Andrew B. Martinez

Locally optimal detection in multivariate non-Gaussian noise

The detection of a vanishingly small, known signal in multi-variate noise is considered. Efficacy is used as a criterion of detector performance, and the locally optimal detector (LOD) for multivariate noise is derived. It is shown that this is a generalization of the well-known LOD for independent, identically distributed (i.i.d.) noise. Several characterizations of multivariate noise are used as examples; these include specific examples and some general methods of density generation. In particular, the class of multivariate densities generated by a zero-memory nonlinear transformation of a correlated Gaussian source is discussed in some detail. The detector structure is derived and practical aspects of obtaining detector subsystems are considered. Through the use of Monte Carlo simulations, the performance of this system if compared to that of the matched filter and of the i.i.d. LOD. Finally, the class of multivariate densities generated by a linear transformation of an i.i.d, noise source is described, and its LOD is shown to be a form frequently suggested to deal with multivariate, non-Gaussian noise: a linear filter followed by a memoryless nonlinearity and a correlator.

Seafloor characterization using texture

Texture analysis is performed on multibeam sonar imagery. A set of 14 texture features is computed using cooccurrence matrices to form the feature space. The dimensionality of the feature space is reduced by extracting the principal components from the original feature space. Classification of the image is performed on the principal components using the K-means algorithm. Results indicate that seafloor bottom types can be characterized by analyzing the texture of bathymetric sonar images.<<ETX>>

Fractal dimension estimation of fractional Brownian motion

Fractal dimension provides an objective means for quantifying the fractal property of an object and comparing objects observed in the natural world. One of the most useful mathematical models for the random fractals found in nature has been fractional Brownian motion. Two algorithms are used to simulate fractional Brownian motion. An important characteristic of fractals useful for their description and classification is their fractal dimension. Several methods are developed to estimate fractal dimension: the variance method, the spectral method, and the morphological method. These methods are used for simulated samples of fractional Brownian motion, and their performances are compared. It is found that the performance of these fractal dimension estimation methods is usually related to what kind of fractals are to be estimated and the range in which the fractal dimension falls.<<ETX>>

Data compression techniques for maps

The efficiencies of various data-compression techniques as applied to color maps are compared. These color maps have certain special characteristics, such as large homogeneous regions, and fine detail, such as lines and lettering. The color maps are first classified using the K-means clustering algorithm with neighborhood classification. Three techniques are investigated, namely, contour, quadtree, and run-length coding. The run-length coding algorithm is modified to allow wrap-around of runs. A modification of the standard binary image quadtree compression algorithm for color images is introduced. In quadtree coding a modified eldest-son eldest-younger-sibling quadtree is used to reduce the memory requirement for storing the quadtree. Lempel-Ziv compression is applied to the classified and unclassified images as well as to the output of the compression algorithms. The algorithms are compared on the compression ratios achieved. The exponential behavior of the histogram of the runs indicates that runs of short run length have higher probability. Accordingly, Huffman coding of the runs would result in more efficient bit assignment and hence greater compression ratios.<<ETX>>

Classification techniques for digital map compression

A comparison is made of the performance of various image classification techniques as applied to color cartographic maps is compared. The maps have a lot of graininess due to imperfections in the printing process, which decreases the efficiency of compression techniques. The color maps are classified using the K-means clustering algorithm and vector quantization (VQ), with neighborhood classification to improve the visual quality and compression ratio. The classification is performed in various image representation schemes. The performance of the classifier is evaluated on the basis of the visual quality of the classified image, the time required to classify the image, and compression achieved on the classified image. In terms of computation times, K-means exhibits a clear lead over the VQ classification scheme. However, the VQ classifier converges in fewer iterations than the K-means algorithm. The algorithms eliminated almost all misclassified pixels that were present in the image. The K-means algorithm with neighborhood classification, however, resulted in the filling in of one of the letters and a deterioration in the quality of the lines.<<ETX>>

AUV positioning using bathymetry matching

A research concern in AUV positioning is the constraint of INS error growth; approaches to this include surfacing for GPS fixes, terrain matching methods and acoustic transponder systems. The paper presents a positioning technique for AUVs that exploits existing bathymetric data in an operation area. Unlike many terrain matching approaches, which do positioning using distinct ocean bottom features, this method generates a position estimate by comparing the in-situ measured depth at the position of the AUV with available bathymetry data in the immediate area. This builds on contemporary AUV INS/VL navigation systems by incorporating a maximum likelihood estimate of position. Particular emphasis is placed on the design of the maximum likelihood estimator module which produces point-wise position estimates and typically contains a large error component with many outliers. This estimate is merged with the output of the AUVs INS/VL system which constrains the INS drift. Further position accuracy and faster convergence to the correct position can be achieved by incorporating a single slant range measurement from the AUV to a fixed location. The slant range is used as external constraint on both the INS and the MLE. The paper describes the implementation of this approach and the results of simulation studies.

A laser sensing scheme for detection of underwater acoustic signals

A technique to detect underwater acoustic signals by utilizing the resultant surface perturbations is discussed. These perturbations result in an amplitude modulation effect on a laser beam reflected by the water surface. A theory to explain this phenomenon is discussed. A detection system based on this theory was developed. Laboratory investigations were conducted to evaluate the characteristics of the system. Preliminary results indicate that detection based on this technique is possible.<<ETX>>

Finite length discrete matched filters

Abstract The matched filter (MF) is well known to be the linear detector that has the maximum output signal-to-noise ratio (SNR). The problem of finding the minimum filter length in discrete time to achieve a certain level of performance is considered when there is some freedom in choosing a signal shape. Upper and lower bounds on the SNR are given in terms of the eigenvalues of the noise covariance matrix. Since these bounds are rather difficult to compute, looser, but easier to compute, bounds are given. Several examples are presented which illustrate the exact and approximate bounds.

Estimation of the composite roughness model parameters

The estimation of the environmental parameters of the Raleigh-Rice approximation of the composite roughness model and the parameters of the Kirchoff approximation for seafloor acoustic backscatter, given backscatter strength and bathymetric data, is investigated. Estimation of these parameters is an inverse problem whose solution gives surface properties from the measurements of the scattered field. The independence of parameters of both approximations is first determined. Noise-free artificial data are generated by the Rayleigh-Rice approximation and the Kirchoff approximation. These artificial data are then used to train a feedforward neural network using the backpropagation learning algorithm. The trained network is used to estimate the independent parameters of the two approximations.<<ETX>>

Fractal-Based Pattern Recognition And Its Applications To Cell Image Analysis

The fractal dimension of a surface is a useful measure of the roughness of the surface. A method of estimating fractal dimension using mathematical morphology is derived and is applied to cell image analysis. By utilizing the fractal dimension property, the cells can be automatically classified as labeled or unlabeled cells.