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Jerome Gilles

Publications and source records attributed to Jerome Gilles.

33 records · Page 2Linked to original sources
arXiv2024

Low-Rank + Sparse Decomposition (LR+SD) for EEG Artifact Removal

Concurrent EEG-fMRI recordings are advantageous over serial recordings, as they offer the ability to explore the relationship between both signals without the compounded effects of nonstationarity in the brain. Nonetheless, analysis of simultaneous recordings is challenging given that a number of noise sources are introduced into the EEG signal even after MR gradient artifact removal with balistocardiogram artifact being highly prominent. Here, we present an algorithm for automatically removing residual noise sources from the EEG signal in a single process using low rank + sparse decomposition (LR+SD). We apply this method to both experimental and simulated EEG data, where in the latter case the true EEG signature is known. The experimental data consisted of EEG data collected concurrently with fMRI (EEG-fMRI) as well as alone outside the scanning environment while subjects viewed Gabor flashes, a perceptual task known to produce event related power diminutions in the alpha spectral band. On the simulated data, the LR+SD method was able to recover the pure EEG signal and separate it from artifact with up to three EEG sources. On the experimental data, LR+SD was able to recover the diminution in alpha spectral power that follows light flashes in concurrent EEG-fMRI data, which was not detectable prior to artifact removal. At the group level, we found that the signal-to-noise ratio was increased ~34\% following LR+SD cleaning, as compared independent component analysis (ICA) in concurrently collected EEG-fMRI data. We anticipate that this method will be highly useful for analyzing simultaneously collected EEG-fMRI data, and downstream for exploring the coupling between these two modalities.

q-bio.NC↗
arXiv2024

Empirical wavelet transform

Some recent methods, like the Empirical Mode Decomposition (EMD), propose to decompose a signal accordingly to its contained information. Even though its adaptability seems useful for many applications, the main issue with this approach is its lack of theory. This paper presents a new approach to build adaptive wavelets. The main idea is to extract the different modes of a signal by designing an appropriate wavelet filter bank. This construction leads us to a new wavelet transform, called the empirical wavelet transform. Many experiments are presented showing the usefulness of this method compared to the classic EMD.

math.FA↗
arXiv2024

2D Empirical Transforms. Wavelets, Ridgelets and Curvelets revisited

A recently developed new approach, called ``Empirical Wavelet Transform'', aims to build 1D adaptive wavelet frames accordingly to the analyzed signal. In this paper, we present several extensions of this approach to 2D signals (images). We revisit some well-known transforms (tensor wavelets, Littlewood-Paley wavelets, ridgelets and curvelets) and show that it is possible to build their empirical counterpart. We prove that such constructions lead to different adaptive frames which show some promising properties for image analysis and processing.

math.FA↗
arXiv2024

Open Turbulent Image Set (OTIS)

Long distance imaging is subject to the impact of the turbulent atmosphere. This results into geometric distortions and some blur effect in the observed frames. Despite the existence of several turbulence mitigation algorithms in the literature, no common dataset exists to objectively evaluate their efficiency. In this paper, we describe a new dataset called OTIS (Open Turbulent Images Set) which contains several sequences (either static or dynamic) acquired through the turbulent atmosphere. For almost all sequences, we provide the corresponding groundtruth in order to make the comparison between algorithms easier. We also discuss possible metrics to perform such comparisons.

cs.CV↗
arXiv2024

Wavelet Burst Accumulation for turbulence mitigation

In this paper, we investigate the extension of the recently proposed weighted Fourier burst accumulation (FBA) method into the wavelet domain. The purpose of FBA is to reconstruct a clean and sharp image from a sequence of blurred frames. This concept lies in the construction of weights to amplify dominant frequencies in the Fourier spectrum of each frame. The reconstructed image is then obtained by taking the inverse Fourier transform of the average of all processed spectra. In this paper, we first suggest to replace the rigid registration step used in the original algorithm by a non-rigid registration in order to be able to process sequences acquired through atmospheric turbulence. Second, we propose to work in a wavelet domain instead of the Fourier one. This leads us to the construction of two types of algorithms. Finally, we propose an alternative approach to replace the weighting idea by an approach promoting the sparsity in the used space. Several experiments are provided to illustrate the efficiency of the proposed methods.

cs.CV↗
arXiv2024

Investigation of moving objects through atmospheric turbulence from a non-stationary platform

In this work, we extract the optical flow field corresponding to moving objects from an image sequence of a scene impacted by atmospheric turbulence \emph{and} captured from a moving camera. Our procedure first computes the optical flow field and creates a motion model to compensate for the flow field induced by camera motion. After subtracting the motion model from the optical flow, we proceed with our previous work, Gilles et al~\cite{gilles2018detection}, where a spatial-temporal cartoon+texture inspired decomposition is performed on the motion-compensated flow field in order to separate flows corresponding to atmospheric turbulence and object motion. Finally, the geometric component is processed with the detection and tracking method and is compared against a ground truth. All of the sequences and code used in this work are open source and are available by contacting the authors.

