Best (Perceptually / Objectively) Super Resolution Methods Out There?
In our days the Deep Neural Network methods certainly are generating best results.
Due to the intense research going on in this field the best method is a moving target hence one can not pin point to one.
One generation before them the best methods were based on Dictionary Learning.
For example you can use the K-SVD for Single Image Super Resolution.
Those approaches / methods works pretty well and are even improved using the EPLL approach.
You should be aware those methods are really slow for real world images.
Probably you should invest in the DNN world.
Pick any one of the latest on ArXiv Sanity.