How Can Convolution and Deconvolution be Defined for 3D Images? I am trying to understand how convolution and deconvolution can be represented for 3D images/ stacks of data. I would prefer it, if you built the these concepts from 1D vectors to 3D matrices in terms of their equations. I am currently writing a report and am trying to represent 3D deconvolution as an equation. 

Please do not hesitate to ask me any questions to clarify this question.
For one variable, we have

$$
y(i) = \sum_m x(i-m) \cdot h(m).
$$

For two variables it's

$$
y(i,j) = \sum_m \sum_n x(m,n) \cdot h(i-m,j-n).
$$

For three:

$$
y(i,j,k) = \sum_m \sum_n \sum_p x(m,n,p) \cdot h(i-m,j-n,k-p).
$$