Unfolding problems often arise in the context of signal processing, data analysis and experimental physics in general. It occurs when the probability distribution of a physical quantity is to be measured but it is randomized (smeared) by some well-described process, such as a non-ideal detector response or a well parametrized physical phenomenon. In such cases it is said that the original probability distribution of interest is folded by a known response function. The reconstruction of the original probability distribution from the measured one and from the response function is called unfolding, which is a delicate problem in signal or data processing. As the unfolding problem is numerically ill-posed, most methods have some relatively arbitrary control parameter on regularization. A large class of these methods, by construction, introduce bias which is difficult to quantify, furthermore sometimes it is difficult to show that the method is consistent, i.e.\ that the bias tends to zero with respect to the control parameters of the method. Quantification of statistical and systematic error of the unfolded distribution is often also an issue. We propose a linear iterative method for which we prove that the bias error converges to zero with increasing iteration order, i.e.\ the metod is consistent. In case of presence of statistical and systematic errors on the measured distribution or the response function, we prove explicit error propagation formulae. With this, an optimal iteration stopping criterion can be defined, and the three important error terms ---the bias error, the statistical error and the systematic error--- of the unfolded distribution can be directly quantified at the optimum.
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