The ConjugateApprox sampler, used for the conjugacy between the LMRF and Gamma distribution, seems unnecessary.
As noted in the reference:
A hybrid Gibbs sampler for edge-preserving tomographic reconstruction with uncertain view angles, by F Uribe, JM Bardsley, Y Dong, PC Hansen, NAB Riis.
Equation (13c) is the density of a Gamma distribution, as shown in Equation (28).
The approximation of the l_1 norms in Equation (13d) by l2 norms, which is what ConjugateApprox does is not necesarry, as (13d) is already the density of a Gamma distribution with:
$\alpha\delta = d + 1$ and $\beta_\delta = ||D_1x||_1 + ||D_2x||_1 + \beta$,
i.e., LMRF and the Gamma distribution form an exact conjugate pair, no need for the approximation.
I am currently not aware of any other "conjugate approximation".
The ConjugateApprox sampler, used for the conjugacy between the LMRF and Gamma distribution, seems unnecessary.
As noted in the reference: A hybrid Gibbs sampler for edge-preserving tomographic reconstruction with uncertain view angles, by F Uribe, JM Bardsley, Y Dong, PC Hansen, NAB Riis. Equation (13c) is the density of a Gamma distribution, as shown in Equation (28).
The approximation of the l_1 norms in Equation (13d) by l2 norms, which is what ConjugateApprox does is not necesarry, as (13d) is already the density of a Gamma distribution with: $\alpha\delta = d + 1$ and $\beta_\delta = ||D_1x||_1 + ||D_2x||_1 + \beta$, i.e., LMRF and the Gamma distribution form an exact conjugate pair, no need for the approximation.
I am currently not aware of any other "conjugate approximation".