An updated review of the subject, including physically realizable examples along with explicit inverses and a computer simulation of the resulting large bandwidth, is given. A discussion of the ill-posedness of a single convolution operator clarifies the necessity of multiple operators. A precisely stated necessary and sufficient condition for inevitability is given. The performance of simultaneous convolution operators when there are sources of additive noise prior to the inverse is addressed. The main point is that for noise typical of electrooptical sensors, invertible multiple operators with their inverses will always outperform any set of single or multiple operators with the inverse omitted. A tutorial on the theory of distributions of compact support, which is used freely throughout the paper, is given in the appendix.