1,372 research outputs found
A unified wavelet-based modelling framework for non-linear system identification: the WANARX model structure
A new unified modelling framework based on the superposition of additive submodels, functional components, and
wavelet decompositions is proposed for non-linear system identification. A non-linear model, which is often represented
using a multivariate non-linear function, is initially decomposed into a number of functional components via the wellknown
analysis of variance (ANOVA) expression, which can be viewed as a special form of the NARX (non-linear
autoregressive with exogenous inputs) model for representing dynamic input–output systems. By expanding each functional
component using wavelet decompositions including the regular lattice frame decomposition, wavelet series and
multiresolution wavelet decompositions, the multivariate non-linear model can then be converted into a linear-in-theparameters
problem, which can be solved using least-squares type methods. An efficient model structure determination
approach based upon a forward orthogonal least squares (OLS) algorithm, which involves a stepwise orthogonalization
of the regressors and a forward selection of the relevant model terms based on the error reduction ratio (ERR), is
employed to solve the linear-in-the-parameters problem in the present study. The new modelling structure is referred to
as a wavelet-based ANOVA decomposition of the NARX model or simply WANARX model, and can be applied to
represent high-order and high dimensional non-linear systems
Single Frame Image super Resolution using Learned Directionlets
In this paper, a new directionally adaptive, learning based, single image
super resolution method using multiple direction wavelet transform, called
Directionlets is presented. This method uses directionlets to effectively
capture directional features and to extract edge information along different
directions of a set of available high resolution images .This information is
used as the training set for super resolving a low resolution input image and
the Directionlet coefficients at finer scales of its high-resolution image are
learned locally from this training set and the inverse Directionlet transform
recovers the super-resolved high resolution image. The simulation results
showed that the proposed approach outperforms standard interpolation techniques
like Cubic spline interpolation as well as standard Wavelet-based learning,
both visually and in terms of the mean squared error (mse) values. This method
gives good result with aliased images also.Comment: 14 pages,6 figure
Image interpolation using Shearlet based iterative refinement
This paper proposes an image interpolation algorithm exploiting sparse
representation for natural images. It involves three main steps: (a) obtaining
an initial estimate of the high resolution image using linear methods like FIR
filtering, (b) promoting sparsity in a selected dictionary through iterative
thresholding, and (c) extracting high frequency information from the
approximation to refine the initial estimate. For the sparse modeling, a
shearlet dictionary is chosen to yield a multiscale directional representation.
The proposed algorithm is compared to several state-of-the-art methods to
assess its objective as well as subjective performance. Compared to the cubic
spline interpolation method, an average PSNR gain of around 0.8 dB is observed
over a dataset of 200 images
Wavelet treatment of the intra-chain correlation functions of homopolymers in dilute solutions
Discrete wavelets are applied to parametrization of the intra-chain two-point
correlation functions of homopolymers in dilute solutions obtained from Monte
Carlo simulation. Several orthogonal and biorthogonal basis sets have been
investigated for use in the truncated wavelet approximation. Quality of the
approximation has been assessed by calculation of the scaling exponents
obtained from des Cloizeaux ansatz for the correlation functions of
homopolymers with different connectivities in a good solvent. The resulting
exponents are in a better agreement with those from the recent renormalisation
group calculations as compared to the data without the wavelet denoising. We
also discuss how the wavelet treatment improves the quality of data for
correlation functions from simulations of homopolymers at varied solvent
conditions and of heteropolymers.Comment: RevTeX, 19 pages, 7 PS figures. Accepted for publication in PR
A multi-wavelet based technique for calculating dense 2D disparity maps from stereo
A vision based approach for calculating accurate 3D models of the objects is presented. Generally industrial visual inspection systems capable of accurate 3D depth estimation rely on extra hardware tools like laser scanners or light pattern projectors. These tools improve the accuracy of depth estimation but also make the vision system costly and cumbersome. In the proposed algorithm, depth and dimensional accuracy of the produced 3D depth model depends on the existing reference model instead of the information from extra hardware tools. The proposed algorithm is a simple and cost effective software based approach to achieve accurate 3D depth estimation with minimal hardware involvement. The matching process uses the well-known coarse to fine strategy, involving the calculation of matching points at the coarsest level with consequent refinement up to the finest level. Vector coefficients of the wavelet transform-modulus are used as matching features, where wavelet transform-modulus maxima defines the shift invariant high-level features with phase pointing to the normal of the feature surface. The technique addresses the estimation of optimal corresponding points and the corresponding 2D disparity maps leading to the creation of accurate depth perception model. <br /
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