Notations |

The size of the images iscolumns byN_{x}lines.N_{y}

is a vector, made from the pixels of an image in a lexicographic order.Xis the value of the site (or pixel)X_{s}.sis the value of the pixel at columnX_{ij}and linei.jis leX^{n}th vector of the chain (n) .X^{n}

Let us write(P) instead ofX(P=x).X

is the original (non corrupted) image.X_{0}is the observed data (corrupted image).Yis the convolution operator (Hmatrix).N_{x}N_{y }

,B^{x}andB^{y}are vectors of the same dimension asW.X

is the generator ofh, it is the Point Spread Function (PSF).H

andD_{x}are the derivative operators applied on the images,D_{y}

with respect to columns and lines :

andd_{x}are the generators ofd_{y}etD_{x}.D_{y}

h^{4}is the generator ofH^{4},H^{4}is a matrix (2)N_{x}^{2}(2)N_{y}^{2}made byextensionof(padding with zeros).H

d^{4}and_{x}d^{4}are the generators of_{y}D^{4}et_{x}D^{4}, derivative operators applied on_{y}symmetrizedimages whose dimension is 22N_{x}.N_{y}represents the Fourier transform.

is the state space, set of images with dimension

and real pixels, ie.N_{x}N_{y}