Reconstruction of the backscatter and extinction coefficients is a crucial step in many quantitative remote sensing applications, such as radar, light detection and ranging (lidar), and sonar. We present a novel stochastic filtering approach for the estimation of the backscatter and extinction coefficients from time-range elastic-backscatter lidar data. The Bayesian perspective is adopted; we take as prior a causal first-order autoregressive Gauss-Markov random field tailored to enforce smoothness on time and range dimensions. By using a reduced-order state-space representation of the prior, we derive a suboptimal stochastic filter that recursively computes the backscatter and extinction coefficients at each range-time inversion cell. The estimator is a kind of adaptive extended Kalman filter, being efficient from the computational point of view. A set of experiments illustrates the effectiveness of the proposed approach, namely its advantage over the classical Klett deterministic approach.

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.

We propose an algorithm for the joint estimation of frequency and frequency-rate in signals affected by fading and AWGN. Instead of processing the raw data directly, a stochastic nonlinear filter (NLF) is used for sequential phase estimation; the concatenated ML frequency and frequency-rate estimators are then fed by the NLF phase outputs. As a result of employing stochastic filtering the ML estimators exhibit enhanced robustness to changes of the signal-to-noise ratio and smaller threshold effects. An application of the proposed algorithm to the quasi-coherent detection of M-DPSK signals in nongeostationary satellite communications is also presented. Simulations show that the proposed receiver is rather insensitive to (time-varying) Doppler frequency shifts in flat-fading Rician channels.

The use of multi-level (QAM-type) modulations in mobile communications affected by fading and Doppler shift imposes a tight control on the carrier frequency offset if quasi-coherent detection is a goal. This aspect is taken into account by the receiver herein proposed. A 16-DAPSK (differential amplitude phase shift-keying) scheme is considered, with one bit being absolutely encoded in amplitude and the other two bits differentially encoded in phase by a 8-state Ungerboeck trellis-code. To estimate the frequency offset the receiver includes a bank of stochastic nonlinear filters, an innovations processor and a modified Kay algorithm. Sequence detection is performed by a gain estimator and a Viterbi algorithm fed by the frequency-corrected input samples. The receiver can cope with considerable phase drifts within the symbol interval, which allows significant Doppler shifts or the operation of free-running oscillators with moderate frequency stabilities and large symbol durations.

An efficient algorithm for the computation of tr{TR/sup -1/}, where T and R are Toeplitz matrices and R is also symmetric positive definite, is presented. The method exploits the fact that the trace of TR/sup -1/ depends only on the sum of the diagonals of R/sup -1/, and not on the whole matrix R/sup -1/. To obtain this sum, a fast efficient technique, built upon the Trench (1964) algorithm for computing the inverse of a Toeplitz matrix, is developed. The complexity of the algorithm depends on the generation function of matrix R and is O(N ln N) for generic functions and O(p ln p) for AR(p) functions.

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.

This paper proposes an importance sampling methodology for the performance evaluation of a class of open-loop receivers with random carrier phase tracking in additive white Gaussian noise channels. The receivers, consisting of a bank of extended Kalman-Bucy filters and a decision algorithm based on the filters' innovations processes, perform symbol-by-symbol phase detection while kepping track of the random phase process within the symbol interval. We use a large deviations approach to start a stochastic importance sampling optimization, both for the irreducible error floor and for the general noisy operation of the receiver. Our simulations show a practical coincidence with conventional Monte Carlo results, with considerable simulation time gains.

Differential detection of phase-shift keying signals entails the ability to establish a stable phase reference based on previous symbol(s). In low bit-rate communications strongly affected by Doppler effect, like those making use of non-geostationary satellites, significant carrier phase drifts may occur within the symbol interval; thus, large irreducible error floors result if the Doppler frequency shift (DFS) is not estimated and subtracted. We propose a state-space based receiver for M-DPSK signals in transmissions affected by fast fading and DFS, which evaluates the multiplicative distortion (amplitude and phase) of the baseband signal and uses those estimates to track the frequency offset. In addition, the proposed receiver can estimate the power of the line-of-sight component and the Rician fading parameter K which allow to monitor the transmission quality and control the transmitted power in adaptive systems. Simulations presented for 4-DPSK show that the performance of the new receiver is superior to that of conventional receivers in the presence of large DFS, exhibiting substantially lower error floors.

