In this paper, we apply the Weyl transform to represent the vocalization of marine mammals. In contrast to other popular representation methods, such as the MFCC and the Chirplet transform, the Weyl transform captures the global information of signals. This is especially useful when the signal has low order polynomial phase. We can reconstruct the signal from the coefficients obtained from the Weyl transform, and perform classification based on these coefficients. Experimental results show that classification using features extracted from the Weyl transform outperforms the MFCC and the Chirplet transform on our collected whales data.

Mammography is currently the most widely utilized tool for detection and diagnosis of breast cancer. However, in women with dense breast tissue, tissue overlap may obscure lesions. Digital breast tomosynthesis can reduce tissue overlap. Furthermore, imaging with contrast enhancement can provide additional functional information about lesions, such as morphology and kinetics, which in turn may improve lesion identification and characterization. The performance of these imaging techniques is strongly dependent on the structural composition of the breast, which varies significantly among patients. Therefore, imaging system and imaging technique optimization should take patient variability into consideration. Furthermore, optimization of imaging techniques that employ contrast agents should include the temporally varying breast composition with respect to the contrast agent uptake kinetics. To these ends, we have developed a suite of 4-D virtual breast phantoms, which are incorporated with the kinetics of contrast agent propagation in different tissues and can realistically model normal breast parenchyma as well as benign and malignant lesions. This development presents a new approach in performing simulation studies using truly anthropomorphic models. To demonstrate the utility of the proposed 4-D phantoms, we present a simplified example study to compare the performance of 14 imaging paradigms qualitatively and quantitatively.

Current mammographic screening for breast cancer is less effective for younger women. To complement mammography for premenopausal women, we investigated the feasibility screening test using 98 blood serum proteins. Because the data set was very noisy and contained only weak features, we used a classifier designed for noisy data: decision fusion. Decision fusion outperformed both a support vector machine (SVM) and linear regression with forward stepwise feature selection on all three two-class classification tasks: normal tissue vs. cancer, normal tissue vs. benign lesions, and benign lesions vs. cancer. Decision fusion detected cancer moderately well (AUC=0.84 on normal vs. cancer), demonstrating promise as a screening tool. Decision fusion also detected benign lesions similarly well (AUC=0.83 on normal vs. benign lesions) and was the only classifier to achieve any success in separating benign from malignant lesions (AUC=0.64 on benign vs. cancer). The classification results suggest that the assayed proteins are more indicative of a secondary effect, such as immune response, rather than specific for breast cancer. In conclusion, the decision fusion classifier demonstrated some promise in detecting breast lesions and outperformed other classifiers, especially for the very noisy classification problem of distinguishing benign from malignant lesions.

Numerous detection algorithms, using various sensor modalities, have been developed for the detection of mines in cluttered and noisy backgrounds. The performance for each detection algorithm is typically reported in terms of the receiver operating characteristic (ROC), which is a plot of the probability of detection versus false alarm as a function of the threshold setting on the output decision variable of each algorithm. In this paper, we present multisensor decision-fusion algorithms that combine the local decisions of existing detection algorithms for different sensors. This offers an expedient, attractive, and much simpler alternative to the design of an algorithm that fuses multiple sensors at the data level, especially in cases of limited training data where it is difficult to make accurate estimates of multidimensional probability density functions. The goal of our multisensor decision-fusion approach is to exploit the complimentary strengths of existing multisensor algorithms so as to achieve performance (ROC) that exceeds the performance of any sensor algorithm operating in isolation. Our approach to multisensor decision fusion is based on the optimal signal detection theory using the likelihood ratio. We consider the optimal fusion of local decisions for two sensors: a ground-penetrating radar and a metal detector. A new robust algorithm for decision fusion that addresses the problem in which the statistics of the training data are not likely to exactly match the statistics of the test data is presented. ROCs are presented and compared for field data

The signal-to-noise ratio of real data is rarely known with complete certainty. However, Bayesian matched-field processing techniques for ocean acoustic source localization often require the signal-to-noise ratio (SNR) to be known a priori. In this paper, the effects of SNR mismatch on the performance of a Bayesian matched-field source localization method, the optimum uncertain field processor (A.M. Richardson and L.W. Nolte, J. Acoust. Soc. Am. vol.89, no.5, 2280-4 (1991)), are investigated. Theoretical and empirical analyses show that when the maximum a posteriori (MAP) estimate is utilized as the source location estimate, the localization performance is unaffected by the uncertainty regarding the SNR, provided that the assumed SNR is sufficiently high.

