smoothing is a useful tool to improve the signal-to-noise ratio of spectroscopic data. This paper reports a new family of smoothing formulas, the Chebyshev filters, which are derived approaching the original data to a...
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smoothing is a useful tool to improve the signal-to-noise ratio of spectroscopic data. This paper reports a new family of smoothing formulas, the Chebyshev filters, which are derived approaching the original data to a polynomial and using the mini-max principle, that is, keeping the maximum error down to a minimum, as fitting criterion. The properties of the filters are studied analyzing their associated transfer functions in the frequency domain. This leads us to the concept of spectral window and spectral window width as tool and parameter, respectively, to remove the high frequency noise components accompanying the experimental data. Also, simple criteria to choose the appropriate width of the spectral windows are put forward. The behaviour of the filters is easy to understand and the filters are fast and simple to use and to program. Finally the proposed smoothing algorithms have been tested using synthetic data as well as X-ray photoelectron spectra and optical absorption spectra. (c) 2006 Elsevier B.V. All rights reserved.
This paper focuses on the class of finite-state, discrete-index, reciprocal processes (reciprocal chains). Such a class of processes seems to be a suitable setup in many applications and, in particular, it appears wel...
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This paper focuses on the class of finite-state, discrete-index, reciprocal processes (reciprocal chains). Such a class of processes seems to be a suitable setup in many applications and, in particular, it appears well-suited for image-processing. While addressing this issue, the aim is 2-fold: theoretic and practical. As to the theoretic purpose, some new results are provided: first, a general stochastic realization result is provided for reciprocal chains endowed with a known, arbitrary, distribution. Such a model has the form of a fixed-degree, nearest-neighbour polynomial model. Next, the polynomial model is shown to be exactly linearizable, which means it is equivalent to a nearest-neighbour linear model in a different set of variables. The latter model turns out to be formally identical to the Levi-Frezza-Krener linear model of a Gaussian reciprocal process, although actually non-linear with respect to the chain's values. As far as the practical purpose is concerned, in order to yield an example of application an estimation issue is addressed: a suboptimal (polynomial-optimal) solution is derived for the smoothing problem of a reciprocal chain partially observed under non-Gaussian noise. To this purpose, two kinds of boundary conditions (Dirichlet and Cyclic), specifying the reciprocal chain on a finite interval, are considered, and in both cases the model is shown to be well-posed, in a 'wide-sense'. Under this view, some well-known representation results about Gaussian reciprocal processes extend, in a sense, to a 'non-Gaussian' case.
Center-based partitioning clustering algorithms rely on minimizing an appropriately formulated objective function, and different formulations suggest different possible algorithms. In this paper, we start with the sta...
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Center-based partitioning clustering algorithms rely on minimizing an appropriately formulated objective function, and different formulations suggest different possible algorithms. In this paper, we start with the standard nonconvex and nonsmooth formulation of the partitioning clustering problem. We demonstrate that within this elementary formulation, convex analysis tools and optimization theory provide a unifying language and framework to design, analyze and extend hard and soft center-based clustering algorithms, through a generic algorithm which retains the computational simplicity of the popular k-means scheme. We show that several well known and more recent center-based clustering algorithms, which have been derived either heuristically, or/and have emerged from intuitive analogies in physics, statistical techniques and information theoretic perspectives can be recovered as special cases of the proposed analysis and we streamline their relationships.
Passive Coherent Location (PCL) radar systems capitalise on illuminators of opportunity such as TV broadcast stations, in order to obtain RF backscatter from targets such as aircraft. In this paper it is envisaged tha...
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Passive Coherent Location (PCL) radar systems capitalise on illuminators of opportunity such as TV broadcast stations, in order to obtain RF backscatter from targets such as aircraft. In this paper it is envisaged that an array of receivers is available, each of which measures both the bearing to an airborne target as well as the Doppler shift of the signal induced by the target's motion. These bearing and Doppler values are then processed by the method invented by Gauss in 1809 called the Gauss-Newton (GN) algorithm [2, 3, 6], which is discussed in further detail in an accompanying paper in these proceedings [7]. Results are presented, based on an extensive simulation study for various target types and varying numbers of receivers.
The smooth Huber approximation to the non-linear l(1) problem was proposed by Tishler and Zang (1982), and further developed in Yang (1995). In the present paper, we use the ideas of Gould (19,89) to give a new algori...
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The smooth Huber approximation to the non-linear l(1) problem was proposed by Tishler and Zang (1982), and further developed in Yang (1995). In the present paper, we use the ideas of Gould (19,89) to give a new algorithm with rate of convergence results for the smooth Huber approximation. Results of computational tests are reported. (c) 2005 Elsevier B.V. All rights reserved.
This paper introduces a variance- and angle-normalized version of the least-squares order-recursive lattice (LSORL) smoother, say, the normalized LSORL smoother, via a geometric approach, The normalized LSORL smoother...
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This paper introduces a variance- and angle-normalized version of the least-squares order-recursive lattice (LSORL) smoother, say, the normalized LSORL smoother, via a geometric approach, The normalized LSORL smoother has excellent round-off noise properties and inherits all the other advantages of the normalized LSORL as well. Simulation results show that the normalized LSORL smoother outperforms the existing LSORL and QRD-based least-squares lattice smoother algorithms when finite-precision arithmetic is used. (C) 2002 Elsevier Science B.V. All rights reserved.
In this paper, a new multigrid interior point approach to topology optimization problems in the context of the homogenization method is presented. The key observation is that nonlinear interior point methods lead to l...
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In this paper, a new multigrid interior point approach to topology optimization problems in the context of the homogenization method is presented. The key observation is that nonlinear interior point methods lead to linear-quadratic subproblems with structures that can be favourably exploited within multigrid methods. Primal as well as primal-dual formulations are discussed. The multigrid approach is based on the transformed smoother paradigm. Numerical results for an example problem are presented.
A new technique for image texture analysis is described which uses the relative frequency of local extremes in grey level as the principal measure. This method is invariant to multiplicative gain changes (such as caus...
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