UniDen: Noise Removal

Project Topic

A unified approach for noise removal methods in picture analysis by combining local smoothing and regularization.

Project Description

A general approach is formulated

• covering most established denoising methods from analytical, computational and statistical image analysis,
• allowing for a general asymptotic theory,
• simplifying exchange of ideas, results and algorithms between different scientific communities active in the field.

Project Members

Project Chair

• Prof. Dr. Jürgen Franke

Participating Research Groups

• Applied Mathematical Statistics Group, University of Kaiserslautern
• Mathematical Image Analysis Group, Saarland University

Scientific Personnel

• Dipl.-Math. Stephan Didas (Mathematical Image Analysis Group)
• Dr. Jean-Pierre Stockis (Applied Mathematical Statistics Group)
• Dr. Joseph Tadjuidje (Applied Mathematical Statistics Group)

External Cooperation

• Prof. Dr. Joachim Weickert (Department of Computer Science / Department of Mathematics, Saarland University)

Project Events and Achievements

• Project start date: April 1st, 2006

Project Publications

On Geometric Ergodicity of CHARME Models

Jürgen Franke, Jean-Pierre Stockis, Kamgaing Joseph Tadjuidje. Technical Report, Report in Wirtschaftsmathematik, University of Kaiserslautern, Technische Universität Kaiserslautern, January, 2007

A note on the identifiability of the conditional expectation for the mixtures of neural networks

Jürgen Franke, Jean-Pierre Stockis, Kamgaing Joseph Tadjuidje. Technical Report, Report in Wirtschaftsmathematik, University of Kaiserslautern, Technische Universität Kaiserslautern, January, 2007

Quantile Sieve Estimates for Time Series

Jürgen Franke, Jean-Pierre Stockis, Kamgaing Joseph Tadjuidje. Technical Report, SFB 649 Discussion Paper, Humboldt University Berlin, Technische Universität Kaiserslautern, January, 2007

Some asymptotics for local least-squares regression with regularization

Jürgen Franke, Kamgaing Joseph Tadjuidje, Stefan Didas, Joachim Weickert. Technical Report, Report in Wirtschaftsmathematik, University of Kaiserslautern, Technische Universität Kaiserslautern, Universität Saarbrücken, January, 2007

Wild bootstrap tests for comparing signals and images

Jürgen Franke, Siana Halim. Technical Report, Report in Wirtschaftsmathematik, University of Kaiserslautern, Technische Universität Kaiserslautern, 2007

A bootstrap test for comparing images in surface inspection

Jürgen Franke, Siana Halim. Technical Report, Preprint series of the DFG priority program 1114 ``Mathematical methods for time series analysis and digital image processing'', Technische Universität Kaiserslautern, November, 2006