and Anderson-Darling (AD) tests. Critical values for the upper tail AD statistic applied to the K-distribution are estimated by Monte Carlo simulation and tabulated here. Results show that the K-distribution and the Weibull distribution provide a good model of noise in clutter-limited environments. However, the K-distribution provides a better fit in the tails, which is important for target detection. The Kolmogorov-Smirnov test is shown to be an unsuitable method of evaluating fit when the tail of a distribution is of greatest interest. We also show that the estimated shape parameter of the K-distribution does provide a simple means of identifying regions dominated by clutter.

Particle Filters In Decision Making Problems Under Uncertainty

by jurica cerovec