cs.CV↗
arXiv2024

Detection of moving objects through turbulent media. Decomposition of Oscillatory vs Non-Oscillatory spatio-temporal vector fields

In this paper, we investigate how moving objects can be detected when images are impacted by atmospheric turbulence. We present a geometric spatio-temporal point of view to the problem and show that it is possible to distinguish movement due to the turbulence vs. moving objects. To perform this task, we propose an extension of 2D cartoon+texture decomposition algorithms to 3D vector fields. Our algorithm is based on curvelet spaces which permit to better characterize the movement flow geometry. We present experiments on real data which illustrate the efficiency of the proposed method.

cs.CV↗
arXiv2024

Empirical curvelet based Fully Convolutional Network for supervised texture image segmentation

In this paper, we propose a new approach to perform supervised texture classification/segmentation. The proposed idea is to feed a Fully Convolutional Network with specific texture descriptors. These texture features are extracted from images by using an empirical curvelet transform. We propose a method to build a unique empirical curvelet filter bank adapted to a given dictionary of textures. We then show that the output of these filters can be used to build efficient texture descriptors utilized to finally feed deep learning networks. Our approach is finally evaluated on several datasets and compare the results to various state-of-the-art algorithms and show that the proposed method dramatically outperform all existing ones.

cs.CV↗
arXiv2024

Evaluation of neural network algorithms for atmospheric turbulence mitigation

A variety of neural networks architectures are being studied to tackle blur in images and videos caused by a non-steady camera and objects being captured. In this paper, we present an overview of these existing networks and perform experiments to remove the blur caused by atmospheric turbulence. Our experiments aim to examine the reusability of existing networks and identify desirable aspects of the architecture in a system that is geared specifically towards atmospheric turbulence mitigation. We compare five different architectures, including a network trained in an end-to-end fashion, thereby removing the need for a stabilization step.

cs.CV↗
arXiv2024

Review of wavelet-based unsupervised texture segmentation, advantage of adaptive wavelets

Wavelet-based segmentation approaches are widely used for texture segmentation purposes because of their ability to characterize different textures. In this paper, we assess the influence of the chosen wavelet and propose to use the recently introduced empirical wavelets. We show that the adaptability of the empirical wavelet permits to reach better results than classic wavelets. In order to focus only on the textural information, we also propose to perform a cartoon + texture decomposition step before applying the segmentation algorithm. The proposed method is tested on six classic benchmarks, based on several popular texture images.

cs.CV↗
arXiv2024

Continuous empirical wavelets systems

The recently proposed empirical wavelet transform was based on a particular type of filter. In this paper, we aim to propose a general framework for the construction of empirical wavelet systems in the continuous case. We define a well-suited formalism and then investigate some general properties of empirical wavelet systems. In particular, we provide some sufficient conditions to the existence of a reconstruction formula. In the second part of the paper, we propose the construction of empirical wavelet systems based on some classic mother wavelets.

math.SP↗
arXiv2024

The Empirical Watershed Wavelet

The empirical wavelet transform is an adaptive multiresolution analysis tool based on the idea of building filters on a data-driven partition of the Fourier domain. However, existing 2D extensions are constrained by the shape of the detected partitioning. In this paper, we provide theoretical results that permits us to build 2D empirical wavelet filters based on an arbitrary partitioning of the frequency domain. We also propose an algorithm to detect such partitioning from an image spectrum by combining a scale-space representation to estimate the position of dominant harmonic modes and a watershed transform to find the boundaries of the different supports making the expected partition. This whole process allows us to define the empirical watershed wavelet transform. We illustrate the effectiveness and the advantages of such adaptive transform, first visually on toy images, and next on both unsupervised texture segmentation and image deconvolution applications.

math.SP↗
arXiv2024

Empirical wavelet frames

Due to their adaptive nature, empirical wavelets had several successes in many fields from engineering, science, medical signal/image processing. Recently, a general theoretical framework has been developed in the one-dimensional case, showing the possibility to build empirical wavelets from any classic mother wavelets. Given extensive literature both in theory and applications of classic wavelet frames, it is legitimate to ask about the feasibility of building empirical wavelet frames. We address this question in this paper. We prove several results which provide conditions on the existence of empirical wavelet frames taking into account the above mentioned adaptability.

math.FA↗
arXiv2024

Empirical Voronoi Wavelets

Recently, the construction of 2D empirical wavelets based on partitioning the Fourier domain with the watershed transform has been proposed. If such approach can build partitions of completely arbitrary shapes, for some applications, it is desirable to keep a certain level of regularity in the geometry of the obtained partitions. In this paper, we propose to build such partition using Voronoi diagrams. This solution allows us to keep a high level of adaptability while guaranteeing a minimum level of geometric regularity in the detected partition.

cs.CE↗