In this paper, the classical analysis of variance is extended to three-dimensional (3-D) Graeco-Latin squares design for multiframe processing applications. Conspicuous physical features, including edges, lines, and corners, can then be expressed as contrast functions. This enables the development of a new methodology for detecting moving objects embedded in noise. The new detector exploits spatial and temporal information uniformly most powerful in a Gaussian environment with unknown and time-varying noise variance. Also found is that a moving object detector based on contrast functions coincides with a sufficient statistic of the generalized likelihood ratio test. Extensive image analysis demonstrates the practicality of the detector and compares favorably to other classes of detectors.

This paper presents a new class of algorithms based on Youden designs to detect and restore edges present in an image imbedded by mixture or “salt and pepper” noise. The mixture noise consists of a uncorrelated or correlated noisy background plus uncorrelated impulsive noise. The objective is to restore pixels affected by the impulsive part of the mixture noise. The approach is to consider that these pixels have lost their true value and their estimate is obtained via the normal equation that yields the least sum of square error (LSSE). This procedure is known in the literature as “The Missing Value Approach Problem”. The estimates are introduced into the image data and an ANOVA technique based on Youden design is carried out. We introduce Youden designs which are special Symmetric Balanced Incomplete block (SBIB) designs, the pertinent statistical tests and estimates of the factor effects. We derive the estimate of the missing value for the uncorrelated noise environment as well as for the correlated one. The high level of performance of these algorithms can be evaluated visually via the input/output images and objectively via the input/output signal-to-noise ratio (SNR).

Abstract In this paper, the application of an edge detection algorithm based on homogeneous tests is extended to the detection of moving objects. In this new detection algorithm, dynamic regions occupied by moving objects on a motion sequence are located by a series of homogeneous tests operating on consecutive frames of the motion sequence. Upon locating the dynamic regions on a frame, further processing is carried out to pinpoint the locations of the moving objects. In general, the new moving object displacement/difference-based detector is implemented by a two-sample sign test, two morphological operators, a new object labeling algorithm, two edge detectors, and some simple operators. The versatility of the proposed detector is demonstrated by the fact that it is made up of distribution-free detection components. The simulation results confirm that the detector performs well in Gaussian and nonGaussian (“salt-and-pepper”) noise environments.

A new class of line detectors based on the theory of linear contrasts is developed. By incorporating the F-statistic and the shape test, the new algorithm detects and locates line features simultaneously, and thereby increases the detection power substantially. Many classes of detectors, including the step edge detector, naturally becomes subclasses of the proposed detector. Mathematical analysis indicates that the new algorithm that accounts for noise dependence performs better than its counterpart that neglects the dependence of noise. A symmetrical balanced incomplete-blocks (SBIB) design is introduced to model real-world images in terms of a treatment group that is associated with preexistent, conspicuous, features such as lines, edges, etc., and an incomplete treatment group that is randomized to accommodate image textures. The new algorithm in conjunction with the SBIB design is applied in the four main directions, perpendicularly to the line under investigation. It is robust, simple, efficient, and amenable to real-time applications. All pertinent statistics for the implementation of the procedure are estimated from data. Extensive computer simulations demonstrate the performance of the proposed detector.

A detector is proposed that is based on a model in which the signal components consist of radiant thermal energy from either the small target or the intense, highly structured background. The resulting statistic is effective in enhancing the target and suppressing cluttered background. Estimation of the system parameters based on stochastic approximation techniques is presented. Simulation results demonstrate the practicality of the proposed detector.

In this paper algorithms of neural-network type are introduced for solving estimation and classification problems when assumptions about independence, Gaussianity, and stationarity of the observation samples are no longer valid. Specifically, the asymptotic normality of several nonparametric classification tests is demonstrated and their implementation using a neural-network approach is presented. Initially, the neural nets train themselves via learning samples for nominal noise and alternative hypotheses distributions resulting in near optimum performance in a particular stochastic environment. In other than the nominal environments, however, high efficiency is maintained by adapting the optimum nonlinearities to changing conditions during operation via parallel networks, without disturbing the classification process. Furthermore, the superiority in performance of the proposed networks over more traditional neural nets is demonstrated in an application involving pattern recognition.

The problem of detection in the presence of a slowly varying not necessarily Gaussian noise is treated in this paper by introducing the generalized linear tests and the generalized quantiles test statistic Ti∗. Detectors based on these tests combine the good qualities of order and partition statistics, i.e., increased efficiency and ease of implementation. Using an array of M sensors, the Ti∗ statistic, which combines the power of rank tests, and the robustness of partition tests, is extended to its multivariate counterpart, and its performance is evaluated for small signal-to-noise-ratio environments.