The problem of cluster defining criteria has been addressed in various forms. In the paper, a cluster isolation criterion is proposed, underlying an hypothesis of smooth dissimilarity increments between neighboring patterns within a cluster. This isolation criterion is merged in a hierarchical agglomerative clustering algorithm, producing a data partitioning and simultaneous accessibility to the intrinsic data inter-relationships in terms of a dendrogram-type graph. By defining adequate dissimilarity measures, the algorithm is applied to vector based pattern analysis and to categorization of structural patterns. Both simulated data and real applications, in the context of automatic analysis of contour images, are presented to illustrate and evaluate the method. Examples demonstrate the versatility of the method in identifying arbitrary shape and size clusters, intrinsically finding the number of clusters.

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.

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.

We propose an open-loop receiver that performs simultaneous channel state estimation and symbol detection in frequency-flat, fast-fading Rician channels affected by large Doppler frequency shifts. This structure includes a Kay (1989) frequency estimator, a bank of nonlinear filters (one for each symbol of the M-ary alphabet) and a symbol decision algorithm. The nonlinear filters estimate the channel state, the errors produced by the Kay estimator, and provide the innovations processes for the symbol detection. This estimation/detection structure exhibits fast phase/frequency acquisition capability which is essential in burst transmissions or with fading channels. The receiver is able to cope with large frequency deviations that are typical in LEO/MEO communication systems.

This paper proposes a restoration scheme for noisy images generated by coherent imaging systems (e.g., synthetic aperture radar, synthetic aperture sonar ultrasound imaging, and laser imaging). The approach is Bayesian: the observed image intensity is assumed to be a random variable with gamma density; the image to be restored (mean amplitude) is modeled by a compound Gauss-Markov random field which enforces smoothness on homogeneous regions while preserving discontinuities between neighboring regions. A Neyman-Pearson detection criterion is used to infer the discontinuities, thus allowing to select a given false alarm probability maximizing the detection probability. The whole restoration scheme is then cast into a maximum a posteriori probability (MAP) problem. An expectation maximization type iterative scheme embedded in a continuation algorithm is used to compute the MAP solution. An application example performed on radar data is presented.

The paper develops an open-loop digital receiver suitable for operation with frequency flat-fading channels disturbed by fast-fading conditions and large carrier phase variations. The receiver consists of a bank of "matched" stochastic nonlinear filters (NLFs) and a maximum a posteriori probability (MAP) decision processor driven by the filters' innovations processes. This structure is able to perform symbol-by-symbol detection while keeping track of multiplicative distortion (carrier amplitude and phase) within the symbol interval. The NLF propagates probability densities represented as products of Tikhonov and Gaussian functions, whose parameters are computed according to a minimum Kullback (1959) distance criterion, i,e,. we adopt an information preserving strategy. This filter is hangup free and outperforms the extended Kalman-Bucy (1972, 1973) filter (EKBF), especially in terms of phase acquisition. These characteristics explain why the NLF-based receiver may exhibit much lower error probabilities than those obtained with an equivalent EKBF-based receiver. Simulations show that the proposed detection/estimation scheme is robust against mistuning of the receiver parameters, being appropriate for all-digital modems in mobile radio communications.

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.

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.

This paper describes an implementation of a long distance echo canceller which copes with double talking situations and exceeds the CCITT G.165 recommendation. The proposed solution is based on short length adaptive filters centered on the positions of the most significant echoes, which are tracked by time-delay estimators. To deal with double talking situations a speech detector is employed. The resulting algorithm enables long-distance echo cancellation with low computational requirements. It reaches greater echo return loss enhancement and shows faster convergence speed as compared with results reported in recent literature.

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.

This paper addresses the problem of language recognition according to stochastic attributed context-free grammars. Starting with an application as the main motivation-automatic sleep analysis-a heuristic recognizer for attributed grammars is proposed. The algorithm (an extension of a previously developed method for stochastic context-free grammars) is there used both in the process of grammar inference and on the classification of sleep macrostructure. The generality of the method features its application into other areas, namely in natural language and speech understanding.

