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Recently, many fast implementations of the bilateral and the nonlocal filters were proposed based on lattice and vector quantization, e.g. clustering, in higher dimensions. However, these approaches can still be inefficient owing to the complexities in the resampling process or in filtering the high-dimensional resampled signal. In contrast, simply scalar resampling the high-dimensional signal after decorrelation presents the opportunity to filter signals using multi-rate signal processing techniques. Cis work proposes the Gaussian lifting framework for efficient and accurate bilateral and nonlocal means filtering, appealing to the similarities between separable wavelet transforms and Gaussian pyramids. Accurately implementing the filter is important not only for image processing applications, but also for a number of recently proposed bilateralregularized inverse problems, where the accuracy of the solutions depends ultimately on an accurate filter implementation. We show that our Gaussian lifting approach filters images more accurately and efficiently across many filter scales. Adaptive lifting schemes for bilateral and nonlocal means filtering are also explored.

We propose the fast optical flow extractor, a filtering method that recovers artifact-free optical flow fields from HEVCcompressed video. To extract accurate optical flow fields, we form a regularized optimization problem that considers the smoothness of the solution and the pixelwise confidence weights of an artifactridden HEVC motion field. Solving such an optimization problem is slow, so we first convert the problem into a confidence-weighted filtering task. By leveraging the already-available HEVC motion parameters, we achieve a 100-fold speed-up in the running times compared to similar methods, while producing subpixel-accurate flow estimates. Je fast optical flow extractor is useful when video frames are already available in coded formats. Our method is not specific to a coder, and works with motion fields from video coders such as H.264/AVC and HEVC.

This paper proposes graph Laplacian regularization for robust estimation of optical flow. First, we analyze the spectral properties of dense graph Laplacians and show that dense graphs achieve a better trade-off between preserving flow discontinuities and filtering noise, compared with the usual Laplacian. Using this analysis, we then propose a robust optical flow estimation method based on Gaussian graph Laplacians. We revisit the framework of iteratively reweighted least-squares from the perspective of graph edge reweighting, and employ the Welsch loss function to preserve flow discontinuities and handle occlusions. Our experiments using the Middlebury and MPI-Sintel optical flow datasets demonstrate the robustness and the efficiency of our proposed approach.

We address the problem of decoding joint photographic experts group (JPEG)-encoded images with less visual artifacts. We view the decoding task as an ill-posed inverse problem and find a regularized solution using a convex, graph Laplacian-regularized model. Since the resulting problem is non-smooth and entails non-local regularization, we use fast high-dimensional Gaussian filtering techniques with the proximal gradient descent method to solve our convex problem efficiently. Our patch-based "coefficient graph" is better suited than the traditional pixel-based ones for regularizing smooth non-stationary signals such as natural images and relates directly to classic non-local means de-noising of images. We also extend our graph along the temporal dimension to handle the decoding of M-JPEG-encoded video. Despite the minimalistic nature of our convex problem, it produces decoded images with similar quality to other more complex, state-of-the-art methods while being up to five times faster. We also expound on the relationship between our method and the classic ANCE method, reinterpreting ANCE from a graph-based regularization perspective.