A wideband optimum uncertain field processor (OUFP) is presented, which when combined with Monte Carlo techniques, provides a computationally efficient and robust technique for matched-field processing (MFP). Under a simulated Hudson Canyon environment, a quantitative, probabilistic analysis of the sensitivity of matched field processing, assuming a known ocean (OMFP), to various kinds of environmental mismatch is shown. Similarly, the performance of the OUFP is calculated. Finally, it is shown that the localization performance of the wideband OUFP and the suboptimum Bartlett processor are in very good agreement with the performance predicted from the simulation results.

Multilayer perceptrons trained with the backpropagation algorithm are tested in detection and classification tasks and are compared to optimal algorithms resulting from likelihood ratio tests. The focus is on the problem of one of M orthogonal signals in a Gaussian noise environment, since both the Bayesian detector and classifier are known for this problem and can provide a measure for the performance evaluation of the neural networks. Two basic situations are considered: detection and classification. For the detection part, it was observed that for the signal-known-exactly case (M=1), the performance of the neural detector converges to the performance of the ideal Bayesian decision processor, while for a higher degree of uncertainty (i.e. for a larger M), the performance of the multilayer perceptron is inferior to that of the optimal detector. For the classification case, the probability of error of the neural network is comparable to the minimum Bayesian error, which can be numerically calculated. Adding noise during the training stage of the network does not affect the performance of the neural detector; however, there is an indication that the presence of noise in the learning process of the neural classifier results in a degraded classification performance.

A neural network detector is compared to an optimal algorithm from signal detection theory for the problem of one of M orthogonal signals in a Gaussian noise environment. A receiver operator characteristics (ROC) analysis is used. The neural detector is a multilayer perceptron trained with the backpropagation algorithm, while the optimal detector operates based on a likelihood ratio test. It was observed that for the signal-known-exactly case (M=1) the performance of the neural detector converges to the performance of the ideal Bayesian decision processor; however, for a higher degree of uncertainty (i.e., for a larger M) the performance of the multilayer perceptron is obviously inferior to that of the optimal detector. In addition, it was concluded that noise information in the training stage affects only slightly the performance of the neural detector. However, the knowledge of the noise distribution proved to be vital for the detection theory processor.>

Examines the performance of signal detectors when processors can have faults. The fault tolerance of two systems, the redundant system and the distributed fusion network, are examined. The optimal fault-tolerant design for each system is presented. The performance of the fault-tolerant systems is compared to the faulty simplex processor. In the absence of processor failures, the redundant system is identical to the simplex processor. However, when failures occur, the redundant system performs better than the simplex processor. The fault-free fusion network does not perform as well as the fault-free simplex processor. However, in the cases examined, when failures occur in systems with many (N> 12) channels, the fusion network performs better than the simplex processor.>

An investigation of multichannel detection of known signals in noise of uncertain covariance resulted in an optimal adaptive array algorithm. The structure of the (Bayes) optimal system for this problem was determined by computing a likelihood ratio using a reproducing prior distribution for the uncertain covariance matrix. The problem could be reparameterized so that the uncertain quantities of interest were an adaptive weighting vector and the residual squared error. There was an optimal estimator for the weighting vector. The estimator was written recursively, resulting in a predictor-corrector algorithm for the required weighting vector. A comparison with the Widrow algorithm was performed. Additional comparisons were made with two variants of the LMS algorithm and the sample matrix inversion algorithm.

Two basic approaches to adaptive signal processing are in common use. The first and most direct involves substituting data-derived estimates of signal and noise autocorrelations into the standard Wiener-Hopf equation. The second uses a stochastic algorithm, such as the LMS, to minimize the mean square error directly. This paper attempts to unify these approaches by deriving an algorithm which substitutes data-derived estimates of the signal and noise autocorrelations into a recursive version of the Wiener-Hopf equation thus eliminating the need for direct matrix inversion. Although clearly an offshoot of the direct method, this algorithm, in its simplest form, is identical to the well-known LMS stochastic algorithm.

