Adaptive iterative algorithms for spiky deconvolution

Considering the joint detection-estimation character that spiky deconvolution problems have, an adaptively contracted (projection) selection operator is introduced to detect the nonzero values of the solution, which can be combined with iterative algorithms to offer very efficient schemes for solving these problems. A number of gradient-type algorithms based on this principle are described, and their performance is illustrated through simulation examples. The approach is based on the idea of reducing the noise and defining the signal in an iterative form. Another possibility is to define the signal and reduce the overall energy outside its domain, also in an iterative form. This algorithm is more expensive from a computational point of view; however, simulations indicate that it has somewhat different properties. It seems to be slightly less robust against the noise, while it offers better resolution and even more accurate amplitude estimates