We present efficient multiscale approaches to the segmentation of natural clutter, specifically grass and forest, and to the enhancement of anomalies in synthetic aperture radar (SAR) imagery. The methods we propose exploit the coherent nature of SAR sensors. In particular, they take advantage of the characteristic statistical differences in imagery of different terrain types, as a function of scale, due to radar speckle. We employ a class of multiscale stochastic processes that provide a powerful framework for describing random processes and fields that evolve in scale. We build models representative of each category of terrain of interest (i.e., grass and forest) and employ them in directing decisions on pixel classification, segmentation, and anomalous behaviour. The scale-autoregressive nature of our models allows extremely efficient calculation of likelihoods for different terrain classifications over windows of SAR imagery. We subsequently use these likelihoods as the basis for both image pixel classification and grass-forest boundary estimation. In addition, anomaly enhancement is possible with minimal additional computation. Specifically, the residuals produced by our models in predicting SAR imagery from coarser scale images are theoretically uncorrelated. As a result, potentially anomalous pixels and regions are enhanced and pinpointed by noting regions whose residuals display a high level of correlation throughout scale. We evaluate the performance of our techniques through testing on 0.3-m resolution SAR data gathered with Lincoln Laboratory's millimeter-wave SAR.

Recently, a class of multiscale stochastic models has been introduced in which random processes and fields are described by scale-recursive dynamic trees. A major advantage of this framework is that it leads to an extremely efficient, statistically optimal algorithm for least-squares estimation. In certain applications, however, estimates based on the types of multiscale models previously proposed may not be adequate, as they have tended to exhibit a visually distracting blockiness. We eliminate this blockiness by discarding the standard assumption that distinct nodes on a given level of the multiscale process correspond to disjoint portions of the image domain; instead, we allow a correspondence to overlapping portions of the image domain. We use these so-called overlapping-tree models for both modeling and estimation. In particular, we develop an efficient multiscale algorithm for generating sample paths of a random field whose second-order statistics match a prespecified covariance structure, to any desired degree of fidelity. Furthermore, we demonstrate that under easily satisfied conditions, we can "lift" a random field estimation problem to one defined on an overlapped tree, resulting in an estimation algorithm that is computationally efficient, directly produces estimation error covariances, and eliminates blockiness in the reconstructed imagery without any sacrifice in the resolution of fine-scale detail.

A class of multiscale stochastic models has been introduced in which Gaussian random processes are described by scale-recursive dynamics that are indexed by the nodes of a tree. One of the primary reasons the framework is useful is that it leads to an extremely fast, statistically optimal algorithm for least-squares estimation in the context of 2-D images. We refine this approach to estimation by eliminating the visually distracting blockiness that has been observed in the previous work. We eliminate the blockiness by discarding the standard assumption that distinct nodes at a given level of our tree correspond to disjoint portions of the image domain; as a consequence of this simple idea, a given image pixel may now correspond to several tree nodes. We develop tools for systematically building overlapping-tree multiscale representations of prespecified statistics, and we develop a corresponding estimation algorithm for this processes. In this way, we achieve nearly optimal estimation results, we generate corresponding error covariance information, and we eliminate blockiness without sacrificing the resolution of fine-scale detail.

A computationally efficient method is described for simulating high-resolution synthetic aperture radar (SAR) imagery. The method involves generating spatially correlated random numbers statistically distributed according to the gamma product model (K-distribution), a non-Gaussian model that has received a great deal of attention in the literature recently. The spatial correlation is created by exploiting the reproductive property of the gamma distribution, and is computed by summing elements of an uncorrelated, gamma distributed random field with properly chosen parameters. Comparisons are presented between the simulated SAR imagery and real SAR imagery gathered with the MIT Lincoln Laboratory millimeter-wave SAR.>