How to build classifier if only 1 image per class available
One image per class in way too less data for building any classifier. Rather than image classification, image similarity matching seems a better approach and so I would suggest you a Siamese network for one-shot learning. 

A Siamese network is a class of neural network that contains two or more identical network and are used to differentiate between the input images by maximizing the minimum distance among the images. This technique is helpful for what we call as One-shot learning. 

But if you only want to build a classifier, here are a few steps you can think about: 


Try to increase your dataset size by adding a few more images to you training set. 
Apply heavy Image-augmentation.
Use a Pre-trained model to try transfer learning.