We develop a method for the formation of spotlight-mode synthetic aperture radar (SAR) images with enhanced features. The approach is based on a regularized reconstruction of the scattering field which combines a tomographic model of the SAR observation process with prior information regarding the nature of the features of interest. Compared to conventional SAR techniques, the method we propose produces images with increased resolution, reduced sidelobes, reduced speckle and easier-to-segment regions. Our technique effectively deals with the complex-valued, random-phase nature of the underlying SAR reflectivities. An efficient and robust numerical solution is achieved through extensions of half-quadratic regularization methods to the complex-valued SAR problem. We demonstrate the performance of the method on synthetic and real SAR scenes.

In this paper we establish a set of results showing that the vertices of any simply-connected planar polygonal region can be reconstructed from a finite number of its complex moments. These results find applications in a variety of apparently disparate areas such as computerized tomography and inverse potential theory, where in the former it is of interest to estimate the shape of an object from a finite number of its projections; while in the latter, the objective is to extract the shape of a gravitating body from measurements of its exterior logarithmic potentials at a finite number of points. We show that the problem of polygonal vertex reconstruction from moments can in fact be posed as an array processing problem, and taking advantage of this relationship, we derive and illustrate several new algorithms for the reconstruction of the vertices of simply-connected polygons from moments.

This paper presents a survey of recent research on sparsity-driven synthetic aperture radar (SAR) imaging.In particular, it reviews (i) analysis and synthesis-based sparse signal representation formulations for SAR image formation together with the associated imaging results; (ii) sparsity-based methods for wide-angle SAR imaging and anisotropy characterization; (iii) sparsity-based methods for joint imaging and autofocusing from data with phase errors; (iv) techniques for exploiting sparsity for SAR imaging of scenes containing moving objects, and (v) recent work on compressed sensing-based analysis and design of SAR sensing missions.

No abstract

Abstruct-A recently developed multiresolution estimation framework offers the possibility of highly efficient statistical analysis, interpolation, and smoothing of extremely large data sets in a multiscale fashion. This framework enjoys a number of advantages not shared by other statistically-based methods. In particular, the algorithms resulting from this framework have complexity that scales only linearly with problem size, yielding constant complexity load per grid point independent of problem size. Furthermore these algorithms directly provide interpolated estimates at multiple resolutions, accompanying error variance statistics of use in assessing resolutionlaccuracy tradeoffs and in detecting statistically significant anomalies, and maximum likelihood estimates of parameters such as spectral power law coefficients. Moreover, the efficiency of these algorithms is completely insensitive to irregularities in the sampling or spatial distribution of measurements and to heterogeneities in measurement errors or model parameters. For these reasons this approach has the potential of being an effective tool in a variety of remote sensing problems. In this paper, we demonstrate a realization of this potential by applying the multiresolution framework to a problem of considerable current interest-the interpolation and statistical analysis of ocean surface data from the TOPEXPOSEIDON altimeter.

We present a novel multi-resolution variational framework for vascular optical coherence elastography (OCE). This method exploits prior information about arterial wall biomechanics to produce robust estimates of tissue velocity and strain, reducing the sensitivity of conventional tracking methods to both noise- and strain-induced signal decorrelation. The velocity and strain estimation performance of this new estimator is demonstrated in simulated OCT image sequences and in benchtop OCT scanning of a vascular tissue sample.

Abstract-Recently, a framework for multiscale stochastic modeling was introduced based on coarse-to-fine scale-recursive dynamics defined on trees. This model class has some attractive characteristics which lead to extremely efficient, statistically optimal signal and image processing algorithms. In this paper, we show that this model class is also quite rich. In particular, we describe how 1-D Markov processes and 2-D Markov random fields (MRF's) can be represented within this framework. The recursive structure of 1-D Markov processes makes them simple to analyze, and generally leads to computationally efficient algorithms for statistical inference. On the other hand, 2-D MRF's are well known to be very difficult to analyze due to their noncausal structure, and thus their use typically leads to computationally intensive algorithms for smoothing and parameter identification. In contrast, our multiscale representations are based on scale-recursive models and thus lead naturally to scale-recursive algorithms, which can be substantially more efficient computationally than those associated with MRF models. In 1-D, the multiscale representation is a generalization of the midpoint deflection construction of Brownian motion. The representation of 2-D MRF's is based on a further generalization to a "midline" deflection construction. The exact representations of 2-D MRF's are used to motivate a class of multiscale approximate MRF models based on one-dimensional wavelet transforms. We demonstrate the use of these latter models in the context of texture representation and, in particular, we show how they can be used as approximations for or alternatives to well-known MRF texture models.

Absfruet-A new approach to regularization methods for image processing is introduced and developed using as a vehicle the problem of computing dense optical flow fields in an image sequence. Standard formulations of this problem require the computationally intensive solution of an elliptic partial differential equation that arises from the often used "smoothness constraint" 'yl". regularization. The interpretation of the smoothness constraint is utilized as a "fractal prior" to motivate regularization based on a recently introduced class of multiscale stochastic models. The solution of the new problem formulation is computed with an efficient multiscale algorithm. Experiments on several image sequences demonstrate the substantial computational savings that can be achieved due to the fact that the algorithm is noniterative and in fact has a per pixel computational complexity that is independent of image size. The new approach also has a number of other important advantages. Specifically, multiresolution flow field estimates are available, allowing great flexibility in dealing with the tradeoff between resolution and accuracy. Multiscale error covariance information is also available, which is of considerable use in assessing the accuracy of the estimates. In particular, these error statistics can be used as the basis for a rational procedure for determining the spatially-varying optimal reconstruction resolution. Furthermore, if there are compelling reasons to insist upon a standard smoothness constraint, our algorithm provides an excellent initialization for the iterative algorithms associated with the smoothness constraint problem formulation. Finally, the usefulness of our approach should extend to a wide variety of ill-posed inverse problems in which variational techniques seeking a "smooth" solution are generally Used.