Optimal rates for total variation denoising

2016/03/30 by Jan-Christian Hütter, Philippe Rigollet, Hütter, Jan-Christian +1 · 3 citations
Computer Science · Engineering · Mathematics · #62C20 #62G05 #62G08 #62H35 #FOS: Mathematics #Image and Signal Denoising Methods #Medical Image Segmentation Techniques #Sparse and Compressive Sensing Techniques #Statistics Theory (math.ST) #math.ST #msc:62C20 #msc:62G05 #msc:62G08 #msc:62H35 #stat.TH

paper · pdf · doi:10.48550/arxiv.1603.09388

30 pages, 3 figures

openalex publication_date 2016/03/30 · arxiv created 2016/06/16 · arxiv updated 2016/06/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Motivated by its practical success, we show that the two-dimensional 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 also present extensions to more than two dimensions as well as several other graphs.

Citations

• Efficient Implementations of the Generalized Lasso Dual Path Algorithm
• Nonlinear total variation based noise removal algorithms
• On pattern recovery of the fused Lasso
• Ideal spatial adaptation by wavelet shrinkage
• Regression modeling on stratified data with the lasso

Cited by

• Graph-based regularization for regression problems with alignment and highly-correlated designs
• Total Variation Regularized Tensor-on-scalar Regression
• A Variational View on Statistical Multiscale Estimation

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