Convex image restoration is a major field in inverse problems. The problem is often addressed by hand-tuning hyper-parameters. We propose an incremental contribution about a Bayesian approach where a convex field is constructed via Location Mixture of Gaussian and the estimator computed with a fast MCMC algorithm. Main contributions are a new field with several operator avoiding crosslike artifacts and a fallback sampling algorithm to prevent numerical errors. Results, in comparison to standard supervised results, have equivalent quality in a quasi-unsupervised approach and go with uncertainty quantification.