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auxiliary variable b, auxiliary images B^{x}, B^{y} (gradients w.r.t. x and y)Posterior distributionsampling triplets (X, B^{x}, B^{y}) in an alternated way on X and B^{x}, B^{y}
the pixels of B^{x} and B^{y} are independent
and the law of X knowing B^{x}, B^{y} is Gaussiansampling X is made in a single pass (unlike Gibbs and Metropolis samplers),
the processing is independent of the neighbourhood size
which provides a fast algorithm for posterior distribution sampling.

Initialization
:
We first calculate the Fourier transform F[h^{4} ] and DCT[Y], and W : 
The pixels b of B^{x} and B^{y} are independent : 
The distribution of X with known B is Gaussian because 






























Prior distribution

Initialization
:
We first calculate the Fourier transform F[h^{4} ] and W_{0} : 
The pixels b of B^{x} and B^{y} are independent : 
The distribution of X with a known B is Gaussian because 





























