Bruce A. Eisenstein

Feature Extraction by System Identification

A method for the extraction of features for pattern recognition by system identification is presented. A test waveform is associated with a parameterized process model (PM) which is an inverse filter. The structure of the PM corresponds to the redundant information in a waveform, and the parameter values correspond to the discriminatory information. The PM used in this research is a linear predictive system whose parameters are the linear predictive coefficients (LPCs). This technique is applied to feature extraction of electrocardiograms (ECGs) for differential diagnosis. The LPCs are calculated for each ECG and used as a feature vector in a hypergeometric affine N-space spanned by the LPCs. The efficacy of this feature extraction technique is tested by three different perturbation methods, namely noise, matrix distortion, and a newly developed method called directed distortion. Both the Euclidean and Itakura distances between feature vectors in N-space are shown in increase with increasing perturbation of the template waveform. The monotonic behavior of a distance measure is a necessary attribute of a valid feature space. Thus the perturbation analyses done in this research verify the viability of using the parameters of a process model as a feature vector in a pattern recognition scheme.

Weak Signal Detection in Non-Gaussian Noise of Unknown Level

An adaptive threshold detector to test for the presence of a weak signal in additive non-Gaussian noise of unknown level is discussed. The detector consists of a locally optimum detector, a noise level estimator, and a decision device. The detection threshold is made adaptive according to the information provided by the noise level estimator in order to keep a fixed false-alarm probability. Asymptotic performance characteristics are obtained indicating relationships among the basic system parameters such as the reference noise sample size and the underlying noise statistics. It is shown that, as the reference noise sample size is made sufficiently large, the adaptive threshold detector attains the performance of a corresponding locally optimum detector for detecting the weak signal were the noise level known.

Statistical Deconvolution of Electrocardiograms

Distortion caused by the passage of an electrocardiogram (ECG) through a linear, time-invariant system can be removed by deconvolving the impulse response of the distorting system from the observation. By modeling the ECG as a cyclostationary signal, the deconvolution can be done without a priori knowledge of the impulse response of the distorting system.

Structural Editing by a Point Density Function

A new algorithm is presented for pattern recognition by clustering. The algorithm is called structural editing by a point density function, or STEP. STEP uses a minimum spanning tree to retain the interpoint structure among the elements of an unclassified training set. The tree is pruned or edited to form clusters based on information provided by a point density function (PDF) estimate. STEP has the capability of detecting clusters of arbitrary shape in the presence of intercluster stray points or outliers. A cluster is not required to correspond to a unimodal PDF estimate. Monte Carlo simulations indicate that STEP performs as well as, or better than, a nearest neighbor classifier which requires a classified training set. A new algorithm for recursively constructing the minimum spanning tree is presented which is computationally simpler than conventional algorithms in many practical applications. Results from applying STEP to the mass screening of breast thermograms are discussed.

Adaptive deconvolution of stochastic signals

An adaptive technique is presented for the restoration of a stochastic signal which has been distorted by passage through a linear; time-invariant system with unknown transfer function. Restoration of a stochastic signal is here defined as the identification of the statistical parameters of the input signal and the re-creation of a restored signal which is statistically similar to the original signal. The restoration is tantamount to deconvolving the observed signal with the inpulse response of the distorting system. Since the required impulse response is unknown, it must be identified or learned in order to be used. Previous researchers in this area have used the term homomorphic filtering to describe forms of deconvolution similar to those used here (1-4).

Crossfrequency estimation for deconvolution

To reduce distortion, a technique is presented for deconvolving the effect of the distorting system on a desired signal. The technique does not require any prior assumptions about the distorting system other than that it is linear and time-invariant. However, we must assume that the desired signal is a sample function from a cyelostationary (CS) random process with known statistics. Many signals of practical importance can be modelled as CS including PAM, FSK, PWM, etc. The technique utilizes inverse filtering with an estimate of the distorting system function which is obtained exclusively from the observed signal and the known and computed properties of CS processes.