Showing papers on "K-distribution published in 1993"

Maximum likelihood estimation of K distribution parameters for SAR data

Abstract: The K distribution has proven to be a promising and useful model for backscattering statistics in synthetic aperture radar (SAR) imagery. However, most studies to date have relied on a method of moments technique involving second and fourth moments to estimate the parameters of the K distribution. The variance of these parameter estimates is large in cases where the sample size is small and/or the true distribution of backscattered amplitude is highly non-Rayleigh. The present authors apply a maximum likelihood estimation method directly to the K distribution. They consider the situation for single-look SAR data as well as a simplified model for multilook data. They investigate the accuracy and uncertainties in maximum likelihood parameter estimates as functions of sample size and the parameters themselves. They also compare their results with those from a new method given by Raghavan (1991) and from a nonstandard method of moments technique; maximum likelihood parameter estimates prove to be at least as accurate as those from the other estimators in all cases tested, and are more accurate in most cases. Finally, they compare the simplified multilook model with nominally four-look SAR data acquired by the Jet Propulsion Laboratory AIRSAR over sea ice in the Beaufort Sea during March 1988. They find that the model fits data from both first-year and multiyear ice well and that backscattering statistics from each ice type are moderately non-Rayleigh. They note that the distributions for the data set differ too little between ice types to allow discrimination based on differing distribution parameters. >

On the Frequency-Length Distribution of the San Andreas Fault System

Abstract: The frequency-length distribution of the San Andreas fault system was analyzed and compared with theoretical distributions. Both density and cumulative distributions were calculated, and errors were estimated. Neither exponential functions nor power laws are consistent with the calculated distributions over the range of studied lengths. The best fit on both density and cumulative distributions was achieved with a gamma function which mixes a power law and an exponential function. At small lengths, the gamma function behaves as a power law with an exponent of −1.3±0.3. At large lengths (above 10km), the distribution is a mixed exponential-power law function with a characteristic length scale of about 23±6 km. The gamma distribution is proposed to result from a length-dependent segmentation of a fractal fault pattern. This study shows the importance of comparing both cumulative and density distributions. It also shows that the studied range of lengths (1–100 km) is not appropriate for measuring power law exponents.

Optimum texture estimators for SAR clutter

Abstract: This paper analyses various estimators for characterizing synthetic aperture radar clutter textures. First, we consider maximum likelihood estimators, which require specific knowledge of the form of the probability distribution of the data but would be expected to yield the best performance. Both K- and Weibull-distributed clutter models, which are often applied to characterize natural SAR clutter, are considered. Though a full maximum likelihood solution is impossible for the K distribution, we derive an approximate one for the multi-look case. We next derive expressions for limiting errors in a variety of direct texture estimators and compare their predicted performance with the maximum likelihood estimates in a search for robust, optimum texture estimators.

Selecting Parameters of Phase Distributions: Combining Nonlinear Programming, Heuristics, and Erlang Distributions

Abstract: Because of their denseness and tractability, phase (PH) distributions are widely used in probabilistic modeling. However, full exploitation of the favorable properties of PH distributions requires the ability to specify PH-distribution parameters to obtain adequate distribution approximations. We combine nonlinear-programming techniques and heuristics to select mixtures of Erlang distributions (a subset of the PH family) to approximate non-PH distributions. Heuristics are used to select the number of Erlang distributions mixed and the order of each mixed Erlang distribution, both of which have an important effect on the range of distribution properties that can be attained. Heuristics are also used for assigning initial values and bounds to the mixing probabilities and the means of the mixed Erlang distributions. Then nonlinear-programming methods are used to determine final values of these continuous parameters. Using a variety of criteria, we show that good fits can often be obtained with a moderate amo...

