José M. N. Leitão

Unsupervised contour representation and estimation using B-splines and a minimum description length criterion

This paper describes a new approach to adaptive estimation of parametric deformable contours based on B-spline representations. The problem is formulated in a statistical framework with the likelihood function being derived from a region-based image model. The parameters of the image model, the contour parameters, and the B-spline parameterization order (i.e., the number of control points) are all considered unknown. The parameterization order is estimated via a minimum description length (MDL) type criterion. A deterministic iterative algorithm is developed to implement the derived contour estimation criterion, the result is an unsupervised parametric deformable contour: it adapts its degree of smoothness/complexity (number of control points) and it also estimates the observation (image) model parameters. The experiments reported in the paper, performed on synthetic and real (medical) images, confirm the adequate and good performance of the approach.

A new cluster isolation criterion based on dissimilarity increments

This paper addresses the problem of cluster defining criteria by proposing a model-based characterization of interpattern relationships. Taking a dissimilarity matrix between patterns as the basic measure for extracting group structure, dissimilarity increments between neighboring patterns within a cluster are analyzed. Empirical evidence suggests modeling the statistical distribution of these increments by an exponential density; we propose to use this statistical model, which characterizes context, to derive a new cluster isolation criterion. The integration of this criterion in a hierarchical agglomerative clustering framework produces a partitioning of the data, while exhibiting data interrelationships in terms of a dendrogram-type graph. The analysis of the criterion is undertaken through a set of examples, showing the versatility of the method in identifying clusters with arbitrary shape and size; the number of clusters is intrinsically found without requiring ad hoc specification of design parameters nor engaging in a computationally demanding optimization procedure.

The Z/spl pi/M algorithm: a method for interferometric image reconstruction in SAR/SAS

This paper presents an effective algorithm for absolute phase (not simply modulo-2-pi) estimation from incomplete, noisy and modulo-2pi observations in interferometric aperture radar and sonar (InSAR/InSAS). The adopted framework is also representative of other applications such as optical interferometry, magnetic resonance imaging and diffraction tomography. The Bayesian viewpoint is adopted; the observation density is 2-pi-periodic and accounts for the interferometric pair decorrelation and system noise; the a priori probability of the absolute phase is modeled by a compound Gauss-Markov random field (CGMRF) tailored to piecewise smooth absolute phase images. We propose an iterative scheme for the computation of the maximum a posteriori probability (MAP) absolute phase estimate. Each iteration embodies a discrete optimization step (Z-step), implemented by network programming techniques and an iterative conditional modes (ICM) step (pi-step). Accordingly, the algorithm is termed ZpiM, where the letter M stands for maximization. An important contribution of the paper is the simultaneous implementation of phase unwrapping (inference of the 2pi-multiples) and smoothing (denoising of the observations). This improves considerably the accuracy of the absolute phase estimates compared to methods in which the data is low-pass filtered prior to unwrapping. A set of experimental results, comparing the proposed algorithm with alternative methods, illustrates the effectiveness of our approach.

Gating Functions for Multipath Mitigation in GNSS BOC Signals

A new multipath mitigation technique is proposed for binary offset carrier (BOC) signals in global navigation satellite systems (GNSS) using the concept of gating function originally conceived for the GPS coarse-acquisition (C/A) code. Specially-tailored pulses are utilized to diminish the number of false-lock points of the code discriminator response and to improve the multipath mitigation capability. The code loop includes only four real correlators (two extra correlators are required for the simplified bump-jumping algorithm with BOC(n,n) signals). Results obtained with BOC(n,n) and BOC(2n,n) signals show that this technique eliminates the multipath ranging errors for reflected rays with relative delays typically above twenty percent of the spreading code chip duration, thus comparing favorably with the conventional receiver correlation techniques.

Unsupervised image restoration and edge location using compound Gauss-Markov random fields and the MDL principle

Discontinuity-preserving Bayesian image restoration typically involves two Markov random fields: one representing the image intensities/gray levels to be recovered and another one signaling discontinuities/edges to be preserved. The usual strategy is to perform joint maximum a posterori (MAP) estimation of the image and its edges, which requires the specification of priors for both fields. Instead of taking an edge prior, we interpret discontinuities (in fact their locations) as deterministic unknown parameters of the compound Gauss-Markov random field (CGMRF), which is assumed to model the intensities. This strategy should allow inferring the discontinuity locations directly from the image with no further assumptions. However, an additional problem emerges: the number of parameters (edges) is unknown. To deal with it, we invoke the minimum description length (MDL) principle; according to MDL, the best edge configuration is the one that allows the shortest description of the image and its edges. Taking the other model parameters (noise and CGMRF variances) also as unknown, we propose a new unsupervised discontinuity-preserving image restoration criterion. Implementation is carried out by a continuation-type iterative algorithm which provides estimates of the number of discontinuities, their locations, the noise variance, the original image variance, and the original image itself (restored image). Experimental results with real and synthetic images are reported.

