William Clement Karl

Feature-enhanced synthetic aperture radar image formation based on nonquadratic regularization

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.

Real-time tracking using level sets

In this paper we propose a novel implementation of the level set method that achieves real-time level-set-based video tracking. In our fast algorithm, the evolution of the curve is realized by simple operations such as switching elements between two linked lists and there is no need to solve any partial differential equations. Furthermore, a novel procedure based on Gaussian filtering is introduced to incorporate boundary smoothness regularization. By replacing the standard curve length penalty with this new smoothing procedure, further speedups are obtained. Another advantage of our fast algorithm is that the topology of the curves can be controlled easily. For the tracking of multiple objects, we extend our fast algorithm to maintain the desired topology for multiple object boundaries based on ideas from discrete topology. With our fast algorithm, a real-time system has been implemented on a standard PC and only a small fraction of the CPU power is used for tracking. Results from standard test sequences and our realtime system are presented.

Probabilistic video stabilization using Kalman filtering and mosaicking

The removal of unwanted, parasitic vibrations in a video sequence induced by camera motion is an essential part of video acquisition in industrial, military and consumer applications. In this paper, we present a new image processing method to remove such vibrations and reconstruct a video sequence void of sudden camera movements. Our approach to separating unwanted vibrations from intentional camera motion is based on a probabilistic estimation framework. We treat estimated parameters of interframe camera motion as noisy observations of the intentional camera motion parameters. We construct a physics-based state-space model of these interframe motion parameters and use recursive Kalman filtering to perform stabilized camera position estimation. A six-parameter affine model is used to describe the interframe transformation, allowing quite accurate description of typical scene changes due to camera motion. The model parameters are estimated using a p-norm-based multi-resolution approach. This approach is robust to model mismatch and to object motion within the scene (which are treated as outliers). We use mosaicking in order to reconstruct undefined areas that result from motion compensation applied to each video frame. Registration between distant frames is performed efficiently by cascading interframe affine transformation parameters. We compare our methods performance with that of a commercial product on real-life video sequences, and show a significant improvement in stabilization quality for our method.

A Real-Time Algorithm for the Approximation of Level-Set-Based Curve Evolution

In this paper, we present a complete and practical algorithm for the approximation of level-set-based curve evolution suitable for real-time implementation. In particular, we propose a two-cycle algorithm to approximate level-set-based curve evolution without the need of solving partial differential equations (PDEs). Our algorithm is applicable to a broad class of evolution speeds that can be viewed as composed of a data-dependent term and a curve smoothness regularization term. We achieve curve evolution corresponding to such evolution speeds by separating the evolution process into two different cycles: one cycle for the data-dependent term and a second cycle for the smoothness regularization. The smoothing term is derived from a Gaussian filtering process. In both cycles, the evolution is realized through a simple element switching mechanism between two linked lists, that implicitly represents the curve using an integer valued level-set function. By careful construction, all the key evolution steps require only integer operations. A consequence is that we obtain significant computation speedups compared to exact PDE-based approaches while obtaining excellent agreement with these methods for problems of practical engineering interest. In particular, the resulting algorithm is fast enough for use in real-time video processing applications, which we demonstrate through several image segmentation and video tracking experiments.

Multiresolution optimal interpolation and statistical analysis of TOPEX/POSEIDON satellite altimetry

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

A fast level set method without solving PDEs [image segmentation applications]

In this paper, we propose a novel and fast level set method without the need for solving PDEs (partial differential equations) while preserving the advantages of level set methods, such as the automatic handling of topological changes. The foundation of our method is the direct use of an optimality condition for the final curve location based on the speed field. By testing this condition, only simple operations like insertion and deletion on two lists of boundary points are needed to evolve the curve. Our method is suitable for a set of general evolution speeds that are composed of two parts: an external speed derived from the image data and a speed term imposing boundary smoothness or regularization. In our experiments, we demonstrate that our algorithm is approximately two orders of magnitude faster than previous optimized narrow band algorithms for image segmentation tasks.

OCT-based arterial elastography: robust estimation exploiting tissue biomechanics

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.

Toward nanometer-scale resolution in fluorescence microscopy using spectral self-interference

We introduce a new fluorescence microscopy technique that maps the axial position of a fluorophore with subnanometer precision. The interference of the emission of fluorophores in proximity to a reflecting surface results in fringes in the fluorescence spectrum that provide a unique signature of the axial position of the fluorophore. The nanometer sensitivity is demonstrated by measuring the height of a fluorescein monolayer covering a 12-nm step etched in silicon dioxide. In addition, the separation between fluorophores attached to the top or the bottom layer in a lipid bilayer film is determined. We further discuss extension of this microscopy technique to provide resolution of multiple layers spaced as closely as 10 nm for sparse systems.

Reconstructing polygons from moments with connections to array processing

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, whereas 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. >

Sparsity-Driven Synthetic Aperture Radar Imaging: Reconstruction, autofocusing, moving targets, and compressed sensing

This article presents a survey of recent research on sparsity-driven synthetic aperture radar (SAR) imaging. In particular, it reviews 1) the analysis and synthesis-based sparse signal representation formulations for SAR image formation together with the associated imaging results, 2) sparsity-based methods for wide-angle SAR imaging and anisotropy characterization, 3) sparsity-based methods for joint imaging and autofocusing from data with phase errors, 4) techniques for exploiting sparsity for SAR imaging of scenes containing moving objects, and 5) recent work on compressed sensing (CS)-based analysis and design of SAR sensing missions.