  Circular convolutions and the corresponding frequency domain formula are
fundamentally important in image restoration; however, in this paper, we'll
prove that the usual computing method of circular convolutions violates the
physical meaning of blur producing. Especially for the image restoration
algorithms in frequency domain, this violation will affect the restoration
result. Relevant problems are proved rigorously and modified formulas are given
in both spatial and frequency domains. Experiments are done to show the effects
of new formulas. For clarity of proving, the one-dimensional case is dealt with
first, which may be useful in one-dimensional signal processing.
