Showing papers by "École normale supérieure de Cachan published in 2023"

A Relaxed Proximal Gradient Descent Algorithm for Convergent Plug-and-Play with Proximal Denoiser

Abstract: This paper presents a new convergent Plug-and-Play (PnP) algorithm. PnP methods are efficient iterative algorithms for solving image inverse problems formulated as the minimization of the sum of a data-fidelity term and a regularization term. PnP methods perform regularization by plugging a pre-trained denoiser in a proximal algorithm, such as Proximal Gradient Descent (PGD). To ensure convergence of PnP schemes, many works study specific parametrizations of deep denoisers. However, existing results require either unverifiable or suboptimal hypotheses on the denoiser, or assume restrictive conditions on the parameters of the inverse problem. Observing that these limitations can be due to the proximal algorithm in use, we study a relaxed version of the PGD algorithm for minimizing the sum of a convex function and a weakly convex one. When plugged with a relaxed proximal denoiser, we show that the proposed PnP- $$\alpha $$ PGD algorithm converges for a wider range of regularization parameters, thus allowing more accurate image restoration.

Observations of the ocean waves directional spreading during the HIGHWAVE project and SUMOS campaign.

Abstract: The directional distribution of ocean waves is of great importance for a better understanding of air-sea interactions. Countless applications in science and engineering, such as, offshore energy production, microseisms prediction, wave climate modelling, coastal erosion, among many others, require precise information about the wave directionality. However, in spite of its importance, this quantity is poorly understood and difficult to accurately model. This study presents observations of the directional spreading parameters obtained from a set of low-cost GPS-based buoys during highly energetic conditions. One of the buoys was anchored off the west coast of Ireland during the HIGHWAVE project. These observations are compared with the measurements of 20 freely drifting buoys deployed in the Bay of Biscay during the SUMOS campaign. Spreading parameters were compared in the framework of widely used parameterisation for the directional distribution. The directional spreading is narrower at the spectral peak and broadens as the frequency moves away towards higher and lower scales. There is a particularly sharp increase in the spreading for f < fp. The results showed that buoy-based observations significantly differ from spatial-based measurements for frequencies around half the spectral peak. The measruements obtained by the drifting buoys show that for 2 < f/fp < 6, the spreading appears to be approximately constant with the frequency and tends to increase again for f > 6fp. The results showed that the directional spreading seems to be independent of the wave age, roughly across the entire range of frequencies. &#160;This may imply that the shape of the directional spectrum is primarily controlled by the non-linear wave-wave interactions rather by the wind forcing. &#160;In the vicinity of the spectral peak, a weakly linear relationship between the directional spreading and the significant wave height was observed. &#160;The results show that as the significant wave height increases by one meter, the spreading decreases by about 4.5&#176;. The preliminary results presented here contribute to the understanding of the directional distribution of ocean waves. However, further observations and comparisons are needed to fully capture the complexity of this phenomenon. Despite being preliminary, these results provide valuable insights and add to the ongoing discussion on this topic. This work was funded by the European Research Council (ERC) under the EU Horizon 2020 research and innovation programme (grant agreement no. 833125-HIGHWAVE). We are very grateful to the scientific team behind the SUMOS campaign for providing the drifting buoys data.

Deep learning approach for real-time tsunami impact forecasting in near field context – application to the French Mediterranean coastline

Abstract: Tsunami warning systems currently focus on the first parameters of the earthquake, based on a 24-hour monitoring of earthquakes, seismic data processing (Magnitude, location), and tsunami risk modelling at basin scale.The French Tsunami Warning Center (CENALT) runs actually two tsunami modelling tools where the water height at the coast is not calculated (i.e., Cassiopee based on a pre-computed database, and Calypso based on real time simulations at basin scale). A complete calculation up to the coastal impact all along the French Mediterranean or coastline is incompatible with real time near field or regional forecast, as nonlinear models require fine topo-bathymetric data nearshore and indeed a considerable computation time (> 45 min). Predicting coastal flooding in real time is then a major challenge in such context. To overcome these limitations, non conventional approches such as machine learning methods are being explored. Among the huge number of actual models, deep learning techniques are becoming increasingly popular. Severals studies have shown the interest of using MLPs (Multilayer perceptrons) and CNNs (Convolutional neural networks) to quickly transform a deep ocean simulation result into a coastal flooding model. Once trained on a specific output area with a large dataset, the networks are able to predict in seconds the tsunami inundation map from any earthquake scenario drawn from a seismic source database representative of the seismotectonic context of the region of interest.A first study training neural networks to predict the maximum water height maps was performed on three specific French cities (Nice, Antibes and Cannes) to evaluate the capacity of the models to reproduce the ground truth. The objective here is to extend the method to predict, in addition to maximum wave heights and runups, maximum retreats and currents along the entire French Mediterranean coastline. The spatial resolution of the finer bathymetric grids is set to 25 meters. To be representative of reality, the training dataset is fed with seismic scenarios derived from the CENALT fault database and taking into account a stochastic slip distribution. The method provides promising early results.