how to reconstruct image from feature space of convolutional neural network?
One choice is to train a neural network model to take these values and output original images.
Notice that usually some data is loss in this process so it might be impossible to reconstruct the image with perfection.
You could try inverting the functional form but:

CNNs usually use ReLu activation which is not bijective.
Pooling layers throws information away (it still could be fixed if we had redundant information)
The weight matrix might not be inversable