DeepAI AI Chat
Log In Sign Up

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

10/27/2017
by   Niels Chr. Overgaard, et al.
LUNDS TEKNISKA HÖGSKOLA
0

A new proof of the equivalence of the Taut String Algorithm and the one-dimensional Rudin-Osher-Fatemi model is presented. Based on duality and the projection theorem in Hilbert space, the proof is strictly elementary. Existence and uniqueness of solutions to both denoising models follow as by-products. The standard convergence properties of the denoised signal, as the regularizing parameter tends to zero, are recalled and efficient proofs provided. Moreover, a new and fundamental bound on the denoised signal is derived. This bound implies, among other things, the strong convergence (in the space of functions of bounded variation) of the denoised signal to the insignal as the regularization parameter vanishes. The methods developed in the paper can be modified to cover other interesting applications such as isotonic regression.

READ FULL TEXT

page 1

page 2

page 3

page 4

12/05/2022

Characterization of incentive compatible single-parameter mechanisms revisited

We reexamine the characterization of incentive compatible single-paramet...
06/15/2021

On Doctrines and Cartesian Bicategories

We study the relationship between cartesian bicategories and a specialis...
01/28/2017

A proof of Hilbert's theorem on ternary quartic forms with the ladder technique

This paper proposes a totally constructive approach for the proof of Hil...
03/25/2021

A formal proof of the Lax equivalence theorem for finite difference schemes

The behavior of physical systems is typically modeled using differential...
04/02/2022

Various proofs of the Fundamental Theorem of Markov Chains

This paper is a survey of various proofs of the so called fundamental th...
05/21/2020

Distributed Verifiers in PCP

Traditional proof systems involve a resource-bounded verifier communicat...
07/27/2020

The Spectral Approach to Linear Rational Expectations Models

This paper considers linear rational expectations models in the frequenc...