A NEW IMAGE DEBLURRING APPROACH USING A SPECIAL CONVOLUTION EXPANSION

M El Rhabi (1) , H. Fenniri (2) , A. Hakim (3) , E. Moreau (4)

1 IMI - Département Ingénierie Mathématique et Informatique, École des Ponts ParisTech
2 CRESTIC - Centre de Recherche en Sciences et Technologies de l'Information et de la Communication - EA 3804
3 UCA - Université Cadi Ayyad [Marrakech]
4 LIS - Laboratoire d'Informatique et Systèmes

The deconvolution problem in image processing consists of reconstructing an original image from an observed and thus a degraded one. This degradation is often modelized as a linear operator plus an additive noise. The linear operator is called the blurring operator and the goal consists of deblurring the image. Very often, the blurring operator is modelized as a convolution whose kernel (the Point Spread Function) is not directly known in practice. In this paper, we first propose a new model for convolution and we validate it through computer simulations. Basically, we expend the kernel leading to a sequence of real coefficients in link with the moment problem. We particularly emphasize the radial isotropic case.

Mots clés: Image restoration; Image deblurring; Blind deblurring; Blind deconvolution; The moment problem

Domaines: Mathématiques [math]; Mathématiques [math]; Analyse numérique [math.NA]; Informatique [cs]; Informatique [cs]; Modélisation et simulation; Informatique [cs]; Traitement des images [eess.IV]

M El Rhabi, H. Fenniri, A. Hakim, E. Moreau. A NEW IMAGE DEBLURRING APPROACH USING A SPECIAL CONVOLUTION EXPANSION. 21st European Signal Processing Conference (EUSIPCO 2013), Sep 2013, Marrakech, Morocco. ⟨hal-01812595⟩