How Can Convolution and Deconvolution be Defined for 3D Images?
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:

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