A constrained iterative multiple operator deconvolution technique

There are two major approaches to the problem of signal deconvolution: Direct methods attempt to explicitly form an inverse operator, while iterative methods rely on successive approximations. In general, direct methods are computationally efficient. Iterative methods enjoy advantages in terms of ill-conditioning and flexibility; in particular, they are easily modified to incorporate constraints that force the solution to exhibit features known a priori. It has previously been shown that the classical direct least squares and regularized least-squares inverse operator methods are equivalent in the limit to corresponding iterative solution methods. In some cases, multiple blurring operators can be used to convert instances of ill-posed problems into ones that are well-posed. A new iterative restoration that corresponds to the direct inversion solution associated with multiple operators is formulated here. This method has the advantages of the constrained iterative routines as well as the advantages associated with multiple operator direct inverse deconvolution. Examples are presented to illustrate that combining a constrained iterative technique with multiple operators can yield a restoration superior to that of a single operator constrained iterative estimate alone or that of a multiple operator direct inverse estimate alone.