Matrix Representation of Linear Systems Relationships
The convolution of the two functions is given by:
for x = 0,1, 2,…,M-1, and y = 0,1, 2,…, N - 1.
The result is periodic with the same period (M x N) as of fe(x,y) and he(x,y).
Overlap of the individual convolution periods is avoided by choosing M ³ (A+C-1) and N ? (B+D-1).
The complete discrete degradation model is given by
where ?e(x,y) is an M x N extended discrete noise image.