A Comment on Learning Analysis Operators

In the blog entry Inpainting Algorithm on GitHub (TV-L2 denoising and inpainting),  Martin Kleinsteuber commented:

Hi everyone, "The first approach may yield better results in the inpainting stage but requires a learning phase." This sentence suggests that an operator has to be learned for every individual inpainting task. However, the operator is learned offline and universal, a replacement for the TV, so to speak. It would be interesting to see how a combination of both approaches would perform

I wholeheartedly agree with Martin, if I gave the impression it was an unsurmountable issue then clearly it is not (if you have the time and inclination to perform this calibration). I also agree with him that given the learned analysis operator, one can use verbatim the methods used by Emmanuel to get similar results and it would be great to eventually compare these two approaches. But, to me, one of the most important aspect of Analysis Operator Learning and Its Application to Image Reconstruction by Simon Hawe, Martin Kleinsteuber, Klaus Diepold is.the following: interesting line of thoughts triggered by this:

"...We want to point out that this choice of parameters leads to a suitable general analysis operator, i.e. an operator with sparsifying property for the class of all natural images. It is thinkable that for more specific classes of images, for example medical imagery, other parameters may lead to a more suitable operator. .."

And indeed where would the learning of the analysis operator be of further interest ? How is the analysis operator different from say the TV if it is learned from samples taken 

• from the same camera with the same lens ? 
• The same cameras with different lenses ? or different setting for those lenses ?
• with widely differing specific natural images ?

Most synthetic experiments perform a calibration of the analysis operator with stock (2d) images, how is the analysis operator different

• with a 3d physical natural scene ? 
• with scenes taken different kind of sensors like SEM or a random lens imager ? 

In the end , how do we compare those different analysis operators ? What sort of information does it bring to the hardware maker ? to the sensor designer ? to the calibration process ?

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