Conversion of pixel plane into a signal (a vector) is a popular topic in pattern recognition, where it is referred to as feature computation. Your signal vector is a set of image features -- that could be rather broad range of characteristics, depending on the context of your needs (eg what sort of signal would better suit you in your downstream needs). Hope this helps.
There are a lot of possibilities. Which one is the best choise depends from your task. For example you may use 2D DCT transform and then zigzag scanning as in JPEG.