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Journal of Nonparametric Statistics Volume 14, 2002 - Issue 1-2
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Original Articles

Smoothers for Discontinuous Signals

G. Winkler Institute of Biomathematics and Biometrics, GSF, National Research Center for Environment and Health, Postfach 1129, Oberschleißheim, D-85758, Germany E-mail: [email protected]
&
V. Liebscher Institute of Biomathematics and Biometrics, GSF, National Research Center for Environment and Health, Postfach 1129, Oberschleißheim, D-85758, Germany E-mail: [email protected]
Pages 203-222 | Published online: 27 Oct 2010

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Martin Storath & Andreas Weinmann. (2023) Smoothing Splines for Discontinuous Signals. Journal of Computational and Graphical Statistics 0:0, pages 1-24.
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S. Enayat Hosseini Aria, Massimo Menenti, Ben G. H. Gorte & Saeid Homayouni. (2020) Unsupervised dimensionality reduction of hyperspectral images using representations of reflectance spectra. International Journal of Remote Sensing 41:20, pages 7820-7845.
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F Friedrich, A Kempe, V Liebscher & G Winkler. (2008) Complexity Penalized M-Estimation. Journal of Computational and Graphical Statistics 17:1, pages 201-224.
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Azhar Khandekar, Raviteja Vangara, Mark Barnes, Marcos Díaz-Gay, Ammal Abbasi, Erik N. Bergstrom, Christopher D. Steele, Nischalan Pillay & Ludmil B. Alexandrov. (2023) Visualizing and exploring patterns of large mutational events with SigProfilerMatrixGenerator. BMC Genomics 24:1.
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Yandi Shen, Qiyang Han & Fang Han. (2022) On a Phase Transition in General Order Spline Regression. IEEE Transactions on Information Theory 68:6, pages 4043-4069.
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Lukas Kiefer, Martin Storath & Andreas Weinmann. (2020) Iterative Potts Minimization for the Recovery of Signals with Discontinuities from Indirect Measurements: The Multivariate Case. Foundations of Computational Mathematics 21:3, pages 649-694.
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Lukas Kiefer, Stefania Petra, Martin Storath & Andreas Weinmann. (2021) Multi-channel Potts-based reconstruction for multi-spectral computed tomography. Inverse Problems 37:4, pages 045004.
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Adityanand Guntuboyina, Donovan Lieu, Sabyasachi Chatterjee & Bodhisattva Sen. (2020) Adaptive risk bounds in univariate total variation denoising and trend filtering. The Annals of Statistics 48:1.
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Lukas Kiefer, Martin Storath & Andreas Weinmann. (2020) An Algorithm for Second Order Mumford--Shah Models Based on a Taylor Jet Formulation. SIAM Journal on Imaging Sciences 13:4, pages 2307-2360.
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Lukas Kiefer, Martin Storath & Andreas Weinmann. (2020) An Efficient Algorithm for the Piecewise Affine-Linear Mumford-Shah Model Based on a Taylor Jet Splitting. IEEE Transactions on Image Processing 29, pages 921-933.
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Martin Holler & Andreas Weinmann. 2020. Handbook of Variational Methods for Nonlinear Geometric Data. Handbook of Variational Methods for Nonlinear Geometric Data 51 93 .
Martin Storath, Lukas Kiefer & Andreas Weinmann. (2019) Smoothing for signals with discontinuities using higher order Mumford–Shah models. Numerische Mathematik 143:2, pages 423-460.
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Lukas Kiefer, Stefania Petra, Martin Storath & Andreas Weinmann. 2019. Scale Space and Variational Methods in Computer Vision. Scale Space and Variational Methods in Computer Vision 406 418 .
Zhou Fan & Leying Guan. (2018) Approximate $\ell_{0}$-penalized estimation of piecewise-constant signals on graphs. The Annals of Statistics 46:6B.
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Denis Fortun, Martin Storath, Dennis Rickert, Andreas Weinmann & Michael Unser. (2018) Fast Piecewise-Affine Motion Estimation Without Segmentation. IEEE Transactions on Image Processing 27:11, pages 5612-5624.
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Jordan Frecon, Nelly Pustelnik, Nicolas Dobigeon, Herwig Wendt & Patrice Abry. (2017) Bayesian Selection for the $\ell _2$ -Potts Model Regularization Parameter: 1-D Piecewise Constant Signal Denoising. IEEE Transactions on Signal Processing 65:19, pages 5215-5224.
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Martin Storath, Dennis Rickert, Michael Unser & Andreas Weinmann. (2017) Fast Segmentation From Blurred Data in 3D Fluorescence Microscopy. IEEE Transactions on Image Processing 26:10, pages 4856-4870.
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Martin Storath, Andreas Weinmann & Michael Unser. (2017) Jump-penalized least absolute values estimation of scalar or circle-valued signals. Information and Inference, pages iaw022.
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Andreas Weinmann, Laurent Demaret & Martin Storath. (2016) Mumford–Shah and Potts Regularization for Manifold-Valued Data. Journal of Mathematical Imaging and Vision 55:3, pages 428-445.
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Kilian Hohm, Martin Storath & Andreas Weinmann. (2015) An algorithmic framework for Mumford–Shah regularization of inverse problems in imaging. Inverse Problems 31:11, pages 115011.
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Andreas Weinmann & Martin Storath. (2015) Iterative Potts and Blake–Zisserman minimization for the recovery of functions with discontinuities from indirect measurements. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471:2176, pages 20140638.
