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

TL;DR

This paper advocates using the computationally efficient MAP inference over sampling-based MMSE for higher-order MRFs in image super resolution, showing comparable or better results with the FoE prior.

Contribution

It demonstrates that MAP inference is preferable for higher-order MRF-based super resolution, offering similar or improved results and greater efficiency compared to MMSE.

Findings

MAP inference is as effective as MMSE for SR with FoE prior.

MAP inference is significantly faster than sampling-based methods.

Incorporating discriminatively trained FoE improves SR results.

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 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.