Which of DFT, DCT and DWT transforms is more robust to noise and geometric transformations in image processing
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