Higher‐order MRFs based image super resolution: why not MAP?

Abstract

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 paper 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. I. INTRODUCTIONMarkov Random Fields (MRFs) based models have a long history in low-level computer vision problems, which treat the image (can be also seen as a label field) as a random field [7]. It is well-known that MRFs are particularly effective for image/label prior modeling in image processing. In a MRF-based prior model, the probability of a whole field is defined based on the potential (or energy) of the local cliques. MRF-based prior models, especially higher-order potentials for enforcing label consistency have demonstrated great successes in the community of multi-label image segmentation [9], [6]. The exploited Y.J. Chen is with the

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