Optimal rates for total variation denoising

Optimal rates for total variation denoising

Motivated by its practical success, we show that the 2D total variation denoiser satisfies a sharp oracle inequality that leads to near optimal rates of estimation for a large class of image models such as bi-isotonic, Hölder smooth and cartoons. Our analysis hinges on properties of the unnormalized Laplacian of the two-dimensional grid such as eigenvector delocalization and spectral decay. We ...

Total Variation Classes Beyond 1d: Minimax Rates, and the Limitations of Linear Smoothers

We consider the problem of estimating a function defined over n locations on a d-dimensional grid (having all side lengths equal to n). When the function is constrained to have discrete total variation bounded by Cn, we derive the minimax optimal (squared) `2 estimation error rate, parametrized by n,Cn. Total variation denoising, also known as the fused lasso, is seen to be rate optimal. Severa...

An Improvement of Steerable Pyramid Denoising Method

The use of wavelets in denoising, seems to be an advantage in representing well the details. However, the edges are not so well preserved. Total variation technique has advantages over simple denoising techniques such as linear smoothing or median filtering, which reduce noise, but at the same time smooth away edges to a greater or lesser degree. In this paper, an efficient denoising method bas...

Convergence of an Iterative Method for Total Variation Denoising

In total variation denoising, one attempts to remove noise from a signal or image by solving a nonlinear minimization problem involving a total variation criterion. Several approaches based on this idea have recently been shown to be very eeective, particularly for denoising functions with discontinuities. This paper analyzes the convergence of an iterative method for solving such problems. The...

Optimal Constructions of Wavelet Coefficients Using Total Variation Regularization in Image Compression