Projection of 2D signal
Yes you can re-represent the 2d signal as a 1-d signal and use signal processing algorithms on it. In doing this you can lose some of benefits of representing the data this way. 

Eg. If you were looking at compression of a mostly continuous 2-d dataset you may get benefits by treating the data as 2-dimensional and compressing in each dimension. Representing the data as concatenated rows or columns introduces discontinuities that the compression won't handle as well.