Signal Processing Algorithms Hans G. Feichtinger (Univ. of Vienna) NuHAG Previous Work * Mathematical methods for image processing (interdisciplinary FSP 1994-2000) * Gabor Analysis (Book, 1998) * Algorithms for irregular sampling (e.g., geophysics) Establish new parallel basic algorithms for * scattered data approximation in 2D/3D * Gabor analysis for images (denoising, space variant filterin Objectives of Planned Work
17
Embed
Signal Processing Algorithms Hans G. Feichtinger (Univ. of Vienna) NuHAG Previous Work * Mathematical methods for image processing (interdisciplinary FSP.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Signal Processing Algorithms Hans G. Feichtinger (Univ. of Vienna) NuHAG
Previous Work * Mathematical methods for image processing (interdisciplinary FSP 1994-2000) * Gabor Analysis (Book, 1998) * Algorithms for irregular sampling (e.g., geophysics)
Establish new parallel basic algorithms for * scattered data approximation in 2D/3D * Gabor analysis for images (denoising, space variant filtering)
Objectives of Planned Work
Signal Processing Algorithms Hans G. Feichtinger (Univ. of Vienna)
Scattered Data (irregular sampling) Problem
Signal model: smooth function f (e.g., band-limited)
Task: Recovery of f from sampling values f(ti)
Methods: linear recovery using iterations: f(t) =if(ti) ei (t)
Numerical aspects: fast iterative (CG-based) algorithms and well structured (e.g., Toeplitz) system matrix.
• image restoration (lost pixel problem)
• geophysical data approximation
• nearest neighborhood approximation
Signal Processing Algorithms Hans G. Feichtinger (Univ. of Vienna)
Signal Processing Algorithms (Scattered Data) Hans G. Feichtinger (Univ. of Vienna)
Signal Processing Algorithms Hans G. Feichtinger (Univ. of Vienna)
Background within NUHAG
* variety of iterative algorithms (CG);
* guaranteed rates of convergence;
* established robustness (e.g., jitter error);
* good locality possible (T. Werther);
* adaptive weights improve condition;
* no a priori information of f is required (function spaces);
Scattered Data or Irregular Sampling Problem (1st step):