English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

A new proof of the equivalence of the Taut String Algorithm and theone-dimensional Rudin-Osher-Fatemi model is presented. Based on duality and theprojection theorem in Hilbert space, the proof is strictly elementary.Existence and uniqueness of solutions to both denoising models follow asby-products. The standard convergence properties of the denoised signal, as theregularizing parameter tends to zero, are recalled and efficient proofsprovided. Moreover, a new and fundamental bound on the denoised signal isderived. This bound implies, among other things, the strong convergence (in thespace of functions of bounded variation) of the denoised signal to the insignalas the regularization parameter vanishes. The methods developed in the papercan be modified to cover other interesting applications such as isotonicregression.

On the Taut String Interpretation of the One-dimensional Rudin-Osher-Fatemi Model: A New Proof, a Fundamental Estimate and Some Applications