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Generalized methods and solvers for noise removal from piecewise constant signals. II. New methods

M. A. Little, N. S. Jones
2011 Proceedings of the Royal Society A  
Finally, overlaps between the methods of this paper and others such as wavelet shrinkage, hidden Markov models, and piecewise smooth filtering are touched on.  ...  Many PWC denoising methods exist, including total variation regularization, mean shift clustering, stepwise jump placement, running medians, convex clustering shrinkage and bilateral filtering; conventional  ...  Running filters based on a variety of linear combinations of rank ordered samples in the window, such as the trimmed mean filter or the double window modified trimmed mean filter are conceptually similar  ... 
doi:10.1098/rspa.2010.0674 pmid:22003313 pmcid:PMC3191852 fatcat:mgmopndl5bb57pwzgwrazwxtpa

Saturating Splines and Feature Selection

Nicholas Boyd, Trevor Hastie, Stephen Boyd, Benjamin Recht, Michael I Jordan
2018 Journal of machine learning research  
We fit saturating splines to data via a convex optimization problem over a space of measures, which we solve using an efficient algorithm based on the conditional gradient method.  ...  We extend the adaptive regression spline model by incorporating saturation, the natural requirement that a function extend as a constant outside a certain range.  ...  Acknowledgments We would like to thank Aaditya Ramdas for many helpful discussions about trend filtering. NB was generously supported by a Google Fellowship from the Hertz Foundation.  ... 
pmid:31007630 pmcid:PMC6474379 fatcat:qmxfha3hunhxpazjx7o2eeqmaq

Page 6617 of Mathematical Reviews Vol. , Issue 90K [page]

1990 Mathematical Reviews  
6617 65D neighborhood B-splines) to adapt the usual B-spline approximation of discrete data, in order to quasi-interpolate or to filter the data.  ...  A very good tool to analyze the global properties is the transfer function of the associated filter, which is also used to determine the coefficients of the above linear combination.”  ... 

Saturating Splines and Feature Selection [article]

Nicholas Boyd, Trevor Hastie, Stephen Boyd, Benjamin Recht, Michael Jordan
2017 arXiv   pre-print
We fit saturating splines to data using a convex optimization problem over a space of measures, which we solve using an efficient algorithm based on the conditional gradient method.  ...  We extend the adaptive regression spline model by incorporating saturation, the natural requirement that a function extend as a constant outside a certain range.  ...  Acknowledgements We would like to thank Aaditya Ramdas for many helpful discussions about trend filtering. NB was generously supported by a Google Fellowship from the Hertz Foundation. References  ... 
arXiv:1609.06764v3 fatcat:3rhg2j2hsvc75kp7inlpfb4bca

Forward-backward splitting in deformable image registration: A demons approach

Michael Ebner, Marc Modat, Sebastiano Ferraris, Sebastien Ourselin, Tom Vercauteren
2018 2018 IEEE 15th International Symposium on Biomedical Imaging (ISBI 2018)  
For the first time in the context of image registration, we show that Tikhonov regularization breaks down to the simple use of B-Spline filtering in the proximal step.  ...  and convex regularization associated with a tractable proximal operator.  ...  illustrate the versatility of FBS by relying on a combination of displacement fields, free-form B-Spline transformation, sum of squared differences (SSD) and normalized mutual information (NMI) in conjunction  ... 
doi:10.1109/isbi.2018.8363755 dblp:conf/isbi/EbnerMFOV18 fatcat:372hiicblbdfxcyrnagm62c7em

Nonlinear spline adaptive filtering

Michele Scarpiniti, Danilo Comminiello, Raffaele Parisi, Aurelio Uncini
2013 Signal Processing  
In this paper a new class of nonlinear adaptive filters, consisting of a linear combiner followed by a flexible memory-less function, is presented.  ...  This new kind of adaptive function is then applied to the output of a linear adaptive filter and it is used for the identification of Wiener-type nonlinear systems.  ...  Acknowledgment The authors would like to thank all anonymous reviewers and the editor for their precious and helpful comments and suggestions in improving the quality of this work.  ... 
doi:10.1016/j.sigpro.2012.09.021 fatcat:f4bf7kgyojfx7mxls2wkcghn4e

A Fast Progressive Image Sampling Using Lifting Scheme And Non-Uniform B-Splines

Siddavatam Rajesh, K. Sandeep, R.K. Mittal
2007 2007 IEEE International Symposium on Industrial Electronics  
An image, which is considered here as the functions of Non-uniform B-splines over the Delaunay triangulation, is developed by using recursively obtained scattered data set of significant pixels.  ...  The efficiency of the present method is shown and the visual qualities of the multiresolution images are compared with those obtained by other methods.  ...  The image is reconstructed by either by linear or cubic splines over the Delaunay Triangulations of adaptively chosen set of significant samples.  ... 
doi:10.1109/isie.2007.4374851 fatcat:7z7gy4dh6vel5bf6d5dumhvd6i

Multiresolution analysis as an approach for tool path planning in NC machining

Ranga Narayanaswami, Junhua Pang
2003 Computer-Aided Design  
Loose Convex Hull The B-spline curve has the convex hull property, which is the B-spline curve lies in the convex hull of the control points.  ...  Combined with convex hull method, an integrated roughto-fine cut strategy was developed.  ... 
doi:10.1016/s0010-4485(02)00050-7 fatcat:fu4qmodzprbk5m6wxouxhsxxzy

