Category: Paper

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Paper

New preprint

“Joint structure-texture low dimensional modeling for image decomposition with a plug and play framework” (Guennec, Aujol, YT) https://hal.science/hal-04648963v1 We describe how structure-texture decomposition is directly linked to the (difficult) design of a regularizer for a complex combination of low dimensional models. Thanks to the PnP approach and DNN, we are able to explicitly design such regularizer in practice with promising results on natural images and inpainting problems.

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Paper Students

Papers accepted !

My two Phd students will present their latest work at

@eusipco2024 in Lyon (congrats!):

P.-J. Bénard : Projected Block Coordinate Descent for sparse spike estimation https://hal.science/hal-04462779v1 (accelerating off-the-grid estimation by leveraging the structure of the problem)

Antoine Guennec : Adaptive parameter selection for gradient-sparse plus low patch-rank recovery: application to image decomposition https://hal.science/hal-04207313v1 (the first application of our work on optimal convex regularization)

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Non classé Paper

New preprint

We uploaded the last work of Hui Shi during her PhD thesis:

Batch-less stochastic gradient descent for compressive learning of deep regularization for image denoising, H. Shi, Y. Traonmilin and J.-F. Aujol, 2023.

Abstract: “We consider the problem of denoising with the help of prior information taken from a database of clean signals or images. Denoising with variational methods is very efficient if a regularizer well adapted to the nature of the data is available. Thanks to the maximum a posteriori Bayesian framework, such regularizer can be systematically linked with the distribution of the data. With deep neural networks (DNN), complex distributions can be recovered from a large training database. To reduce the computational burden of this task, we adapt the compressive learning framework to the learning of regularizers parametrized by DNN. We propose two variants of stochastic gradient descent (SGD) for the recovery of deep regularization parameters from a heavily compressed database. These algorithms outperform the initially proposed method that was limited to low-dimensional signals, each iteration using information from the whole database. They also benefit from classical SGD convergence guarantees. Thanks to these improvements we show that this method can be applied for patch based image denoising.”

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Paper

New preprint

Adaptive Parameter Selection For Gradient-sparse + Low Patch-rank Recovery: Application To Image Decomposition. A. Guennec, J.-F. Aujol, Y. Traonmilin. 2023.

Abstract: “In this work, we are interested in gradient sparse + low patchrank signal recovery for image structure-texture decomposition. We locally model the structure as gradient-sparse and the texture as of low patch-rank. Moreover, we propose a rule based upon theoretical results of sparse + low-rank matrix recovery in order to automatically tune our model depending on the local content and we numerically validate this proposition.”

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Paper Talk

SampTA Paper

Our paper “Disentangled latent representations of images with atomic autoencoders” will be presented at the SampTA conference by A. Newson.

Abstract: “We present the atomic autoencoder architecture, which decomposes an image as the sum of elementary parts that are parametrized by simple separate blocks of latent codes. We show that this simple architecture is induced by the definition of a general atomic low-dimensional model of the considered data. We also highlight the fact that the atomic autoencoder achieves disentangled low-dimensional representations under minimal hypotheses. Experiments show that their implementation with deep neural networks is successful at learning disentangled representations on two different examples: images constructed with simple parametric curves and images of filtered off-the-grid spikes.”

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Paper

New preprint

We uploaded the following preprint on the geometry of non-convex sparse spike estimation:

On strong basins of attractions for non-convex sparse spike estimation: upper and lower bounds, Y. Traonmilin, J.F. Aujol, A. Leclaire and P.J. Bénard. (EFFIREG)

“Abstract: In this article, we study the size of strong basins of attractions for the non-convex sparse spike estimation problem. We first extend previous results to obtain a lower bound on the size of sets where gradient descent converges with a linear rate to the minimum of the non-convex objective functional. We then give an upper bound that shows that the dependency of the lower bound with respect to the number of measurements reflects well the true size of basins of attraction for random Gaussian Fourier measurements. These theoretical results are confirmed by experiments.”

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Paper

New preprint

A preprint of the work on off-the-grid super resolution of our student P.J. Bénard is available.

Fast off-the-grid sparse recovery with over-parametrized projected gradient descent, P.J. Bénard, Y. Traonmilin and J.F. Aujol

Abstract: “We consider the problem of recovering off-the-grid spikes from Fourier measurements. Successful methods such as sliding Frank-Wolfe and continuous orthogonal matching pursuit (OMP) iteratively add spikes to the solution then perform a costly (when the number of spikes is large) descent on all parameters at each iteration. In 2D, it was shown that performing a projected gradient descent (PGD) from a gridded over-parametrized initialization was faster than continuous orthogonal matching pursuit. In this paper, we propose an off-the-grid over-parametrized initialization of the PGD based on OMP that permits to fully avoid grids and gives faster results in 3D.”

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Paper

New preprint

Our student Axel Baldanza uploaded a new preprint: “Piecewise linear prediction model for action tracking in sports“.

Abstract: “Recent tracking methods in professional team sports
reach very high accuracy by tracking the ball and players.
However, it remains difficult for these methods to perform
accurate real-time tracking in amateur acquisition conditions
where the vertical position or orientation of the camera is not
controlled and cameras use heterogeneous sensors. This article
presents a method for tracking interesting content in an amateur
sport game by analyzing player displacements. Defining optical
flow of the foreground in the image as the player motions,
we propose a piecewise linear supervised learning model for
predicting the camera global motion needed to follow the action.”

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Paper

New preprint

We uploaded our new preprint:

"A theory of optimal convex regularization for low-dimensional recovery", Y. Traonmilin, R. Gribonval and S. Vaiter

Abstract : We consider the problem of recovering elements of a low-dimensional model from under-determined linear measurements. To perform recovery, we consider the minimization of a convex regularizer subject to a data fit constraint. Given a model, we ask ourselves what is the “best” convex regularizer to perform its recovery. To answer this question, we define an optimal regularizer as a function that maximizes a compliance measure with respect to the model. We introduce and study several notions of compliance. We give analytical expressions for compliance measures based on the best-known recovery guarantees with the restricted isometry property. These expressions permit to show the optimality of the ℓ 1-norm for sparse recovery and of the nuclear norm for low-rank matrix recovery for these compliance measures. We also investigate the construction of an optimal convex regularizer using the example of sparsity in levels.

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Paper

New preprint

The final version of our work on sketched image denoising is available as a preprint: “Compressive learning for patch-based image denoising” , Hui Shi, Yann Traonmilin and Jean-François Aujol.