Total variation denoising | EPFL Graph Search

In signal processing, particularly , total variation denoising, also known as total variation regularization or total variation filtering, is a noise removal process (filter). It is based on the principle that signals with excessive and possibly spurious detail have high total variation, that is, the integral of the absolute is high. According to this principle, reducing the total variation of the signal—subject to it being a close match to the original signal—removes unwanted detail whilst preserving important details such as . The concept was pioneered by L. I. Rudin, S. Osher, and E. Fatemi in 1992 and so is today known as the ROF model. This noise removal technique has advantages over simple techniques such as linear smoothing or median filtering which reduce noise but at the same time smooth away edges to a greater or lesser degree. By contrast, total variation denoising is a remarkably effective edge-preserving filter, i.e., simultaneously preserving edges whilst smoothing aw

Deep Gaussian denoiser epistemic uncertainty and decoupled dual-attention fusion

Majed El Helou, Xiaoyu Lin, Xiaoqi Ma, Sabine Süsstrunk

Following the performance breakthrough of denoising networks, improvements have come chiefly through novel architecture designs and increased depth. While novel denoising networks were designed for real images coming from different distributions, or for specific applications, comparatively small improvement was achieved on Gaussian denoising. The denoising solutions suffer from epistemic uncertainty that can limit further advancements. This uncertainty is traditionally mitigated through different ensemble approaches. However, such ensembles are prohibitively costly with deep networks, which are already large in size. Our work focuses on pushing the performance limits of state-of-the-art methods on Gaussian denoising. We propose a model-agnostic approach for reducing epistemic uncertainty while using only a single pretrained network. We achieve this by tapping into the epistemic uncertainty through augmented and frequency-manipulated images to obtain denoised images with varying error. We propose an ensemble method with two decoupled attention paths, over the pixel domain and over that of our different manipulations, to learn the final fusion. Our results significantly improve over the state-of-the-art baselines and across varying noise levels.

2021

Good Vibrations and Unknown Excitations

Dalia Salem Hassan Fahmy El Badawy

Inspired by the human ability to localize sounds, even with only one ear, as well as to recognize objects using active echolocation, we investigate the role of sound scattering and prior knowledge in regularizing ill-posed inverse problems in acoustics. In particular, we study direction of arrival estimation with one microphone, acoustic imaging with a small number of microphones, and microphone array localization. Not only are these problems ill-posed but also non-convex in the variables of interest when formulated as optimization problems. To restore well-posedness, we thus use sound scattering which we construe as a physical form of regularization. We additionally use standard regularization in the form of appropriate priors on the variables. The non-convexity is then handled with tools such as linearization or semidefinite relaxation. We begin with direction of arrival estimation. While conventional approaches require at least two microphones, we show how to estimate the direction of one or more sound sources using only one. This is made possible thanks to regularization by sound scattering which we achieve by compact structures made from LEGO that scatter the sound in a direction-dependent manner. We also impose a prior on the source spectra where we assume they can be sparsely represented in a learned dictionary. Using algorithms based on non-negative matrix factorization, we show how to use the LEGO devices and a speaker-independent dictionary to successfully localize one or two simultaneous speakers. Next, we study acoustic imaging of 2D shapes using a small number of microphones. Unlike in echolocation where the source is known, we show how to image an unknown object using an unknown source. In this case, we enforce a prior on the object using a total variation norm penalty but no priors on the source. We also show how to use microphones embedded in the ears of a dummy head to benefit from the diversity encoded in the head-related transfer function. We then propose an algorithm to jointly reconstruct the shape of the object and the sound source spectrum. We demonstrate the effectiveness of our approach using numerical and real experiments with speech and noise sources. Finally, the need to know the microphone positions in acoustic imaging and a number of other applications led us to study microphone localization. We assume the positions of the loudspeakers are also unknown and that all devices are not synchronized. In this case, the times of arrival from the loudspeakers to the microphones are shifted by unknown source emission times and unknown sensor capture times. We thus propose an objective that is timing-invariant allowing us to localize the setup without first having to estimate the unknown timing information. We also propose an approach to handle missing data as well as show how to include side information such as knowledge of some of the distances between the devices. We derive a semidefinite relaxation of the objective which provides a good initialization to a subsequent refinement using the Levenberg-Marquardt algorithm. Using numerical and real experiments, we show we can localize unsynchronized devices even in near-minimal configurations.

EPFL2020

Good Vibrations and Unknown Excitations

Dalia Salem Hassan Fahmy El Badawy

EPFL2020