Which of DFT, DCT and DWT transforms is more robust to noise and geometric transformations in image processing I am currently studying about image watermarking and I have been testing these 3 domains to embed the watermark at. 

My question is, how do these domains hold up to noise addition or geometric transformations, regardless of watermark embeding. 

To be more precise, I want to find the relationship between an original image and a transformed one (with the transformations being the ones I mentioned in the title, where geometric transformations include rigid and non-rigid ones) in these domains, and which one holds best at minor and/or major changes. 

Also, I would like to learn about the generic pros and cons of these domains, compared to one another, aswell as why it is said to be better to use one instead of the others in watermarking. 

Sources would be apreciated. Thank you!
From the perspective of numerical analysis, the most robust transformations are unitary orthogonal matrices because they have a condition number of one.  Indeed the condition number is the metric that defines robustness.  You can find this in Stuart’s Introduction to Matrix Computations or the more advanced book by Golub and Van Loan.  

A related way of looking at perturbation sensitivity are the Holder p norms for Matrices also covered in Stewart