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Martin Storath, Andreas Weinmann, Jürgen Frikel & Michael Unser. (2015) Joint image reconstruction and segmentation using the Potts model. Inverse Problems 31:2, pages 025003.
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Knut Landmark, Anne H. Schistad Solberg, Andreas Austeng & Roy Edgar Hansen. (2014) Bayesian Seabed Classification Using Angle-Dependent Backscatter Data From Multibeam Echo Sounders. IEEE Journal of Oceanic Engineering 39:4, pages 724-739.
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Martin Storath, Andreas Weinmann & Laurent Demaret. (2014) Jump-Sparse and Sparse Recovery Using Potts Functionals. IEEE Transactions on Signal Processing 62:14, pages 3654-3666.
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Klaus Frick, Axel Munk & Hannes Sieling. (2014) Multiscale Change Point Inference. Journal of the Royal Statistical Society Series B: Statistical Methodology 76:3, pages 495-580.
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Martin Storath & Andreas Weinmann. (2014) Fast Partitioning of Vector-Valued Images. SIAM Journal on Imaging Sciences 7:3, pages 1826-1852.
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Laurent Demaret, Felix Friedrich, Volkmar Liebscher & Gerhard Winkler. (2013) Complexity L0-Penalized M-Estimation: Consistency in More Dimensions. Axioms 2:3, pages 311-344.
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Angélique Berthelot, Anne H.S. Solberg & Leiv-J. Gelius. (2013) Texture attributes for detection of salt. Journal of Applied Geophysics 88, pages 52-69.
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Daniele Angelosante & Georgios B Giannakis. (2012) Group lassoing change-points in piecewise-constant AR processes. EURASIP Journal on Advances in Signal Processing 2012:1.
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Gro Nilsen, Knut Liestøl, Peter Van Loo, Hans Kristian Moen Vollan, Marianne B Eide, Oscar M Rueda, Suet-Feung Chin, Roslin Russell, Lars O Baumbusch, Carlos Caldas, Anne-Lise Børresen-Dale & Ole Christian Lingjærde. (2012) Copynumber: Efficient algorithms for single- and multi-track copy number segmentation. BMC Genomics 13:1.
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Fatemeh Kaveh, Hege Edvardsen, Anne-Lise Børresen-Dale, Vessela N Kristensen & Hiroko K Solvang. (2011) Allele-specific disparity in breast cancer. BMC Medical Genomics 4:1.
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Angélique Berthelot, Anne H. S. Solberg, Erlend Morisbak & Leiv-J Gelius. (2011) Salt diapirs without well defined boundaries - a feasibility study of semi-automatic detection. Geophysical Prospecting 59:4, pages 682-696.
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R. Barbuzza & A. Clausse. (2011) Metropolis Monte Carlo for tomographic reconstruction with prior smoothness information. IET Image Processing 5:2, pages 198.
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Marianne Brodtkorb EideKnut LiestølOle Christian LingjærdeMarit E. HystadStine H. KresseLeonardo Meza-ZepedaOla MyklebostGunhild TrøenHege Vangstein Aamot, Harald Holte, Erlend Bremertun SmelandJan Delabie. (2010) Genomic alterations reveal potential for higher grade transformation in follicular lymphoma and confirm parallel evolution of tumor cell clones. Blood 116:9, pages 1489-1497.
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Leif Boysen, Angela Kempe, Volkmar Liebscher, Axel Munk & Olaf Wittich. (2009) Consistencies and rates of convergence of jump-penalized least squares estimators. The Annals of Statistics 37:1.
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THILO MEYER-BRANDIS & PETER TANKOV. (2011) MULTI-FACTOR JUMP-DIFFUSION MODELS OF ELECTRICITY PRICES. International Journal of Theoretical and Applied Finance 11:05, pages 503-528.
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O. Wittich, A. Kempe, G. Winkler & V. Liebscher. (2008) Complexity penalized least squares estimators: Analytical results. Mathematische Nachrichten 281:4, pages 582-595.
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Giuseppe Papari, Nicolai Petkov & Patrizio Campisi. (2007) Artistic Edge and Corner Enhancing Smoothing. IEEE Transactions on Image Processing 16:10, pages 2449-2462.
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Are C. Jensen & Anne Schistad Solberg. (2007) Fast Hyperspectral Feature Reduction Using Piecewise Constant Function Approximations. IEEE Geoscience and Remote Sensing Letters 4:4, pages 547-551.
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A. Kovac. (2007) Smooth functions and local extreme values. Computational Statistics & Data Analysis 51:10, pages 5155-5171.
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M. Felsberg, P.-E. Forssen & H. Scharr. (2006) Channel smoothing: efficient robust smoothing of low-level signal features. IEEE Transactions on Pattern Analysis and Machine Intelligence 28:2, pages 209-222.
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Gerhard Winkler, Angela Kempe, Volkmar Liebscher & Olaf Wittich. 2005. Innovations in Classification, Data Science, and Information Systems. Innovations in Classification, Data Science, and Information Systems 295 302 .
David Strong & Tony Chan. (2003) Edge-preserving and scale-dependent properties of total variation regularization. Inverse Problems 19:6, pages S165-S187.
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Ansgar Steland. (2003) Jump-preserving monitoring of dependent time series using pilot estimators. Statistics & Decisions 21:4-2003, pages 343-366.
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