Contents/conteúdo

Mathematics Department Técnico Técnico

Mathematics, Systems and Robotics Seminar  RSS

Sessions

06/02/2004, 15:00 — 16:00 — Room P5, Mathematics Building
Gabriel Pires and Mário Figueiredo, CAM/IST and ISR/IST

"Partial Differential Equations and Image Processing" and "Iterative Algorithms for Wavelet-based Image Restoration"

  • Gabriel Pires - Partial Differential Equations and Image Processing

    Abstract: A complete classification of image multiscale transforms, satisfying a list of formal requirements, will be given. The classical models and new ones, which all are partial differential equations, will be characterized namely in terms of invariance properties.

  • Mário Figueiredo - Iterative Algorithms for Wavelet-based Image Restoration

    Abstract: Wavelet-based methods had a strong impact on the field of image processing, especially in coding and denoising. Wavelet-based image denoising methods yield state-of-the-art performance at very low computational cost. However, image restoration (deconvolution) is a more challenging problem than denoising, and applying wavelets to it has proved to be a non-trivial task. The crux of the difficulty lies in the fact that deconvolution is most easily dealt with in the Fourier domain, while image modelling is best handled in the wavelet domain.

    In this talk, after briefly reviewing wavalet-based image modelling and denoising, I will describe recently proposed algorithms for wavelet-based image deconvolution. These algorithms provide maximum penalized likelihood (MPL) estimates, under wavelet-based penalties, for which there are no closed-form solutions. I will show how such iterative algorithms can be derived from two different approaches. In the first approach, the observation model is re-written by inserting auxiliary latent variables which open the door to the use of the expectation-maximization (EM) algorithm. In the second approach, the iterative algorithm is derived directly in a bound optimization framework. In both cases, the resulting algorithms, which are very simple, alternate between a Fourier-based step and a wavelet-based step. Experimental results show that these algorithms achieve state-of-the-art performance on benchmark image deconvolution problems.

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