Ultrasound echo evaluation by K-distribution

Abstract: The ultrasonic echo backscattered from tissues is modeled using non-Rayleigh statistics, namely the K distribution. Through simulation using a one dimensional discrete scattering model, the properties of statistics governing the echo envelope are investigated. Deviations from Rayleigh are observed as the variation in the scattering cross sections become random. The density function of the backscattered envelope fits the K-distribution very well. The validity of the model was also tested using tissue mimicking phantoms. Results indicate that the parameters of the K distribution can be used to separate and identify regions on the basis of the uniformity of scattering cross sections of the scatterers

Maintaining Discrete Probability Distributions Optimally

Abstract: Consider a distribution as an abstract data type that represents a probability distribution f on a finite set and supports a generate operation, which returns a random value distributed according to f and independent of the values returned by previous calls. We study the implementation of dynamic distributions, which additionally support changes to the probability distribution through update operations, and show how to realize distributions on {1,..., n} with constant expected generate time, constant update time, O(n) space, and O(n) initialization time. We also consider generalized distributions, whose values need not sum to 1, and obtain similar results.

The phase statistics of a multichannel radar interferometer

Abstract: The analysis in this paper is concerned with the problem of determining the phase statistics of the output of a multichannel coherent radar interferometer. The 2N channels of the radar consist of the outputs from N pairs of antennae. Each antenna receives a random electromagnetic wave field which has circular normal first-order statistics with an arbitrary coherence function. Each antenna in each pair receives a wave at a different time, the time difference Δt between each antenna in each pair being the same for all pairs. The signals received by each pair are independent. The signals from each pair are combined to give G(t, Δt)=Σk=1 N Sk(t) Sk*(t+Δt) where, for example, the signals from each antenna in the kth pair are Sk(t) and Sk(t+Δt). The probability density function of the modulus and phase of G(t, Δt) is worked out. The joint density is shown to be a type of generalized K distribution, and the phase distribution is shown to be a hypergeometric function. The results show that it is possible...

Characterizations of gamma, inverse Gaussian, and negative binomial distributions via their length-biased distributions

Abstract: A general form for characterizing inverse Gaussian and Wald distributions, based on their respective length-biased distributions, is introduced. Further results for characterizations of the gamma distribution, the negative binomial distribution and some mixtures of them by using their lengthbiased distributions are establised.

Marginal distributions of quasiprobabilities in quantum optics.

Abstract: Marginal properties of arbitrary s-ordered quasiprobability distribution functions are investigated. The positivity of marginal distributions for all quasiprobabilities, interpolating between the Wigner function and the Q representation of the density operator (s≤0), is proven. We also show that, on the contrary, marginal distributions of the remaining quasiprobabilities, interpolating between the Wigner function and the P representation (s>0), can take on negative values. General formulas for the marginal distributions are given, and their relations to the actual quantum-mechanical probability distributions for position and momentum are established

Possibility of approximating multimodal distributions by mixtures of standard probability density functions

Abstract: Specific aspects of the approximation of multirnodal distributions are discussed. It is shown that the formulation of an algorithm for the approximation of multimodal probability density functions by mixtures of standard distributions is a solvable problem, since it is proved that a finite mixture of distributions belonging to the author's “extended” Pearson system is separable.

Johnson Distributions for Fitting Weighted Sums of Sigmoided Neuron Outputs

Abstract: : In this paper, it is shown that a continuum of distributions best characterizes the hidden layer outputs of a multilayer perceptron when trained as a 0-1 classifier and tested with a range of signal-to-noise ratio (SNR) input distributions. A four parameter system of transformed normal distributions, known as the Johnson system of distributions, is utilized to illustrate the shape of output distributions as a function of input SNR levels. Neural networks, Active signal processing.

Some characterizations of distributions of the exponential-type

Abstract: We consider a particular subclass of the two-parameter exponential family with natural parameters γ1, γ2 and characterize those distributions of the family having a ratio of the mean value and the variance that is a linear function of γ1 by the form of the moment generating function. As special cases we find the normal and the gamma distributions.

Probability distributions for the overlaps and self-correlations of the pure states of an n-vector model

Abstract: The probability distributions for the overlaps between and the self-correlations of the pure states of the Stanleyn-vector model with infinite-range interactions are derived. These probability distributions represent two new order parameters for the model and are intimately related to the parameters which arise naturally within the replica formalism for the treatment of the corresponding quenched random-bond model. In contrast to then = 1 Ising case, the probability distributions are nontrivial whenn > 1 and an additional parameter for self-correlation has to be introduced.