We introduce a fully adaptive active contour model in which no parameters have to be set a priori or tuned by the user. It is based on elliptic Fourier contour description and on the minimum description length (MDL) principle. The proposed technique estimates all the observation model parameters (e.g., noise variances), the order of the contour description (number of Fourier coefficients), and the contour itself.

This paper addresses the problem of clustering of syntactic patterns using string descriptions. A new similarity measure between strings is proposed based on the search of common subpatterns by means of Solomonoff's coding. This coding scheme is further explored in an agglomerative clustering algorithm, which uses a minimum description length (MDL) type criterion.

Presents a new method for endocardial (inner) and epicardial (outer) contour estimation from sequences of echocardiographic images. The framework herein introduced is fine-tuned for parasternal short axis views at the papillary muscle level. The underlying model is probabilistic; it captures the relevant features of the image generation physical mechanisms and of the heart morphology. Contour sequences are assumed to be two-dimensional noncausal first-order Markov random processes; each variable has a spatial index and a temporal index. The image pixels are modeled as Rayleigh distributed random variables with means depending on their positions (inside endocardium, between endocardium and pericardium, or outside pericardium). The complete probabilistic model is built under the Bayesian framework. As estimation criterion the maximum a posteriori (MAP) is adopted. To solve the optimization problem, one is led to (joint estimation of contours and distributions' parameters), the authors introduce an algorithm herein named iterative multigrid dynamic programming (IMDP). It is a fully data-driven scheme with no ad-hoc parameters. The method is implemented on an ordinary workstation, leading to computation times compatible with operational use. Experiments with simulated and real images are presented.

This paper formulates interferometric image reconstruction as a 2D absolute phase estimation problem. The original phase image is modeled as a sample of a Gauss Markov random field; the observations are the noisy in-phase (cosine) and quadrature (sine) images. The proposed solution combines features of the iterated conditional modes algorithm with nonlinear stochastic absolute phase estimation concepts. Examples of important applications are: interferometric synthetic aperture radar, optical interferometry, magnetic resonance imaging, and diffraction tomography.

Accurate and fully automatic assessment of vessel (stenoses) dimensions in angiographic images has been sought as a diagnostic tool, in particular for coronary heart disease. Here, the authors propose a new technique to estimate vessel borders in angiographic images, a necessary first step of any automatic analysis system. Unlike in previous approaches, the obtained edge estimates are not artificially smoothed; this is extremely important since quantitative analysis is the goal. Another important feature of the proposed technique is that no constant background is assumed, this making it well suited for nonsubtracted angiograms. The key aspect of the authors' approach is that continuity/smoothness constraints are not used to modify the estimates directly derived from the image (which would introduce distortion) but rather to elect (without modifying) candidate estimates. Robustness against unknown background is provided by the use a morphological edge operator, instead of some linear operator (such as a matched filter) which has to assume known background and known vessel shape.

This paper introduces an improved stochastic context-free language recognizer. The algorithm is basically a best-first search on the state space of dotted rules, following Earley's (1986) notation. Using heuristic merit functions; the algorithm produces the possible successors of a node (representing a state) and proceeds by exploring the most promising generated node. Two simple grammar independent heuristics are introduced: (1) ensuring convergence to a solution; and (2) guaranteeing the choice of the solution with the highest probability. It is shown that the algorithm outperforms Earley's method in both time and space domains. Several test grammars are used to illustrate the method and show its superior performance.>

This paper considers the design of phase estimators by combining concepts of stochastic nonlinear filtering and information theory. To propagate the involved probability density functions, adequate finite representations are needed. This is accomplished in this work by adopting minimum Kullback (1978) distance criteria. Applied to the important and paradigmatic cyclic phase estimation problem, our approach leads to consistent and systematic design methods. The resulting simple and parallelizable structure outperforms the commonly used extended Kalman-Bucy filter in tracking and acquisition situations. These features make the developed nonlinear filter suited to digital communications (carrier synchronization).>

