Node-Adaptive Regularization for Graph Signal Reconstruction

Adaptive Regularization Parameter for Graph Cut Segmentation

Graph cut minimization formulates the segmentation problem as the liner combination of data and smoothness terms. The smoothness term is included in the energy formulation through a regularization parameter. We propose that the trade-off between the data and the smoothness terms should not be balanced by the same regularization parameter for the whole image. In order to validate the proposed id...

Uniform Convergence of Adaptive Graph-Based Regularization

The regularization functional induced by the graph Laplacian of a random neighborhood graph based on the data is adaptive in two ways. First it adapts to an underlying manifold structure and second to the density of the data-generating probability measure. We identify in this paper the limit of the regularizer and show uniform convergence over the space of Hölder functions. As an intermediate s...

Adaptive Regularization: Towards Self-Calibrated Reconstruction

Regularization Tools and Models for Image and Signal Reconstruction

* ABSTRACT The present paper proposes a synthetic overview of regularization techniques for the reconstruction of piecewise regular signals and images. The stress is put on Tikhonov penalized approach and on subsequent non-quadratic and halfquadratic generalizations. On one hand, a link is made between the detection-estimation formulation and the non-convex penalization approach. On the other h...

A Graph Diffusion LMS Strategy for Adaptive Graph Signal Processing

Graph signal processing allows the generalization of DSP concepts to the graph domain. However, most works assume graph signals that are static with respect to time, which is a limitation even in comparison to classical DSP formulations where signals are generally sequences that evolve over time. Several earlier works on adaptive networks have addressed problems involving streaming data over gr...