The Wikipedia article on the Point Spread Function (link) discusses how an imaging system can be conceptually described using linear system theory. A convolution of the PSF with the image in the spatial domain is equivalent to a multiplication in the Fourier domain.
Given $m \times n$ matrices $\bf{A}$ and $\bf{B}$, and assuming that $\bf{A}$ is an image and $\bf{B}$ is another matrix, the addition of the two matrices in the spatial domain is:
$\bf{A} + \bf{B} = \bf{C}$
However, can this addition be expressed as a convolution in the spatial domain? Could I re-write the addition equation as a convolution?