How could I use a 16x16 image as an input in a HMM? And at the same time how would I train it? Can I use backpropagation?
You wouldn't, normally. A HMM is used to model sequences of observations, and it would not make sense to use it for image recognition. Unless they are sequential, such as strokes in handwriting.
HMMs are typically used in fields such as speech recognition and part-of-speech tagging. Here you observe a sequence of events that you want to fit to a model in order to classify the individual observations.