Total Variation Meets Topological Persistence: A First Encounter

We present first insights into the relation between two popular yet apparently dissimilar approaches to denoising of one dimensional signals, based on (i) total variation (TV) minimization and (ii) ideas from topological persistence. While a close relation between (i) and (ii) might phenomenologically not be unexpected, our work appears to be the first to make this connection precise for one dimensional signals. We provide a link between (i) and (ii) that builds on the equivalence between TV-L2 regularization and taut strings and leads to a novel and efficient denoising algorithm that is contrast preserving and operates in O(n logn) time, where n is the size of the input.