EXACT DECONVOLUTION FOR MULTIPLE CONVOLUTION-OPERATORS - AN OVERVIEW, PLUS PERFORMANCE CHARACTERIZATIONS FOR IMAGING SENSORS

Deconvolution of a single convolution equation is an ill-posed problem. Deconvolution in general need not be. The inversion of a set of simultaneous convolution equations in Rn can be a well-posed problem, with the inverse (deconvolution) given also by convolution operators. Whenever such a set of convolution equations represents a set of physically realizable devices (for example, transducers, sensors) then one has, after deconvolution, essentially an arbitrary bandwidth device. The first part is an updated review of the subject, including physically realizable examples along with explicit inverses and a computer simulation of the resulting large bandwidth. 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 invertibility is given. The second part addresses the performance of these simultaneous convolution operators when there are sources of additive noise prior to the inverse: For noise typical of electro-optical sensors, invertible multiple operators with their inverse will always outperform any set of single or multiple operators with the inverse omitted. The Appendix contains a tutorial on the theory of distributions of compact support, which is used freely throughout this paper. © 1990 IEEE