A generalized version of the iterative conditional modes (ICM) method for image enhancement is developed. The proposed algorithm utilizes the characteristic of Markov random fields (MRF) in modeling the contextual information embedded in image formation. To cope with real images, a new local MRF model with a second-order neighborhood is introduced. This model extracts contextual information not only from the intensity levels but also from the relative position of neighboring cliques. Also, an outlier rejection method is presented. In this method, the rejection depends on each candidate's contribution to the local variance. To cope with a mixed noise case, a hypothesis test is implemented as part of the restoration procedure. The proposed algorithm performs signal adaptive, nonlinear, and recursive filtering. In comparing the performance of the new procedure with several well-known order statistic filters, the superiority of the proposed algorithm is demonstrated both in the mean-square-error (MSE) and the mean-absolute-error (MAE) senses. In addition, the new algorithm preserves the details of the images well. It should be noted that the blurring effect is not considered.

In this paper, the theory of robust partition detectors is extended to the dependent noise case where the observable samples satisfy strong mixing conditions, and the underlying stationary noise process is non-Gaussian in general. The statistical properties of the test statistics are investigated and the asymptotic normality of the test has been proved in the dependent noise environments. The locally optimum scores of the test are computed for signals with low signal-to-noise ratio by miximizing its asymptotic efficiency. The robust characteristics and asymptotic behavior of the test are also analyzed.

The effects of dependent sampling on the sequential m-interval polynomial approximation (MIPA) array processing detectors are considered. This problem is approached on a weak signal basis; bivariate and Markovian types of dependence are used separately to model the dependence among the data samples. For practical implementations, we assume that the noise is independent between sensors; we will allow only temporal dependence to exist among the data collected by each sensor. Based on the relative efficiency criteria, the performance of these detectors is compared to that of their corresponding independent noise counterpart. It is concluded that improved performance is achieved.

In this paper, edge preserving recursive estimators are proposed For restoring images corrupted by noise. Edge detection using a 5/spl times/5 Graeco-Latin squares (GLS) mask is carried out as the first step for preserving edges. The GLS mask preprocessor determines the orientation of edges in horizontal, vertical, 45/spl deg/ diagonal, or 135/spl deg/ diagonal directions. The actual removal of noise is done in the second step. If the noise is Gaussian, the center pixel in the 5/spl times/5 mask is estimated using a multiple linear regression model fitted to the noisy image on the same side of the edge. The parameters of the regression model are estimated using the least squares estimator. The least squares estimator is made recursive using the Robbins-Monro stochastic approximation (RMSA) algorithm. The RMSA guarantees convergence of the estimate in the mean square sense and with probability one. If the Gaussian noise is contaminated by a small percentage of heavy tailed (impulsive) noise (salt and pepper noise), the recursive least square estimator is robustized using a symmetrical version of Wilcoxon signed rank statistic. The GLS mask for edge detection uses an F-ratio test which is robust for small deviations from normality assumption of the noise. The mathematical properties and various forms of convergence of the robustized algorithm are shown in the appendix. The efficacy of the proposed restoration procedures are demonstrated on two types of images ("girl" and "house").>

The M-ary PSK system over nonlinear satellite channels, in the presence of an arbitrary number of interferers and additive Gaussian noise on the uplink and downlink paths, is investigated. The effect of intersymbol interference due to the transmitter filter is also included. The bit error probabilities are obtained using the Gauss quadrature formula and a two-dimensional moment technique.>

An experimental design approach that treats the gray-level value of each pixel as an observation is proposed. Any pixel corrupted by salt-and-pepper noise is considered to be a missing observation. An estimate of a missing observation is derived using a 5*5*5*5 Graeco-Latin squares experimental design model fitted to a 5-pixel*5-pixel mask. Edge-preserving smoothing of images corrupted by a mixture of Gaussian and salt-and-pepper noise is carried out in two steps. First a 5*5*5*5 Graeco-Latin squares mask is used to determine the presence of horizontal, vertical, 45 degrees diagonal, or 135 degrees diagonal edges and localize them using analysis of variance (ANOVA) on contrasts. The center pixel in the 5-pixel*5-pixel mask is then replaced by the average of all the pixels on the same side of the edge that includes the center pixel. The process is powerful and efficient. The uniformly most powerful property of the ANOVA methodology in the presence of Gaussian noise ensures the optimum suppression of the Gaussian noise background.>

A two-dimensional Kalman filtering scheme based on the Roesser local state-space model is given. This algorithm does not provide the conditional mean with respect to previously scanned data; rather, it generates the best gain sequence with respect to local data and prediction. This procedure is also compared experimentally to an optimal filter on noisy images, and it is observed that similar performances in terms of minimum mean square error and an enormous reduction in computations are obtained.>

In this paper new classes of algorithms are developed for processing of two-dimensional image data imbedded in correlated noise. The algorithms are based on modifications of standard analysis of variance (ANOVA) techniques involving Latin Square (LS) technique and ensuring their proper operation in dependent noise. The LS technique enables us to analyse three effects, including the gray level (or diagonal) effect instead of two based on the same data, for two-way designs. Though the theoretical development leading to the actual image processing procedure is laborious and complicated, the actual procedure is simple, robust and useful in real-time applications. The efficiency of all algorithms for processing image data corrupted by statistically-dependent noise is verified by extensive Monte-Carlo simulations.

