On the Taut String Interpretation and Other Properties of the Rudin–Osher–Fatemi Model in One Dimension
We study the one-dimensional version of the Rudin–Osher–Fatemi (ROF) denoising model and some related TV-minimization problems. A new proof of the equivalence between the ROF model and the so-called taut string algorithm is presented, and a fundamental estimate on the denoised signal in terms of the corrupted signal is derived. Based on duality and the projection theorem in Hilbert space, the proo