The size of the images is N_x columns by N_y lines.

X is a vector, made from the pixels of an image in a lexicographic order.
X_s is the value of the site (or pixel) s.
X_ij is the value of the pixel at column i  and line j.
Xⁿ is le nth vector of the chain (Xⁿ) .
Let us write P(X) instead of P(x=X).

X₀ is the original (non corrupted) image.
Y is the observed data (corrupted image).
H is the convolution operator (N_xN_y matrix).

B^x, B^y and W are vectors of the same dimension as X.

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

D_x and D_y are the derivative operators applied on the images,
with respect to columns and lines :

d_x and d_y are the generators of D_x et D_y.

h⁴ is the generator of H⁴, H⁴ is a matrix (2N_x)²(2N_y)² made by extension of H (padding with zeros).

d⁴_x and d⁴_y are the generators of D⁴_x et D⁴_y, derivative operators applied on symmetrized images whose dimension is 2N_x2N_y.

represents the Fourier transform.

  is the state space, set of images with dimension N_xN_y and real pixels, ie.