One popular method for the recovery of an ideal intensity image from corrupted or indirect measurements is regularization: minimize an objective function which enforces a roughness penalty in addition to coherence with the data. Linear estimates are relatively easy to compute but generally introduce systematic errors; for example, they are incapable of recovering discontinuities and other important image attributes. In contrast, nonlinear estimates are more accurate, but often far less accessible. This is particularly true when the objective function is non-convex and the distribution of each data component depends on many image components through a linear operator with broad support. Our approach is based on an auxiliary array and an extended objective function in which the original variables appear quadratically and the auxiliary variables are decoupled. Minimizing over the auxiliary array alone yields the original function, so the original image estimate can be obtained by joint min...

Associative memories are conventionally used to represent data with very simple structure: sets of pairs of vectors. This paper describes a method for representing more complex compositional structure in distributed representations. The method uses circular convolution to associate items, which are represented by vectors. Arbitrary variable bindings, short sequences of various lengths, simple framelike structures, and reduced representations can be represented in a fixed width vector. These representations are items in their own right, and can be used in constructing compositional structures. The noisy reconstructions extracted from convolution memories can be cleaned up by using a separate associative memory that has good reconstructive properties.

. Quadratic Assignment Problems model many applications in diverse areas such as operations research, parallel and distributed computing, and combinatorial data analysis. In this paper we survey some of the most important techniques, applications, and methods regarding the quadratic assignment problem. We focus our attention on recent developments. 1. Introduction Given a set N = f1; 2; : : : ; ng and n \Theta n matrices F = (f ij ) and D = (d kl ), the quadratic assignment problem (QAP) can be stated as follows: min p2\Pi N n X i=1 n X j=1 f ij d p(i)p(j) + n X i=1 c ip(i) ; where \Pi N is the set of all permutations of N . One of the major applications of the QAP is in location theory where the matrix F = (f ij ) is the flow matrix, i.e. f ij is the flow of materials from facility i to facility j, and D = (d kl ) is the distance matrix, i.e. d kl represents the distance from location k to location l [62, 67, 137]. The cost of simultaneously assigning facility i to locat...

We present a new “second generation” reconstruction algorithm for irregular sampling, i.e. for the problem of recovering a band-limited function from its non-uniformly sampled values. The efficient new method is a combination of the adaptive weights method which was developed by the two first named authors and the method of conjugate gradients for the solution of positive definite linear systems. The choice of ”adaptive weights” can be seen as a simple but very efficient method of preconditioning. Further substantial acceleration is achieved by utilizing the Toeplitztype structure of the system matrix. This new algorithm can handle problems of much larger dimension and condition number than have been accessible so far. Furthermore, if some gaps between samples are large, then the algorithm can still be used as a very efficient extrapolation method across the gaps.

Subdivision surfaces are a convenient representation for modeling objects of arbitrary topological type. In this dissertation, we investigate the analysis of a piecewise smooth subdivision scheme, and we apply the scheme to reconstruct objects from non-uniformly sampled data points. Defined as the limit of repeated refinement of a mesh of 3D control points, subdivision surfaces require analysis to establish convergence to a well-defined, tangent plane smooth G1 surface. Recent research has focused on analyzing smooth surface schemes in which the rules are symmetrical about each vertex and edge. However, a scheme for creating surfaces with sharp features has rules that do not exhibit this symmetry. In this dissertation, we extend the use of eigenanalysis and characteristic maps to analyze a piecewise smoot...

Distributed representations are attractive for a number of reasons. They offer the possibility of representing concepts in a continuous space, they degrade gracefully with noise, and they can be processed in a parallel network of simple processing elements. However, the problem of representing nested structure in distributed representations has been for some time a prominent concern of both proponents and critics of connectionism [Fodor and Pylyshyn 1988; Smolensky 1990; Hinton 1990]. The lack of connectionist representations for complex structure has held back progress in tackling higher-level cognitive tasks such as language understanding and reasoning. In this thesis I review connectionist representations and propose a method for the distributed representation of nested structure, which I call "Holographic Reduced Representations " (HRRs). HRRs provide an implementation of Hinton's [1990] "reduced descriptions". HRRs use circular convolution to associate atomic items, which are rep...

The Generalized Dimension Exchange (GDE) method is a fully distributed load balancing method that operates in a relaxation fashion for multicomputers with a direct communication network. It is parameterized by an exchange parameter that governs the splitting of load between a pair of directly connected processors during load balancing. An optimal would lead to the fastest convergence of the balancing process. Previous work has resulted in the optimal for the binary n-cubes. In this paper, we derive the optimal 's for the k-ary n-cube network and its variants---the ring, the torus, the chain, and the mesh. We establish the relationships between the optimal convergence rates of the method when applied to these structures, and conclude that the GDE method favors high dimensional k-ary n-cubes. We also reveal the superiority of the GDE method to another relaxation-based method, the diffusion method. We further show through statistical simulations that the optimal 's do speed up the GDE...

Restoration of images that have been blurred by the effects of a Gaussian blurring function is an ill-posed but well-studied problem. Any blur that is spatially invariant can be expressed as a convolution kernel in an integral equation. Fast and effective algorithms then exist for determining the original image by preconditioned iterative methods. If the blurring function is spatially variant, however, then the problem is more difficult. In this work we develop fast algorithms for forming the convolution and for recovering the original image when the convolution functions are spatially variant but have a small domain of support. This assumption leads to a discrete problem involving a banded matrix. We devise an effective preconditioner and prove that the preconditioned matrix differs from the identity by a matrix of small rank plus a matrix of small norm. Numerical examples are given, related to the Hubble Space Telescope Wide-Field / Planetary Camera. The algorithms that we develop ...

The feedback delay network (FDN) has been proposed for digital reverberation. Also proposed with similar advantages is the digital waveguide network (DWN). This paper notes that the commonly used FDN with an N × N orthogonal feedback matrix is isomorphic to a normalized digital waveguide network consisting of one scattering junction and a vector transformer joining N reflectively terminated branches. Generalizations of FDNs and DWNs are discussed. The general case of a losslessness FDN feedback matrix is shown to be any matrix having unit-modulus eigenvalues and linearly independent eigenvectors. A special class of FDNs using circulant matrices is proposed. These structures can be efficiently implemented and allow control of the time and frequency behavior. Applications of circulant feedback delay networks in

Abstract—This paper proposes a design methodology to stabilize relative equilibria in a model of identical, steered particles moving in the plane at unit speed. Relative equilibria either correspond to parallel motion of all particles with fixed relative spacing or to circular motion of all particles around the same circle. Particles exchange relative information according to a communication graph that can be undirected or directed and time-invariant or timevarying. The emphasis of this paper is to show how previous results assuming all-to-all communication can be extended to a general communication framework. Index Terms—Cooperative control, geometric control, multiagent systems, stabilization. I.