  A trainable filter-based higher-order Markov Random Fields (MRFs) model - the
so called Fields of Experts (FoE), has proved a highly effective image prior
model for many classic image restoration problems. Generally, two options are
available to incorporate the learned FoE prior in the inference procedure: (1)
sampling-based minimum mean square error (MMSE) estimate, and (2) energy
minimization-based maximum a posteriori (MAP) estimate. This letter is devoted
to the FoE prior based single image super resolution (SR) problem, and we
suggest to make use of the MAP estimate for inference based on two facts: (I)
It is well-known that the MAP inference has a remarkable advantage of high
computational efficiency, while the sampling-based MMSE estimate is very time
consuming. (II) Practical SR experiment results demonstrate that the MAP
estimate works equally well compared to the MMSE estimate with exactly the same
FoE prior model. Moreover, it can lead to even further improvements by
incorporating our discriminatively trained FoE prior model. In summary, we hold
that for higher-order natural image prior based SR problem, it is better to
employ the MAP estimate for inference.
