How to approach a problem if I am new in the field? I recently came across a problem related to image recognition in Deep Learning. One fine morning, I was struck with the idea that possibly I could do something about it if I merged GANs with CNNs. As of now, I only know what these networks are capable of.

Now how should I go about this? Should I first pick a standard book (say Ian Goodfellow's Deep Learning) and read it from cover to cover? Or should I straightaway read some research articles, identify areas I am weak in, and then dig deep into those very areas from standard texts.

In other words, is it better to complete everything I can get my hands on before starting to work on this idea? Or should I start on it and fill the gaps as they come by.

P.S. My background in courses in statistical learning, probability, and calculus ensures I can completely understand the math behind the above stated topics.
I am still learning, but this is how a few advisors taught me how to approach my field.

First, look for a recent structured literature review of the filed and taxonomies. They give you a good starting point as all relevant paper (hopefully anyway) are listed there, and this gives you a perfect index to learn about the filed. Of cause, if there is none, you could be the first to create one ;).

Then its time to read a lot, create a stack of all relevant paper — Mark of any references that look to help and add them to the stack. Keep going and once your stack starts to shrink more than it grows you should have a grasp about the filed. 

In order to do this in a reasonable time you do not have to read every paper deeply. Try to get the idea, and try to fit them into your understanding of the filed. Only read paper deeply that help you further your research question, other just skim. 

Other tested methods include: Ask your advisor and other colleagues in around you, they might have looked into it already and can point you to relevant material.