Generalized Total Variation Denoising Via Augmented Lagrangian Cycle Spinning With Haar Wavelets

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SLITRONOMY: Towards a fully wavelet-based strong lensing inversion technique

Frédéric Courbin, Aymeric Alexandre Galan, Rémy Elie Joseph, Austin Chandler Peel

Strong gravitational lensing provides a wealth of astrophysical information on the baryonic and dark matter content of galaxies. It also serves as a valuable cosmological probe by allowing us to measure the Hubble constant independently of other methods. T ...

EDP SCIENCES S A2021

Learning-based Image Coding: Early Solutions Reviewing and Subjective Quality Evaluation

Touradj Ebrahimi, Pinar Akyazi

Nowadays, image and video are the data types that consume most of the resources of modern communication channels, both in fixed and wireless networks. Thus, it is vital to compress visual data as much as possible, while maintaining some target quality leve ...

SPIE-INT SOC OPTICAL ENGINEERING2021

Superluminal Motion-Assisted Four-Dimensional Light-in-Flight Imaging

Edoardo Charbon, Kazuhiro Morimoto, Andrei Ardelean, Ming-Lo Wu

Advances in high-speed imaging techniques have opened new possibilities for capturing ultrafast phenomena such as light propagation in air or through media. Capturing light in flight in three-dimensional xyt space has been reported based on various types o ...

American Physical Society2021

Last iterate convergence of SGD for Least-Squares in the Interpolation regime

Aditya Vardhan Varre, Nicolas Henri Bernard Flammarion, Loucas Pillaud-Vivien

Motivated by the recent successes of neural networks that have the ability to fit the data perfectly \emph{and} generalize well, we study the noiseless model in the fundamental least-squares setup. We assume that an optimum predictor fits perfectly inputs ...

Advances in Neural Information Processing Systems 20212021

Eigendecomposition-Free Training of Deep Networks for Linear Least-Square Problems

Pascal Fua, Mathieu Salzmann, Fei Wang, Kwang Moo Yi, Zheng Dang, Yinlin Hu

Many classical Computer Vision problems, such as essential matrix computation and pose estimation from 3D to 2D correspondences, can be tackled by solving a linear least-square problem, which can be done by finding the eigenvector corresponding to the smal ...

IEEE COMPUTER SOC2021

Convex optimization in sums of Banach spaces

Michaël Unser, Shayan Aziznejad

We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a finite sum of compo ...

2021

Wavelet analysis of the Besov regularity of Levy white noise

Julien René Pierre Fageot, Shayan Aziznejad

We characterize the local smoothness and the asymptotic growth rate of the Levy white noise. We do so by characterizing the weighted Besov spaces in which it is located. We extend known results in two ways. First, we obtain new bounds for the local smoothn ...

2020

Wavelet-Fourier CORSING techniques for multidimensional advection-diffusion-reaction equations

Fabio Nobile, Simone Brugiapaglia

We present and analyze a novel wavelet-Fourier technique for the numerical treatment of multidimensional advection–diffusion–reaction equations based on the COmpRessed SolvING (CORSING) paradigm. Combining the Petrov–Galerkin technique with the compressed ...

2021

Systematic analysis of wavelet denoising methods for neural signal processing

Silvestro Micera

Objective. Among the different approaches for denoising neural signals, wavelet-based methods are widely used due to their ability to reduce in-band noise. All wavelet denoising algorithms have a common structure, but their effectiveness strongly depends o ...

IOP PUBLISHING LTD2020

On the 2D Post-Processing of Brillouin Optical Time-Domain Analysis

Luc Thévenaz, Simon Adrien Zaslawski, Zhisheng Yang

The benefits and limitations inherent to the 2D post-processing of measurements from Brillouin optical time-domain analyzers are investigated from a fundamental point of view. In a preliminary step, the impact of curve fitting on the precision of the estim ...

IEEE Institute of Electrical and Electronics Engineers2020

The n-term Approximation of Periodic Generalized Levy Processes

Michaël Unser, John Paul Ward, Julien René Pierre Fageot

In this paper, we study the compressibility of random processes and fields, called generalized Levy processes, that are solutions of stochastic differential equations driven by d-dimensional periodic Levy white noises. Our results are based on the estimati ...

2020

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