Microwave broadband reflectometry is used to determine the spatial distribution of plasma density (density profile) in experimental nuclear fusion devices. The position of each plasma reflecting layer is evaluated by Abel integration of the phase rate of the reflectometric signal that results from mixing the plasma incident and reflected waves. The signal processing problem is cast in the stochastic nonlinear filtering framework. The phase/frequency corresponding to the reflecting layer dynamics is modeled as a two-dimensional Markovian process, from which only one component (phase) is observed. Guided by these (noisy) observations a suboptimal filter propagates the joint (phase/frequency) a posteriori probability density function, allowing to estimate the phase rate. The purpose is to develop a robust and versatile tool to process reflectometric data.>

Discontinuity-preserving Bayesian image restoration, based on Markov random fields (MRF), involves an intensity field, representing the image to be restored, and an edge (discontinuity) field. The usual strategy is to perform joint maximum a posteriori (MAP) estimation of the intensity and discontinuity fields, this requiring the specification of Bayesian priors. Departing from this approach, we interpret the discontinuity locations as deterministic unknown parameters of the intensity field. This leads to a parameter estimation problem with the important feature of having an unknown number of parameters. We introduce a discontinuity-preserving image restoration criterion (and an algorithm to implement it) based on the minimum description length (MDL) principle and built upon a compound Gauss-Markov random field (CGMRF) model; the proposed formulation does not involve the specification of a prior for the edge field which is adaptively inferred from the data.>

In this paper, a solution to the problem of introducing a priori information in phrase structured syntactic pattern recognition systems is proposed. The method consists of devising subpatterns (representing regularities in the symbol sequences) by means of Solomonoff coding, and using these subpatterns as a priori information for constraining the production of structural samples, which serve as input to grammar inference algorithms. We have shown, in a previous work, the adequacy of syntactic modeling in automatic sleep analysis. In this paper, a further improvement is achieved by applying the proposed methodology.

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.

An algorithm is introduced for discontinuity-preserving visual surface reconstruction, inspired by the formulation of the problem as the fitting of a weak membrane to the observed data. The method slowly applies the data 'force' to a weak membrane, which is allowed to tear when the tension exceeds a certain threshold. The algorithm is named simulated tearing (ST). Formally, ST is a deterministic continuation method, i.e., the problem to be solved is embedded in a family of problems, of which the first member has a simple solution. The proposed method is tested and compared with mean field annealing (MFA), using real and synthetic images. It is concluded that ST is simpler, faster, and slightly outperforms MFA. ST allows implementation based on integer arithmetic.>

Two neural algorithms for image restoration are proposed. The image is considered degraded by linear blur and additive white Gaussian noise. Maximum a posteriori estimation and regularization theory applied to this problem lead to the same high dimension optimization problem. The developed schemes, one having a sequential updating schedule and the other being fully parallel, implement iterative minimization algorithms which are proved to converge. The robustness of these algorithms with respect to finite numerical precision is studied. Examples with real images are presented.>

The hypnogram is a schematic representation of sleep dynamics as a sequence of stages along the night. In a sense, it is a model of the so called sleep macrostructure. This paper considers the hypnogram as expression of a language whose structure is to be analysed and modeled in terms of stochastic grammars. These are inferred using Crespi-Reghizzi's method. A parsing algorithm, exploring the particular structure of the inferred grammars, has been developed. Classification strategies for both noisy and non-noisy patterns is also discussed. An example concerning a population of normals and a population of psychiatric (dysthymic) patients is presented.>

A method for left ventricular contour determination in digital angiographic images is presented. The problem is formulated in a Bayesian framework, adopting as the estimation criterion the maximum a posterior probability (MAP). The true contour is modeled as a one-dimensional noncausal Gauss-Markov random field and the observed image is described as the superposition of an ideal image (deterministic function of the real contour) with white Gaussian noise. The proposed algorithm estimates simultaneously the contour and the model parameters by implementing an adaptive version of the iterated conditional modes algorithm. The convergence of this scheme is proved and its performance evaluated on both synthetic and real angiographic images. The method exhibits robustness against image artifacts and the contours obtained are considered good by expert clinicians. Being completely data-driven and fast, the proposed algorithm is suitable for routine clinical use.