Stephen M. Kogon

Signal modeling with self-similar /spl alpha/-stable processes: the fractional Levy stable motion model

The purpose of the correspondence is the introduction of fractional Levy stable motion (fLsm) as a model for signals with long-memory and high variability commonly encountered in natural processes. We present a concise description of this model from a signal processing viewpoint and its successful application to real-world infrared signals for the purpose of resolution enhancement via stochastic interpolation.

Beamspace techniques for hot clutter cancellation

In airborne radar applications, hot clutter refers to terrain-reflected jammer multipath interference which is spatially distributed throughout the mainbeam and sidelobes of the radar receiver. Most current cancellation methods use a single reference beam to cancel the mainbeam hot clutter interference. However these cancellers are computationally intensive and suffer from blind interval effects due to the size of the temporal window required for effective mitigation. We propose a full beamspace canceller implemented as a generalized sidelobe canceller for hot clutter mitigation. The proposed canceller exploits the spatial nature of the interference by utilizing delayed replicas of the jammer signal at all azimuth angles to significantly reduce the temporal extent of the canceller. By trading off temporal for spatial degrees of freedom, the full beamspace approach is able to drastically reduce the size of the temporal window required, achieving effective cancellation with fewer total degrees of freedom and a significant reduction in the blind interval. Results comparing the proposed full beamspace and the single-beam cancellers are reported using data collected in the Mountaintop program.

INFRARED SCENE MODELING AND INTERPOLATION USING FRACTIONAL LÉVY STABLE MOTION

Many data arising from natural phenomena exhibit 1/f behavior, indicating a long-range dependence structure in the increments. The data is said to be self-similar or fractal, which has been traditionally modeled by fractional Brownian motion (fBm). This stochastic fractal model assumes a Gaussian distribution of the increments which is at times too rigid, particularly for data emanating from a long-tailed distribution. Therefore, the fractional Levy stable motion stochastic process is proposed as a means of modeling a wider range of data. For these processes the increments are assumed to be from the family of stable distributions which have been shown to be good models of long-tailed behavior. The model is applied to data from infrared scenes and used to perform fractal interpolation, preserving not only the self-similarity, but also the probability distribution of the increments over the newly generated scales. This offers a flexible new model for a broader class of data than the fBm model.

Linear parametric models for signals with long-range dependence and infinite variance

Two models of long-range dependence with finite and infinite variance that have been proposed in the mathematics literature are considered. The models are used for the characterization of experimental data in order to determine the possible benefits they offer over existing models. They are presented under a unified framework and their similarities and differences are investigated by applying the models to real world data in the form of infrared background signals.

Reduced-rank terrain scattered interference mitigation

Radar systems are particularly vulnerable to the interference produced by jammer multipath reflections known as terrain scattered interference (TSI) or hot clutter. This interference is due to the diffuse scattering of jammer energy off large patches of terrain and consequently is present over large angular regions and large range intervals. Cancellation methods attempt to exploit the temporal correlation present in the TSI by using a large number of temporal taps. However, the adaptive degrees of freedom typically required for cancellation to the noise floor tend to be very large, motivating the investigation into various rank reduction strategies. In this paper we look at various methods of reducing the computational complexity of the canceller while maximizing the cancellation achieved. The canceller used is based on a beamspace transformation that is shown to yield certain advantages for rank reduction purposes. Results are demonstrated on experimental data collected as part of the Navy/ARPA Mountaintop program.

Harmonic long-memory models

In this paper we address the modeling of long-memory signals with strong harmonic components. Current long-memory models, such as the fractional unit-pole model, fail to address the possibility of periodicities in the data. An example of harmonic long-memory signals is found in heart rate variability signals. We propose the harmonic fractional unit-pole model for modeling both the long-memory and harmonic components. The model is obtained by moving the fractional order pole on the unit circle away from zero frequency in a complex conjugate pair. The characteristics of the model, namely the power spectral density and the autocorrelation function are derived. A method is then given for the generation of harmonic long-memory signals. Finally the harmonic fractional unit-pole model is used to characterize heart rate variability signals.

Fractal-based modeling and interpolation of non-Gaussian images

In modeling terrain images corresponding to infrared scenes it has been found the images are characterized by a long-range dependence structure and high variability. The long-range dependence manifests itself in a `1/f type behavior in the power spectral density and statistical self-similarity, both of which suggest the use of a stochastic fractal model. The traditional stochastic fractal model is fractional Brownian motion, which assumes the increment process arises from a Gaussian distribution. This model has been found to be rather limiting due to this restriction and therefore is incapable of modeling processes possessing high variability and emanating from long-tailed non-Gaussian distributions. Stable distributions have been shown to be good models of such behavior and have been incorporated into the stochastic fractal model, resulting in the fractional Levy stable motion model. The model is demonstrated on a terrain image and is used in an interpolation scheme to improve the resolution of the image.