Multisensor data from sonar arrays are usually temporally and spatially dependent. In addition, in some environments the noise field in which the sonar system must operate is contaminated by impulsive and non-Gaussian interference. A natural way to include these effects is to formulate a statistic based upon the likelihood ratio. However, implementing a multisensor likelihood ratio statistic in its full generality is a formidable task. Our approach to solving the implementation complexity problem is to partition the amplitude of each sensor output intomintervals and model the resulting data as a finite Markov chain. Certain performance measures for fixed-sample-size and sequential detection statistics based on Markov chains are considered.

In this paper, the problem of signal detection in severe and/or changing noise environment is considered. The detector operates at near-optimum levels for a particular noise environment and is robust by maintaining high efficiency in other than nominal noise environments by adapting its optimum nonlinearity using an m-interval approximation of it. It is shown that the sequential MIPA detectors are asymptotically optimum, increase their transmission rate up to four times as compared to their fixed-sample size counterparts, and are highly insensitive to variation of noise if compared to detectors based on min-max theory.

In this paper, the theory of sequential partition detectors with dependent sampling is introduced. A new formulation is given which predicts the thresholds under q-dependent sampling in order to maintain the same error probabilities as in the independent sampling case. A comparison is made between independent and dependent sequential partition detectors based on the average time to detection. Under stated conditions dependent sequential partition detectors show improved efficiency for both Lehmann and shift of the mean alternatives.

The theory of them-interval partition detector is extended to include the analysis and design of nonconstant signals. Using the derived locally most powerful scores, the performance of this detector is investigated. A discrete formulation is used to select the signal and correlation function of the detector to optimize a performance index that reflects the system constraints. Though the detector appears to be similar to a conventional correlation detector, it retains the robustness properties of them-interval detector. In addition, a method is presented whereby dependent samples may be used while still retaining nonparametric operation of the detector.

A design procedure for the receiver of a pulse amplitude modulation system is developed for data transmission in the presence of intersymbol interference and noise. In the receiver, an estimate of each source symbol is made based on the WienerKolmogorov theory of minimum variance estimation for stationary time series. The resulting structure is called a recursive equalizer and its taps are obtained by taking the canonical factorization of the spectral density function followed by the operations of polynomial multiplication and division. The performance of the system is evaluated by calculating the probability of error versus signal-signal-to-noise ratio and Comparing it to the performance of a conventional tapped delay line equalizer. The specific example presented uses raised-cosine signaling through a channel with slope-attenuation distortion and a zero phase characteristic. For this example, the recursive equalizer is shown to exhibit superior-performance.

A new class of nonparametric detectors based onm- interval partitioning is introduced. It is easier to treat analytically and implement practically than the widely used class of nonparametric detectors based on rank partitioning of the received signal space. In addition, these new detectors are robust or relatively insensitive to the underlying noise distribution. If the quantiles of the noise distribution are known exactly, the structure of the detector is particularly simple. Some general results for an adaptive system, when the quantiles of the noise distribution must be estimated, were also obtained.

The design of useful signaling alphabets in a burst-noise environment is treated as a discrete signal-design problem. A binary alphabet with minimum Gabor bandwidth is formulated as a discrete optimization problem to illustrate the design philosophy. The solution is obtained by using an eigenvalue approach. This technique is extended to the design of signals in a burst-noise environment where the burst is simulated by the removal of samples. Higher order alphabets are constructed for specific sample sizes and their performance evaluated.

In this paper, permutation channels, which include the rank channels and doubly uniform channels, are defined. A lower bound on the capacities of these channels is obtained with help of nonparametric signal-detection theory. This bound reduces to the actual capacity for memoryless doubly uniform channels by properly selecting the associated nonparametric detectors, The lower bounds on the capacities of the rank channels are expressed in terms of Kendalrs rank correlation coefficient. When the signal power is low, the comparison between a rank channel and a memoryless binary symmetric channel is expressed in terms of the Pitman-Noether asymptotic relative efficiency.

