Reconstructing a classified image from a simple Convolution Neural Network
You should have a look to cGAN implementation and why not DeepDream from Google ;)
The answer is yes it is possible, however it's not straight forward
I have a CNN trained on a classification task (Network is simple, 2 convolution + pooling layers and 2x fully connected layers). I would like to use this to reconstruct an image if I input a classification label. 
Is this possible to achieve? 
Is it possible to share weights between corresponding layers in the 2 networks?