Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke





.......................

.......................


Publications [#287170] of Ingrid Daubechies

Papers Published

  1. Daubechies, I; Teschke, G, Variational image restoration by means of wavelets: Simultaneous decomposition, deblurring, and denoising, Applied and Computational Harmonic Analysis, vol. 19 no. 1 (2005), pp. 1-16 [doi]
    (last updated on 2017/12/15)

    Abstract:
    Inspired by papers of Vese-Osher [Modeling textures with total variation minimization and oscillating patterns in image processing, Technical Report 02-19, 2002] and Osher-Solé-Vese [Image decomposition and restoration using total variation minimization and the H-1 norm, Technical Report 02-57, 2002] we present a wavelet-based treatment of variational problems arising in the field of image processing. In particular, we follow their approach and discuss a special class of variational functionals that induce a decomposition of images into oscillating and cartoon components and possibly an appropriate 'noise' component. In the setting of [Modeling textures with total variation minimization and oscillating patterns in image processing, Technical Report 02-19, 2002] and [Image decomposition and restoration using total variation minimization and the H-1 norm, Technical Report 02-57, 2002], the cartoon component of an image is modeled by a BV function; the corresponding incorporation of BV penalty terms in the variational functional leads to PDE schemes that are numerically intensive. By replacing the BV penalty term by a B11(L1) term (which amounts to a slightly stronger constraint on the minimizer), and writing the problem in a wavelet framework, we obtain elegant and numerically efficient schemes with results very similar to those obtained in [Modeling textures with total variation minimization and oscillating patterns in image processing, Technical Report 02-19, 2002] and [Image decomposition and restoration using total variation minimization and the H-1 norm, Technical Report 02-57, 2002]. This approach allows us, moreover, to incorporate general bounded linear blur operators into the problem so that the minimization leads to a simultaneous decomposition, deblurring and denoising. © 2004 Elsevier Inc. All rights reserved.

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320