In this paper, signal design in a burst-noise environment is considered. Two distinct approaches are presented, each resulting in a class of signals for which the trade-off between signal bandwidth and immunity to large-amplitude bursts is shown. In the first approach the design is treated as an optimization problem subject to energy and endpoint constraints in a fixed time interval, and a uniform probability distribution of the location of the burst within the interval. The second approach considers signal design as a two-player differential game, where design flexibliity is obtained through the second player's choice of an initial value in the resulting differential equation. Performance curves for signals designed by using both methods are compared. It is shown how the first design procedure is easily extended toM-ary alphabets, thus obtaining the full advantage of the proposed technique.

A new general approach to the formulation of a non-parametric detector using dependent samples is introduced and applied to a space-diversity system employing dc signaling. A comparison based on a form of asymptotic relative efficiency is made between the new detector and a Mann-Whitney detector. Under certain conditions the new procedure demonstrates an improvement in transmission efficiency.

A coding scheme based on the properties of rank vectors is presented. The new codes are based on the theory of permutation groups by introducing a new notation for the group operation that simplifies the generation and decoding of desirable rank codes. The use of group theory is made possible by the introduction of the Kendall correlation coefficient as a measure of the distance between code words. This technique provides a method for the choice of rank vector code words superior to those that have been proposed in the past. Much of the terminology used in block coding can also be used to describe rank vector codes, but the actual quantities involved are quite different. The rank vector codes discussed in the paper offer the advantage of low sensitivity of the probability of error to the noise distribution because of the nonparametric character of rank vector detection schemes. Bounds that have been verified by extensive computer simulation have been derived for the probability of error.

This paper considers the design of binary bandlimited receiver signals as well as the design of the receiver filter for signal immunity to intersymbol interference and additive colored Gaussian noise. The design problem is treated in the frequency domain. The maximum probability of error is minimized by choosing signals with zero intersymbol interference. When transmission is below the Nyquist rate, bandlimited signals with gradual cutoff are designed. Other waveforms, with intersymbol interference but possessing no sequences of unbounded amplitude, are also investigated. Examples are given demonstrating the application of the theory.

The design of time-limited binary signals imbedded in colored Gaussian noise resulting from passing white noise through a channel of known transfer function is investigated. It is shown that, for a class of channels whose magnitude characteristic is expressible as the ratio of polynomials with the numerator divisible by and of lower or the same degree as the denominator, the output noise kernel (correlation function) and its inverse will have Fourier transforms which are reciprocals of each other. The above assumption results in an expression for probability of error which is independent of the received waveform and depends solely on the transmitter signal-to-noise ratio. The additional freedom of design afforded by the above enables one to impose further restrictions in the form of energy concentration in the frequency domain on the received signal without deterioration of system performance. Some such bandwidth constraints and their associated optimum signal designs are considered in this paper.

The proposed detector uses three vector samples to decide which one of two distinct stationary or quasi-stationary stochastic processes is present at its input. A reference sample is obtained from each of the two processes during an initial learning interval, and the third sample is taken on the decision interval. It is assumed that independent samples can be obtained from the stochastic processes. A weighted linear combination of two2-sample Mann-Whitney statistics defined on the three vector samples is used at the detector. An upper bound on the asymptotic or large-sample error probability is obtained, which indicates that, unlike the2-sample detector, the new detector is insensitive to the {\em a priori} signal probability and operates well in an unspecified environment. Comparisons are made between the proposed model and the standard2-sample model at both small and large values of signal-to-noise ratio. An extension to intermediate values of signal-to-noise ratio is obtained by considering two examples, dc signal in additive noise and Lehmann's nonparametric class of alternatives. Owing mainly to an invariant optimum threshold setting, the proposed procedure results in a significantly better performance over a wide range of signal-to-noise ratio.

This paper considers the basic problem of transmitting digital information through a noisy channel with minimum probability of error in finite time. The transmitted signals are average-power limited, and the noise is assumed to be additive Gaussian with a power spectrum which may be nonwhite. A theory of so-called efficient codes (minimax, equal separation, and nearly equal separation) is developed. Efficient codes are formed from weighted sums of eigenfunctions generated by an integral equation with its kernel corresponding to the inverse Fourier transform of the Gaussian noise power spectrum. In addition, the theory of equidistant and nearly equidistant codes [1] is extended to the case of nonwhite Gaussian noise. It is shown that efficient codes perform better than equidistant codes if the noise is nonwhite; i.e., properly chosen waveforms are more efficient than binary coding. Performance results are given for several different codes when the interference is white Gaussian noise and when the noise power density increases with increasing frequency. The detection scheme used does not require estimation of the signal or the noise levels at the receiver and is thus independent of fading.