Numerical Differentiation of Noisy, Nonsmooth Data. (17th April 2011) - Chartrand, Rick
Abstract : We consider the problem of differentiating a function specified by noisy data. Regularizing the differentiation process avoids the noise amplification of finite-difference methods. We use total-variation regularization, which allows for discontinuous solutions. The resulting simple algorithm accurately differentiates noisy functions, including those which have a discontinuous derivative.