Ill-posed inverse problems call for adapted models to define relevant solutions. Dictionary learning for sparse representation is often an efficient approach. In many methods, the size of the dictionary is fixed in advance and the noise level as well as regularization parameters need some tuning. Indian Buffet process dictionary learning (IBP-DL) is a Bayesian non para-metric approach which permits to learn a dictionary with an adapted number of atoms. The noise and sparsity levels are also inferred so that the proposed approach is really non para-metric: no parameters tuning is needed. This work adapts IBP-DL to the problem of image inpainting by proposing an accelerated collapsed Gibbs sampler. Experimental results illustrate the relevance of this approach.