Data augmentation for very small image datasets

I am looking for techniques for augmenting very small image datasets. I have a classification problem with 3 classes. Each class consists of 20 different shapes. The shapes are similar between the classes, but the task is to identify which class the shapes belong to. Per shape, I have between 1 and 35 training examples. For two classes, I have 25 training examples per shape, but the number of examples per shape for the third classes is usually around 5. Now, what data augmentation schemes do you recommend? Geometric / affine transformations seem like a good place to start. However, I have also thought of applying Fast Fourier Transform (do the forward transform, add some noise, do the inverse transform). GANs seem infeasible, right? Not enough data, I suspect. In any case, I am grateful for your advice.

In my opinions, you have around $$25\times 20 \times 2 + 5 \times 20 = 1100$$ samples, so the list of problems is: