In this paper, we develop a procedure to factorize a broadband signal into the product of a narrow-band modulator and a wide-band carrier. The approach is based on using the Singular Value Decomposition theorem and the Discrete Fourier Transform. Finally, some experiments on synthetic and speech signals are provided to show the effectiveness of the proposed approach.

Filtering in digital images via Integral Image yields fast computation times for uniform filtering. The extension by Heckbert to perform filtering via repeated integration provides a way for non-uniform filtering, but has its own limitations. A recent method by Hussein et al. provides non-uniform filtering by Euler expansion of filtering kernels, and is called kernel integral method. We propose a simplification for non-uniform filtering by stacking of box filters from a single integral image. Results show speedups of as much as 40:1, similar to run time performance gains in kernel integral method, when comparing to naïve nonuniform filtering, while at the same time reducing the setup time drastically.

When objects in images are small or blurred enough, geometric features are inadequate for reliable pattern recognition. We introduce the Pattern Recognition by Cluster Accumulation (PRCA) method to show that pattern recognition performance can be improved in this situation by using radiometric features for object detection. In addition, PRCA uses clustering to provide feature selection and dimensionality reduction. It uses accumulation to provide robustness against translation, rotation, cluster shape distortion, and inappropriate splitting or merging of clusters. We find that PRCA performs faster than normalized cross correlation and faster than mutual information methods.

This paper presents a method of realizing artificial neural networks (ANNs) hardware implementation using field programmable analog arrays (FPAAs). A simplified realization for neurons with piecewise linear activation functions is used to reduce the complexity of the neural network architecture. A feedforward neural network is implemented using multi-chip FPAAs. Anadigm's commercially available AN221E04 FPAA chips are adopted as the platform for simulation and experiments. The FPAA based ANN classifies two groups of data with zero error at a speed of 6.0 Million Connections Per Second (MCPS). The result is more than 1400 times faster than software implementation. The ANN architecture is also expandable to perform more complicated tasks by incorporating more FPAA chips into the implementation. The programmability of the FPAA makes rapid prototyping possible.

A simulated annealing (SA) algorithm called Sample-Sort that is artificially extended across an array of samplers is proposed. The sequence of temperatures for a serial SA algorithm is replaced with an array of samplers operating at static temperatures and the single stochastic sampler is replaced with a set of samplers. The set of samplers uses a biased generator to sample the same distribution of a serial SA algorithm to maintain the same convergence property. Sample-Sort was compared to SA by applying both to a set of global optimization problems and found to be comparable if the number of iterations per sampler was sufficient. If the evaluation phase dominates the computational requirements, Sample-Sort could take advantage of parallel processing.

A novel objective function is presented that incorporates both local and global errors as well as model parsimony in the construction of wavelet neural networks. Two methods are presented to assist in the minimization of this objective function, especially the local error term. First, during network initialization, a locally adaptive grid is utilized to include candidate wavelet basis functions whose local support addresses the local error of the local feature set. This set can be either user-defined or determined using information derived from the wavelet transform modulus maxima representation. Next, during the network construction, a new selection procedure based on a subspace projection operator is presented to help focus the selection of wavelet basis functions to reduce the local error. Simulation results demonstrate the effectiveness of these methodologies in minimizing local and global error while maintaining model parsimony and incurring a minimal increase on computational complexity.

In this paper, we introduce a simple procedure to predict wiring delay in bi-directional buses and a way of properly sizing the driver for each of its port. In addition, we propose a simple calibration procedure to improve its delay prediction over the Elmore delay of the RC tree. The technique is fast, accurate, and ideal for implementation in floorplanner during behavioral synthesis.

The challenge of a network topology design is to provide a configuration with minimum cost given specified constraints. Network topology design is NP-hard and known. Algorithms to solve these problems run in time that increases exponentially with the number of choices. The economic importance of determining the placement of switches in an ATM network justifies heuristic methods to find a good configuration within a reasonable amount of time. In this paper, two types of heuristic algorithms are compared. The first algorithm is based on swapping used switch locations with unused switch locations. The second algorithm is a genetic algorithm.

Anisotropic diffusion is a powerful method for image feature extraction in which blurring is allowed to occur except at edges. Mean field annealing (MFA) is an image optimization technique which is used to find the best estimation of a blurred, noisy corrupted image. We show that MFA is versatile enough to be used for image feature extraction as well. Furthermore, the two major problems in anisotropic diffusion (white noise and geometric interpretation) can be solved by few modifications of the MFA equation. Finally, experiments and results are presented.

The techniques of a posteriori image restoration and iterative image feature extraction are described and compared. Image feature extraction methods known as graduated nonconvexity (GNC); variable conductance diffusion (VCD), anisotropic diffusion, and biased anisotropic diffusion (BAD), which extract edges from noisy images, are compared with a restoration/feature extraction method known as mean field annealing (MFA). All are shown to be performing the same basic operation: image relaxation. This equivalence shows the relationship between energy minimization methods and spatial analysis methods and between their respective parameters of temperature and scale. As a result of the equivalence, VCD is demonstrated to minimize a cost function, and that cost is specified explicitly. Furthermore, operations over scale space are shown to be a method of avoiding local minima.>

This paper describes a new algorithm for the placement of analog modules. The algorithm is a hybrid of greedy partitioning and mean field annealing techniques. The sensitivities of performance functions are used to compute the changes in the functions during the placement process. The objective function is designed to incorporate the effect of the performance functions in terms of their slacks beyond the design constraints along with other requirements such as area and aspect ratio. The algorithm has been implemented and results are tested for seven commercial bipolar circuits.>

