John D. Gorman

Applications of entropic spanning graphs

This article presents applications of entropic spanning graphs to imaging and feature clustering applications. Entropic spanning graphs span a set of feature vectors in such a way that the normalized spanning length of the graph converges to the entropy of the feature distribution as the number of random feature vectors increases. This property makes these graphs naturally suited to applications where entropy and information divergence are used as discriminants: texture classification, feature clustering, image indexing, and image registration. Among other areas, these problems arise in geographical information systems, digital libraries, medical information processing, video indexing, multisensor fusion, and content-based retrieval.

Lower bounds for parametric estimation with constraints

A Chapman-Robbins form of the Barankin bound is used to derive a multiparameter Cramer-Rao (CR) type lower bound on estimator error covariance when the parameter theta in R/sup n/ is constrained to lie in a subset of the parameter space. A simple form for the constrained CR bound is obtained when the constraint set Theta /sub C/, can be expressed as a smooth functional inequality constraint. It is shown that the constrained CR bound is identical to the unconstrained CR bound at the regular points of Theta /sub C/, i.e. where no equality constraints are active. On the other hand, at those points theta in Theta /sub C/ where pure equality constraints are active the full-rank Fisher information matrix in the unconstrained CR bound must be replaced by a rank-reduced Fisher information matrix obtained as a projection of the full-rank Fisher matrix onto the tangent hyperplane of the full-rank Fisher matrix onto the tangent hyperplane of the constraint set at theta . A necessary and sufficient condition involving the forms of the constraint and the likelihood function is given for the bound to be achievable, and examples for which the bound is achieved are presented. In addition to providing a useful generalization of the CR bound, the results permit analysis of the gain in achievable MSE performance due to the imposition of particular constraints on the parameter space without the need for a global reparameterization. >

Image registration with minimum spanning tree algorithm

Registration is a fundamental task in image processing and quite a few registration techniques have been developed in various fields. In this paper we propose a novel graph-representation method for image registration with Renyi entropy as the dissimilarity metric between the images. The image matching is performed by minimizing the length of the minimum spanning tree (MST) which spans the graph generated from the overlapped images. Our method also takes advantage of the minimum k-point spanning tree (k-MST) approach to robustify the registration against spurious discrepancies in the images. The proposed algorithm is tested in two applications: registering magnetic resonance (MR) images, and registering an electro-optical image with a terrain height map. In both cases the algorithm is shown to be accurate and robust.

Multiresolution detection of coherent radar targets

We develop and investigate several novel multiresolution algorithms for detecting coherent radar targets embedded in clutter. These multiresolution detectors exploit the fact that prominent target scatterers interfere in a characteristic manner as resolution is changed, while multiresolution clutter signatures are random. We show, both on simulated and collected synthetic aperture radar data, that these multiresolution algorithms yield significant detection improvements over single-pixel, single-resolution constant false alarm rate (CFAR) methods that use only the finest available resolution.

SAR imaging and multiresolution analysis

Many synthetic aperture radar (SAR) image formation algorithms require the computation of a multidimensional Fourier transform of irregularly sampled or unequally spaced data samples. We apply a recently developed algorithm, the unequally spaced FFT (USFFT), to SAR image formation and compare its accuracy and complexity to a conventional algorithm. We find that the USFFT algorithm allows comparable accuracy to traditional approaches at a slightly reduced computational cost. We briefly discuss extensions of the USFFT algorithm to multiresolution SAR imaging.

On the application of Cramer-Rao type lower bounds for constrained estimation

Using limiting forms of the Chapman-Robbins (1951) version of the Barankin bound, a study is made of the effect of parameter constraints on local lower bounds on estimator covariance. One such limiting form is the Cramer-Rao bound, for which constraints are seen to induce an oblique projection of the columns of the inverse Fisher information matrix onto a linear subspace tangent to the parameter constraint set. Another limiting form is the Bhattacharyya bound, which is defined in terms of higher-order Fisher information. For the Bhattacharyya bound, parameter constraints induce a transformation of the higher-order Fisher information that depends on the tangent space projection operator and its derivatives.<<ETX>>

Lower bounds on parametric estimators with constraints

It is demonstrated that implicit constraints of the form G( theta )=0 can be incorporated into the Cramer-Rao lower bound. Constraints on the estimator restrict the local movement of the estimator theta (X) under statistical fluctuation in the observation vector X. A modified Cramer-Rao bound can be obtained by incorporating these restrictions into the formulation of the unconstrained bound. Conversely, when the parameter is constrained, the observation vector X is only allowed to vary according to the probability distribution F/sub theta /, where theta is confirmed to the constraint set. The Fisher information matrix for the case of a constrained parameter can be written as a projection of the unconstrained Fisher matrix onto a subspace defined by the constraint. Conditions under which an estimator achieves the lower bound for constrained estimation are derived, and an example of an estimator that achieves the bound for the linear Gaussian problem is presented.<<ETX>>

A multiresolution approach to target detection in synthetic aperture radar data

We demonstrate the utility of a multiresolution approach for target detection in SAR imagery. In particular, man-made objects exhibit characteristic phase and amplitude fluctuations as the image resolution is varied, while natural terrain (i.e. clutter) has a random signature. We show that the multiresolution clutter process decomposes into a Brownian motion process in resolution. We then construct an optimal invariant multiresolution detector based on a derived multiresolution increments process and show that it significantly outperforms a standard energy detector operating on the finest available SAR resolution.<<ETX>>

Robust material identification in hyperspectral data via multiresolution wavelet techniques

Reviews the characteristics of hyperspectral imaging sensors and describes several important data exploitation applications in remote sensing. The authors then focus on a particular signal processing application, material identification, and propose a novel algorithm based on multiresolution wavelet techniques. Finally, they demonstrate the multiresolution material identification algorithm on data collected with a all-band hyperspectral sensor.

Multiresolution generalized likelihood ratio detection approach to target screening in synthetic aperture radar data

We present a detection concept for initial target screening based on features that are derived from a multiresolution decomposition of synthetic aperture radar (SAR) data. The physical motivation of the multiresolution feature-based approach is the exploitation of signature oscillations produced by the interference between prominant scatterers in cultural objects when resolution is varied. We develop a generalized likelihood ratio test detector which differentiates between first order autoregressive multiresolution processes attributed to different spatial areas. We then derive two special cases of this detector motivated by arguments regarding the clutter statistics. We show that these schemes significantly outperform a standard energy detector operating on the finest available SAR resolution only.