Is it possible to use deep learning on small number of samples but each sample has a large amount data? I have around 50 subjects and each subject has weeks worth of time series data.  The task is to identify whether a subject has as specific condition.  We have been running wavelet transformations in 30s windows across the time series and then summarizing across spectral band groupings to get a data matrix of subject x spectral band (50x6).  Although this method does reasonably well at detecting the condition, I'm nervous that this may wash away important temporal information.  

Is it possible to use the wavelet transformations as images and feed this through a convolutional network?

To clarify, there are 50 subjects each with ~350 30s intervals of data.  The wavelets are run on each 30s interval producing 350 wavelet transformations per subject.  The wavelet transformations (previously) are summarized into power per spectral band, however, I would like to use each wavelet transformation as an image so each subject would now have ~350 images.
You have a database of 50x6 currently.

When you run a exercise of deep learning on images, you have n (images) x (width(px) x height(px) x 3) variables.

You have similarly characterized dataset when you use the wavelet transforms, so it is possible. You have to be very cautious because you will have more variables than n, so the danger of overfitting increases a lot.