A method for adaptive linear estimation is proposed based on a Time Domain Orthogonality condition. This algorithm arises naturally from the criterion used rather than through the application of a numerical analysis method as in the derivation of the LMS Gradient Algorithm. However, in addition to being a new and potentially useful algorithm, the resulting recursive method is suprisingly similar to the LMS Gradient Algorithm. With the addition of certain simplifying assumptions, the TDO algorithm reduces to the LPIS Gradient Algorithm except that a data dependent term replaces the constant parameter µ found In the LMS Gradient Method. In fact, it is shown that this data dependent term is an estimate of the optimum µ for maximum rate of convergence.

An Adaptive Linear Estimation Algorithm which can be applied to the Spectral Line Enhancement problem is proposed. Through computer simulation, the rate of convergence of the proposed method is found to be significantly better than that of the LMS Gradient Algorithm for the problem considered. Also, this increased performance is obtained with only a modest increase in computational complexity.

A relationship between the likelihood ratio and a generalized causal conditional mean estimator is presented for the doubly composite hypotheses problem. The observation statistics are arbitrary and need not be Gaussian. The relationship parallelsthe well-known relationship for the Gaussian noise and composite signal hypothesis case, and the likelihood ratio can still be viewed as an estimator-correlator operation.

A variety of likelihood ratios are derived for detecting Gauss-Markov and finite-state Markov sequences in additive Gaussian noise. The Bayesian recursions appropriate to related filtering problems are exploited, together with "known-form" likelihood ratios, to obtain the desired results. In the derivation of a discrete-time Gauss-Markov likelihood ratio, a "pure" causal estimator-correlator structure is sought and a "locally stable" state estimator is encountered that is of some interest in its own right. The likelihood ratio is "pure" in the sense that the locally stable estimator is used in precisely the same manner as the stored replica is used in known-form signal detection problems to form the likelihood ratio. Consequently, the likelihood ratio is devoid of the extra data-dependent term that arises whenever one uses least squares state estimators to form the likelihood ratio statistic. The locally stable estimator equalizes, within a constant related to the {\em a priori} and {\em a posteriori} filtering error covariances, the {\em a priori} and {\em a posteriori} filtering densities. Heuristically, the estimator is a compromise between the one-step predictor and the filtered estimator of a discrete-time Kalman filter. When the observation noise covariance is unknown, a generalization of the so-called unknown level problem, then a Wishart prior is assigned to the innovations covariance and an integral representation is obtained for the desired likelihood ratio. The representation suggests a parallel structure for approximating the likelihood ratio when the observation noise covariance is unknown. Finally, the likelihood ratio for detecting finite-state Markov sequences is derived to illustrate that in general no "pure" estimator-correlator structure can exist when the state-space is finite.

The probability of error of the optimal decoder, based on the criterion of minimizing bit-error rate, is calculated for a Markov source imbedded in additive Gaussian noise for several specific cases. The tradeoff between bit-error rate and complexity of a simplified decoder is presented for various signal-to-noise ratios and Markov dependency.

The performance of a likelihood ratio processor must often be determined via computer simulation. This correspondence suggests an effective method of calculating the receiver operating characteristic (ROC) that avoids emphasizing the upper tail region of the likelihood ratio's estimated probability density function. A specific example is presented.

A new philosophy for designing detection devices, which embodies some of the better features of the classical generalized likelihood ratio test and the classical Bayes test, is presented. A feature of the new Bayes generalized likelihood ratio test is that it provides a unified procedure for utilizing parameter estimates in detector design. Its use depends on the existence of an asymptotically unbiased estimator for the unknown parameters. If such an estimator is easily implemented, then the new test should be particularly attractive.

The purpose of this presentation is to develop and evaluate an algorithm for determining a finite memory detector applicable to statistical signal detection theory. In the Bayesian signal detection theory, infinite soft or changeable memory is tacitly assumed. Since an infinite memory is physically unrealizable, this study postulates a finite memory scheme which is applicable to a large class of signal detection problems. A general sequentially operating finite memory detector design is obtained and then evaluated for the signal known exactly and the signal known except amplitude problems. Detection performance as a function of memory size is presented for finite observation records using the receiver operating characteristic and plots of probability of decision error versus time. These results show the tradeoff between memory size and processing time to achieve a given detection performance. An important result is that for finite sample records a small finite memory detector with a memory size on the order of 7 states, i.e., a 3-bit computer word, yields detection performance very near that of the optimum infinite memory detector.

A fundamental spatial property is noted that relates the likelihood ratio for random signals in Gaussian noise to conditional-mean parameter estimation. This allows a geometric interpretation of the estimation-correlation operation. Some additional properties exhibited by the likelihood ratio are also presented.