Point spread function (PSF) expressed as a convolution and a sum 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?

Convolution is used to describe not only linear, but also shift-invariant system.

For $\mathbf{A}+\mathbf{B}=\mathbf{C}$, it's not even a linear system unless $\mathbf{B}=0$ (I assume $\mathbf{A}$ is the input, $\mathbf{C}$ is the output).