A new stochastic optimization strategy is introduced which cascades many Metropolis-like procedures to sample a Boltzmann distribution at fixed temperatures. Global optimization of an objective f(x) in a certain class is shown to require O((/spl Delta//T/sub low/)/sup 2/) computational effort where /spl Delta/=max/sub x,x'/(f(x)-f(x')) and T/sub low/ is a low enough temperature that the Boltzmann function of f at T/sub low/ acceptably small except for optimal x. This theoretical advantage is confirmed by experimental results which are presented for a problem in vector quantization and for seven standard test problems in nonlinear optimization.>

A novel method for obtaining dense displacement fields from a sequence of frames is presented. The algorithm is based on modeling the displacement field as a Markov random field, hence making it possible to use the equivalence of a Markov random field and a Gibbs distribution. The Gibbs distribution is used to define a mean field probability density function, and the displacement field is found using a mean field annealing algorithm. Mean field annealing is a technique which finds the global or near global minima in nonconvex optimization problems. Analysis of the algorithm and experimental results are presented.>

Motion estimation is cast as a problem in energy minimization. This is achieved by modeling the displacement field as a Markov random field. The equivalence of a Markov random field and a Gibbs distribution is then used to convert the problem into one of defining an appropriate energy function that describes the motion and any constraints imposed on it. The energy function is then minimized using the mean field annealing algorithm, a technique which finds the global or near-global minima in nonconvex optimization problems. Analysis of the algorithm and experimental results are presented.>

We derive the learning theory recently reported by Tishby, Levin, and Solla (TLS) directly from the principle of maximum entropy instead of statistical mechanics. The theory generally applies to any problem of modeling data. We analyze an elementary example for which we find the predictions consistent with intuition and conventional statistical results and we numerically examine the more realistic problem of training a competitive net to learn a one-dimensional probability density from samples. The TLS theory is useful for predicting average training behavior.

Optimization problems are approached using mean field annealing (MFA), which is a deterministic approximation, using mean field theory and based on Peierls's inequality, to simulated annealing. The MFA mathematics are applied to three different objective function examples. In each case, MFA produces a minimization algorithm that is a type of graduated nonconvexity. When applied to the ;weak-membrane' objective, MFA results in an algorithm qualitatively identical to the published GNC algorithm. One of the examples, MFA applied to a piecewise-constant objective function, is then compared experimentally with the corresponding GNC weak-membrane algorithm. The mathematics of MFA are shown to provide a powerful and general tool for deriving optimization algorithms.

The generalization ability of a neural network in a specific application is of interest to many neural network designers. In this paper, learning theory is applied to a neural network used for incipient fault detection in single-phase induction motors. This paper will show that learning theory can help determine the proper number of training examples needed to reach a specific performance level, so that excessive and unnecessary training examples can be avoided. Comparisons of the results of learning theory and Monte Carlo estimate are presented, showing that learning theory is a useful and reliable tool to obtain information about the training process of a given neural network.

A numerical method for finding the global minimum of nonconvex functions is presented. The method is based on the principles of simulated annealing, but handles continuously valued variables in a natural way. The method is completely general, and optimizes functions of up to 30 variables. Several examples are presented. A general-purpose program, INTEROPT, is described, which finds the minimum of arbitrary functions, with user-friendly, quasi-natural-language input.>

A principle source of noise in X-ray and emission computer tomography is at the detectors that measure the projection of the object. The noise can be approximated by additive, signal-independent white Gaussian statistics by ignoring the negligible effects of scattering and diffraction of the source beam. The back-projection filter that is used significantly alters power spectral density of the noise, such that the back-projected noise at each reconstructed point is no longer white. However, to effectively restore the reconstructed image using maximum a posteriori techniques via mean field annealing (MFA), a reasonable estimate of the autocorrelation of the back-projected noise is necessary. This work derives the autocorrelation and power spectra of the reconstructed noise for parallel, fan, and cone beam projections and also shows some preliminary results of MFA restorations.>

The problem of pose determination of a surface in a range image is described as a six-degree-of-freedom optimization problem, where the surface is expressed by a quadratic equation. The tree annealing algorithm, a general-purpose technique for finding minima of functions of continuously valued variables, is presented. The technique is applied to the pose determination of analytic surfaces and is shown to be quite effective even in the presence of considerable amounts of noise in the images.>

A planar or quadric surface can be fit to a segment of range data in a locally optimal sense by selecting the minimum eigensolution of a scatter matrix for that segment. We obtain a globally optimal fit by perturbing the local eigensystems with constraints reflecting relations among the corresponding primitives of a model. These pairwise relations define a view-invariant description of the model. For segments containing a few hundred pixels, the resulting perturbation is small enough to justify a linear treatment of the coupled system. From this globally optimal fit, we determine the pose of the object algebraically.

A general three dimensional image analysis environment is presented. The environment proved extremely flexible, and a three dimensional object recognition system was designed using this environment. The recognition system addresses all the issues associated with view independent object recognition. The particular concentration of this paper is the development of an active model matching approach called a procedural model The procedural model uses the surface geometry available in a range image to limit the amount of searching that must be done. The surface geometry is determined by solving an eigensystem, and utilized to determine the pose of the object.

In this paper, we describe the fundamental differences between three-dimensional (range) images and two-dimensional (luminance) images. A number of problems arise which are unique to range data, including in particular a strong sensitivity to quantization effects. Although range images and luminance images are both arrays of scalars, the range image conceptually represents a surface in space and cannot be naively manipulated using the conventional image processing functions such as 3 × 3 convolution kernels. If the range data are regarded as a sampling of a surface parametrized by the focal plane coordinates, it is possible to find a representation for the surface normal and for the surface curvature in terms of familiar-looking convolution kernels.