Fast reconstruction of linearly distorted signals

A product expansion of the inverse operator is used to derive a class of iterative algorithms that have a pth-order rate of convergence. Compared to the linear algorithm, the number of iterations required to obtain a given reconstruction is reduced from pⁿ to n. The primary difference between these algorithms and the linear algorithm is that they update both the estimate of x and the operator D, rather than the estimate alone. Several methods that may be used to incorporate linear and nonlinear constraints are also proposed. Finally, some examples of linear inverse problems are presented and the differences in rates of convergence for the linear and the pth-order algorithms are compared