Time-scale analysis for signal (and image) denoising

 

The modelling of the time scale structure of the wavelet coefficients through the superposition of simple atoms allows us to achieve an efficient scheme for denoising. In fact, atoms spreading in the time scale plane is formally the solution of differential equations with proper initial conditions. Intensive experimental results show the competitive performances of the proposed approach in terms of signal to noise ratio (SNR) and visual quality.

 

Slides of EUSIPCO 06

 

The numerical solution of the ordinary differential equation to compute the trajectories of true atoms (they are not noise) is computationally expensive. Nonetheless, it is possible to show how the numerical solution of such equations can be avoided leading to a speed up of the scale linking computation. This result is achieved through a suitable projection space of the wavelet local extrema, requiring just least squares and filtering operations and then a low computational time.

 

Slides of ICIAR 08

 

 


References:

  1. V. Bruni, D. Vitulano, Image De-noising via Overlapping Atoms, ICIAR '04, Porto, Portugal, pp. 179-186, Vol. 3211, Springer ISDN 3-540-23223-0, October 2004, Special Issue in Lecture Notes in Computer Science.

  2. V. Bruni, B. Piccoli, D. Vitulano, ''Signal and Image Denoising via Scale-Space Atoms'' in Proceedings of IEEE 14-th European Signal Processing Conference Florence, Italy, September 2006.

  3. V. Bruni, B. Piccoli, D. Vitulano, A Fast Scheme for Multiscale Signal Denoising, Proceedings of 5th International Conference on Image Analysis and Recognition, ICIAR, pp. 23-32, Povoa de Varzim, Portugal, 2008, Special Issue in Lecture Notes in Computer Science.

  4. V. Bruni, D. Vitulano, Image denoising using similarities in the time scale plane, accepted to ACIVS 2008.

  5. V. Bruni, D. Vitulano, Wavelet based Signal De-noising via Simple Singularities Approximation, Signal Processing, Vol. 86, pp. 859-876, 2006.

  6. V. Bruni, B. Piccoli, D. Vitulano, ''Wavelets and PDE for Image Denoising'', Electronic Letters on Computer Vision and Image Analysis, Special Issue on Partial Differential Equations Methods in Graphics and Vision, Vol. 6, No. 2 pp. 36-53, January 2008.

  7. V. Bruni, B. Piccoli, D. Vitulano, ''Time-scale Analysis for Fast Signal Denoising", Signal, Image and Video Processing, Springer, ISSN 1863-1703 (PRINT) 1863-1711 (ONLINE), June, 2008.