A total variation based regularizer promoting piecewise-Lipschitz reconstructions
We introduce a new regularizer in the total variation family that promotes reconstructions with a given Lipschitz constant (which can also vary spatially). We prove regularizing properties of this functional and investigate its connections to total variation and infimal convolution type regularizers TVLp and, in particular, establish topological equivalence. Our numerical experiments show that the proposed regularizer can achieve similar performance as total generalized variation while having the advantage of a very intuitive interpretation of its free parameter, which is just a local estimate of the norm of the gradient. It also provides a natural approach to spatially adaptive regularization.
Code (0)
등록된 구현이 없습니다.
Methods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Supervised Learning of Sparsity-Promoting Regularizers for Denoising
We present a method for supervised learning of sparsity-promoting regularizers for image denoising. Sparsity-promoting regularization is a key ingredient in solving modern image reconstruction problems; however, the oper…
Collaborative FilteringDenoisingDictionary LearningImage Denoising+1Learning Sparsity-Promoting Regularizers using Bilevel Optimization
We present a method for supervised learning of sparsity-promoting regularizers for denoising signals and images. Sparsity-promoting regularization is a key ingredient in solving modern signal reconstruction problems; how…
Bilevel OptimizationCollaborative FilteringDenoisingDictionary Learning+1Fast & Robust Image Interpolation using Gradient Graph Laplacian Regularizer
In the graph signal processing (GSP) literature, it has been shown that signal-dependent graph Laplacian regularizer (GLR) can efficiently promote piecewise constant (PWC) signal reconstruction for various image restorat…
Image RestorationTotal Generalized Variation of the Normal Vector Field and Applications to Mesh Denoising
We propose a novel formulation for the second-order total generalized variation (TGV) of the normal vector on an oriented, triangular mesh embedded in $\R^3$. The normal vector is considered as a manifold-valued function…
Total Generalized Variation regularization closes the gap between neural-eld and classical methods in seismic travel-time tomography
Travel-time tomography forces a trade-off between mesh resolution and stability in which the regularizer choice dominates what can be recovered. We introduce MIMIR, a differentiable framework that represents the 2D veloc…