Absolute phase image reconstruction: a stochastic nonlinear filtering approach

This paper formulates and proposes solutions to the problem of estimating/reconstructing the absolute (not simply modulo-2pi) phase of a complex random field from noisy observations of its real and imaginary parts. This problem is representative of a class of important imaging techniques such as interferometric synthetic aperture radar, optical interferometry, magnetic resonance imaging, and diffraction tomography. We follow a Bayesian approach; then, not only a probabilistic model of the observation mechanism, but also prior knowledge concerning the (phase) image to be reconstructed, are needed. We take as prior a nonsymmetrical half plane autoregressive (NSHP AR) Gauss-Markov random field (GMRF). Based on a reduced order state-space formulation of the (linear) NSHP AR model and on the (nonlinear) observation mechanism, a recursive stochastic nonlinear filter is derived, The corresponding estimates are compared with those obtained by the extended Kalman-Bucy filter, a classical linearizing approach to the same problem. A set of examples illustrate the effectiveness of the proposed approach.

Nonparametric estimation of mean Doppler and spectral width

This paper proposes a new nonparametric method for estimation of spectral moments of a zero-mean Gaussian process immersed in additive white Gaussian noise. Although the technique is valid for any order moment, particular attention is given to the mean Doppler (first moment) and to the spectral width (square root of the centered second spectral moment). By assuming that the power spectral density (PSD) of the underlying process is bandlimited, the maximum-likelihood estimates of its spectral moments are derived. A suboptimal estimate based on the sample covariance is also studied. Both methods are robust in the sense that they do not rely on any assumption concerning the PSD (besides being bandlimited). Under weak conditions, the set of estimates based on sample covariance is unbiased and strongly consistent. Compared with the classical pulse pair and the periodogram-based estimators, the proposed methods exhibit better statistical properties for asymmetric spectra and/or spectra with large spectral widths, while involving a computational burden of the same order.

Sequential and parallel image restoration: neural network implementations

Sequential and parallel image restoration algorithms and their implementations on neural networks are proposed. For images degraded by linear blur and contaminated by additive white Gaussian noise, maximum a posteriori (MAP) estimation and regularization theory lead to the same high dimension convex optimization problem. The commonly adopted strategy (in using neural networks for image restoration) is to map the objective function of the optimization problem into the energy of a predefined network, taking advantage of its energy minimization properties. Departing from this approach, we propose neural implementations of iterative minimization algorithms which are first proved to converge. The developed schemes are based on modified Hopfield (1985) networks of graded elements, with both sequential and parallel updating schedules. An algorithm supported on a fully standard Hopfield network (binary elements and zero autoconnections) is also considered. Robustness with respect to finite numerical precision is studied, and examples with real images are presented.

Adaptive B-splines and boundary estimation

This paper describes a boundary estimation scheme based on a new adaptive approach to B-spline curve fitting. The number of control points of the spline, their locations, and the observation parameters, are all considered unknown. The optimal number of control points is estimated via a new minimum description length (MDL) type criterion. The result is an adaptive parametrically deformable contour which also estimates the observation model parameters. Experiments on synthetic and real (medical) images confirm the adequacy and good performance of the approach.

Strobe Pulse Design for Multipath Mitigation in BOC GNSS Receivers

Binary offset carrier (BOC) modulations have been considered for the new GNSS signals since they achieve better tracking performance than PSK in the presence of channel noise and multipath. Besides, the concept of delay lock-loop based on symmetrical strobe pulses can be extended to BOC signals with significant advantage in the close-in multipath region. Herein, a new approach to the design of asymmetrical strobe pulses for BOC signals is proposed. A target code discriminator response with desirable characteristics is defined allowing to determine the strobe pulse as the solution of an integral equation. The resulting pulse provides good multipath mitigation capability, extended code tracking range, and lack of false code lock points.