Is it feasible to perform PCA on large size images prior to classification?

Question

I have a dataset composed of $970$ images with size $256\times256$, so I have a data matrix $X \in \mathbb{R}^{970\times65536}$. My idea is to compute the PCA transformation in the training phase considering the whole data-set and then transform the single images before sending them to a classification algorithm (e.g., SVM or a DNN).

The problem is that the eigenvalue decomposition requires is it practically infeasible with a covariance matrix $C \in \mathbb{R}^{256^2\times256^2}$. Is it still possible to use PCA in this situation?