Bounds on the accuracy of Gaussian ARMA parameter estimation methods based on sample covariances

The asymptotic accuracy of Gaussian ARMA parameter estimation methods based on a fixed number of sample covariances is considered. Several key results are briefly reviewed, including: i) a general asymptotic expression for the error covariance of the ARMA parameter estimates; ii) the fact that this error covariance is always greater than a certain lower bound; iii) the fact that this lower bound is strictly greater than the Cramer-Rao bound; iv) an explicit ARMA estimation technique that asymptotically achieves the bound. The key result of this note is a proof that this lower bound approaches the Cramer-Rao bound as the number of sample covariances tends to infinity.     

Computer image generation for flight simulators: the Gabor approach

A formalism for image representation in the combined frequency-position space is presented using the generalized Gabor approach. This approach uses elementary functions to which the human visual system is particularly sensitive and which are efficient for the analysis and synthesis of visual imagery. The formalism is also compatible with the implementation of a variable resolution system wherein image information is nonuniformly distributed across the visual field in accordance with the human visual system's ability to process it. When used with a gaze-slaved visual display system, imagery generated using the techniques described here affords a combination of high resolution and wide field-of-view. This combination is particularly important in high-fidelity, computergenerated, visual environments as required, for instance, in flight simulators.     

On the computation of an asymptotic bound for estimating autoregressive signals in white noise

The Cramer-Rao lower bound (CRLB) provides a useful reference for evaluating the performance of parameter estimation techniques. This paper considers the problem of estimating the parameters of an autoregressive signal corrupted by white noise. An explicit formula is derived for computing the asymptotic CRLB for the signal and noise parameters. Formulas for the asymptotic CRLB for functions of the signal and noise parameters are also presented. In particular, the center frequency, bandwidth and power of a second order process are considered. Some numerical examples are presented to illustrate the usefulness of these bounds in studying estimation accuracy.     

Performance analysis of parameter estimation algorithms based on high-order moments

Recently, there has been a considerable interest in parametric estimation of non-Gaussian processes, based on high-order moments. Several researchers have proposed algorithms for estimating the parameters of AR, MA and ARMA processes, based on the third-order and fourth-order cumulants. These algorithms are capable of handling non-minimum phase processes, and some of them provide a good trade-off between computational complexity and statistical efficiency. This paper presents some results about the performance of algorithms based on high-order moments. A general lower bound is derived for the variance of estimates based on high-order sample moments. This bound, which is shown to be asymptotically tight, is neither the Cramer-Rao bound nor a trivial extension thereof. The performance of weighted least squares estimates of the type recently proposed in the literature is investigated. An expression for the variance of such estimates is derived and the existence of an optimal weight matrix is proven. The general formulae are specialized to MA and ARMA processes and used to analyse the performance of some algorithms in detail. The analytic results are verified by Monte Carlo simulations for some specific test cases. A by-product of this paper is the derivation of asymptotic formulae for the variances and covariances of the sample third-order moments of a certain class of processes.     

Real Two Dimensional Scaled Matching

Scaled Matching refers to the problem of finding all locations in the text where the pattern, proportionally enlarged according to an arbitrary real-sized scale, appears. Scaled matching is an important problem that was originally inspired by Computer Vision. Finding a combinatorial definition that captures the concept of real scaling in discrete images has been a challenge in the pattern matching field. No definition existed that captured the concept of real scaling in discrete images, without assuming an underlying continuous signal, as done in the image processing field. We present a combinatorial definition for real scaled matching that scales images in a pleasing natural manner. We also present efficient algorithms for real scaled matching. The running times of our algorithms are as follows. For T, a two-dimensional n×n text array, and P, an m×m pattern array, we find in T all occurrences of P scaled to any real value in time O(nm ³+n ² mlog m). Research of A. Amir partially supported by ISF grant 282/01 and NSF grant CCR-01-04494.     

Improved Algorithms for Polynomial-Time Decay and Time-Decay with Additive Error

We consider the problem of maintaining polynomial and exponential decay aggregates of a data stream, where the weight of values seen from the stream diminishes as time elapses. These types of aggregation were discussed by Cohen and Strauss (J. Algorithms 1(59), 2006), and can be used in many applications in which the relative value of streaming data decreases since the time the data was seen. Some recent work and space efficient algorithms were developed for time-decaying aggregations, and in particular polynomial and exponential decaying aggregations. All of the work done so far has maintained multiplicative approximations for the aggregates. In this paper we present the first O(log N) space algorithm for the polynomial decay under a multiplicative approximation, matching a lower bound. In addition, we explore and develop algorithms and lower bounds for approximations allowing an additive error in addition to the multiplicative error. We show that in some cases, allowing an additive error can decrease the amount of space required, while in other cases we cannot do any better than a solution without additive error.     

The flavor of pomegranate fruit: a review

Despite the increasing commercial importance of pomegranate, especially because of its recently discovered health‐promoting benefits, relatively little is yet known regarding its sensory quality and flavor preferences, or about the biochemical constituents that determine its sensory characteristics. The perceived flavor of pomegranate fruit results from the combination of various taste, aroma and mouthfeel sensations. The taste is governed mainly by the presence of sugars (glucose and fructose) and organic acids (primarily citric and malic acids). The aroma evolves from the presence of dozens of volatiles, including alcohols, aldehydes, ketones, and terpenes, which provide a mixture of various ‘green’, ‘woody’, ‘earthy’, ‘fruity’, ‘floral’, ‘sweet’ and ‘musty’ notes. In addition, the sensory satisfaction during the eating of pomegranate arils is complemented by various mouthfeel sensations, including seed hardness and astringency sensations. In the present review we will describe the sensory quality and flavor preferences of pomegranate fruit, including the genetic diversity in flavor characteristics among distinct varieties. In addition, we will describe the dynamic changes that occur in fruit flavor during fruit ripening and postharvest storage. © 2013 Society of Chemical Industry     

Orthogonal decompositions of 2-D nonhomogeneous discrete random fields

Imposing atotal-order on a two-dimensional (2-D) discrete random field induces an orthogonal decomposition of the random field into two components: Apurely-indeterministic field and adeterministic one. The purely-indeterministic component is shown to have a 2-D white-innovations driven moving-average representation. The 2-D deterministic random field can be perfectly predicted from the field's past with respect to the imposed total-order definition. The deterministic field is further orthogonally decomposed into anevanescent field, and aremote past field. The evanescent field is generated by the columnto-column innovations of the deterministic field with respect to the imposed nonsymmetrical-half-plane total-ordering definition. The presented decomposition can be obtained with respect to any nonsymmetrical-half-plane total-ordering definition, for which the nonsymmetrical-half-plane boundary line has rational slope.