Active noise control techniques for nonlinear systems [article]

Lu Lu, Kai-Li Yin, Rodrigo C. de Lamare, Zongsheng Zheng, Yi Yu, Xiaomin Yang, Badong Chen
2022 arXiv   pre-print
Moreover, we emphasize recent advances of NLANC algorithms, such as spline ANC algorithms, kernel adaptive filters, and nonlinear distributed ANC algorithms.  ...  Most of the literature focuses on the development of the linear active noise control (ANC) techniques.  ...  The first attempt of convex combination for NLANC can be found in [173] .  ... 
arXiv:2110.09672v2 fatcat:yjivwjydw5bpxpz7jvkc6jsjo4

Generalized methods and solvers for noise removal from piecewise constant signals. I. Background theory

M. A. Little, N. S. Jones
2011 Proceedings of the Royal Society A  
Many PWC denoising methods exist, including total variation regularization, mean shift clustering, stepwise jump placement, running medians, convex clustering shrinkage and bilateral filtering; conventional  ...  This paper (part I, the first of two) shows that most of these methods are associated with a special case of a generalized functional, minimized to achieve PWC denoising.  ...  This section has shown how adapting the discretization size of the Euler integrator leads to a number of well-known clustering algorithms for appropriate combinations of loss functions.  ... 
doi:10.1098/rspa.2010.0671 pmid:22003312 pmcid:PMC3191861 fatcat:2v2dzj2itjda3lmrdgnh5kuuly

JPEG2000-Compatible Scalable Scheme for Wavelet-Based Video Coding

Thomas André, Marco Cagnazzo, Marc Antonini, Michel Barlaud
2007 EURASIP Journal on Image and Video Processing  
Whereas hybrid video coders must undergo significant changes in order to support scalability, our coder only requires a specific wavelet filter for temporal analysis, as well as an adapted bit allocation  ...  procedure based on models of rate-distortion curves.  ...  One can notice that the smoothing spline curve is convex, whereas the interpolation spline is not. In Fig. 2b , we reported the first derivatives of the same experimental curve and of the splines.  ... 
doi:10.1155/2007/30852 fatcat:sd4wq7hxgndc3nam6nafjvacwq

JPEG2000-Compatible Scalable Scheme for Wavelet-Based Video Coding

Thomas André, Marco Cagnazzo, Marc Antonini, Michel Barlaud
2007 EURASIP Journal on Image and Video Processing  
Whereas hybrid video coders must undergo significant changes in order to support scalability, our coder only requires a specific wavelet filter for temporal analysis, as well as an adapted bit allocation  ...  procedure based on models of rate-distortion curves.  ...  One can notice that the smoothing spline curve is convex, whereas the interpolation spline is not. In Fig. 2b , we reported the first derivatives of the same experimental curve and of the splines.  ... 
doi:10.1186/1687-5281-2007-030852 fatcat:3hpop3jlrfg3vp3acipjsvufka

Analytic antialiasing with prism splines

Michael D. McCool
1995 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques - SIGGRAPH '95  
After sampling, digital signal processing can be used to evaluate exactly and efficiently the sampled result of any analytic spline filter in the span of the box spline basis used as the original analytic  ...  The theory of the multivariate polyhedral splines is applied to analytic antialiasing: a triangular simplex spline is used to represent surface intensity, while a box spline is used as a filter.  ...  ACKNOWLEDGEMENTS This research was conducted while I was a Ph.D. student under the capable supervision of Eugene Fiume at the Dynamic Graphics Project at the University of Toronto.  ... 
doi:10.1145/218380.218499 dblp:conf/siggraph/McCool95 fatcat:nujbmkanmff2lp6277omjvjog4

OUP accepted manuscript

2020 Monthly notices of the Royal Astronomical Society  
Furthermore, the trend filtering estimate can be computed with practical and scalable efficiency via a specialized convex optimization algorithm, e.g. handling sample sizes of n 10 7 within a few minutes  ...  When the underlying signal is spatially heterogeneous, trend filtering is superior to any statistical estimator that is a linear combination of the observed data -including kernel smoothers, LOESS, smoothing  ...  Definition Trend filtering can be viewed as a blending of the strengths of variable-knot regression splines (local adaptivity and interpretabil-ity) and the strengths of smoothing splines (simplicity and  ... 
doi:10.1093/mnras/staa106 fatcat:yooqwlandremnefztfkw4psukm

Material Approximation of Data Smoothing and Spline Curves Inspired by Slime Mould [article]

Jeff Jones, Andrew Adamatzky
2015 arXiv   pre-print
We find that the virtual material relaxes more strongly to high-frequency changes in data which can be used for the smoothing (or filtering) of data by ap- proximating moving average and low-pass filters  ...  The relaxation and minimisation properties of the model enable the spatial computation of B-spline curves (approximating splines) in 2D datasets.  ...  Using a combination of attractant and repellent stimuli the method is also capable of approximating the Convex Hull, Concave Hull and Voronoi diagram [22] .  ... 
arXiv:1503.03264v1 fatcat:vyslepam55b73f5lzo4lu2mhfu
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