Accelerated graph-based spectral polynomial filters

Graph-based spectral denoising is a low-pass filtering using the eigendecomposition of the graph Laplacian matrix of a noisy signal. Polynomial filtering avoids costly computation of the eigendecomposition by projections onto suitable Krylov subspaces. Polynomial filters can be based, e.g., on the bilateral and guided filters. We propose constructing accelerated polynomial filters by running flexible Krylov subspace based linear and eigenvalue solvers such as the Block Locally Optimal Preconditioned Conjugate Gradient (LOBPCG) method.Comment: 6 pages, 6 figures. Accepted to the 2015 IEEE International Workshop on Machine Learning for Signal Processin

Accelerated graph-based nonlinear denoising filters

Denoising filters, such as bilateral, guided, and total variation filters, applied to images on general graphs may require repeated application if noise is not small enough. We formulate two acceleration techniques of the resulted iterations: conjugate gradient method and Nesterov's acceleration. We numerically show efficiency of the accelerated nonlinear filters for image denoising and demonstrate 2-12 times speed-up, i.e., the acceleration techniques reduce the number of iterations required to reach a given peak signal-to-noise ratio (PSNR) by the above indicated factor of 2-12.Comment: 10 pages, 6 figures, to appear in Procedia Computer Science, vol.80, 2016, International Conference on Computational Science, San Diego, CA, USA, June 6-8, 201

Bilateral Filter: Graph Spectral Interpretation and Extensions

In this paper we study the bilateral filter proposed by Tomasi and Manduchi, as a spectral domain transform defined on a weighted graph. The nodes of this graph represent the pixels in the image and a graph signal defined on the nodes represents the intensity values. Edge weights in the graph correspond to the bilateral filter coefficients and hence are data adaptive. Spectrum of a graph is defined in terms of the eigenvalues and eigenvectors of the graph Laplacian matrix. We use this spectral interpretation to generalize the bilateral filter and propose more flexible and application specific spectral designs of bilateral-like filters. We show that these spectral filters can be implemented with k-iterative bilateral filtering operations and do not require expensive diagonalization of the Laplacian matrix