366 citations · 967 across the 53 of their papers we have counts for
25 papers · 1 filter
Physics Matters in PnP: Recovery Guarantees with the MMSE and NN Denoisers
Tobias Wolf, Jalal Fadili, Jin Guo +1
We investigate the forward-backward-splitting version of the Plug and Play (PnP) method for linear ill-posed problems with MMSE estimators as denoisers. In contrast to existing lit…
Low Complexity Regularized Phase Retrieval
Jean-Jacques Godeme, Jalal Fadili
In this paper, we study the phase retrieval problem in the situation where the vector to be recovered has an a priori structure that can encoded into a regularization term. This re…
Stable Phase Retrieval with Mirror Descent
Jean-Jacques Godeme, Jalal Fadili, Claude Amra +1
In this paper, we aim to reconstruct an n-dimensional real vector from m phaseless measurements corrupted by an additive noise. We extend the noiseless framework developed in [15],…
A Quasi-Newton Primal-Dual Algorithm with Line Search
Shida Wang, Jalal Fadili, Peter Ochs
Quasi-Newton methods refer to a class of algorithms at the interface between first and second order methods. They aim to progress as substantially as second order methods per itera…
Geometric characterizations for strong minima with applications to nuclear norm minimization problems
Jalal Fadili, Tran T. A. Nghia, Duy Nhat Phan
In this paper, we introduce several geometric characterizations for strong minima of optimization problems. Applying these results to nuclear norm minimization problems allows us t…
Continuous Newton-like Methods featuring Inertia and Variable Mass
Camille Castera, Hedy Attouch, Jalal Fadili +1
We introduce a new dynamical system, at the interface between second-order dynamics with inertia and Newton's method. This system extends the class of inertial Newton-like dynamics…
Provable Phase Retrieval with Mirror Descent
Jean-Jacques Godeme, Jalal Fadili, Xavier Buet +3
In this paper, we consider the problem of phase retrieval, which consists of recovering an -dimensional real vector from the magnitude of its linear measurements. We propose…
From the Ravine method to the Nesterov method and vice versa: a dynamical system perspective
H. Attouch, J. Fadili
We revisit the Ravine method of Gelfand and Tsetlin from a dynamical system perspective, study its convergence properties, and highlight its similarities and differences with the N…
Global Convergence of Model Function Based Bregman Proximal Minimization Algorithms
Mahesh Chandra Mukkamala, Jalal Fadili, Peter Ochs
Lipschitz continuity of the gradient mapping of a continuously differentiable function plays a crucial role in designing various optimization algorithms. However, many functions ar…
First-order optimization algorithms via inertial systems with Hessian driven damping
Hedy Attouch, Zaki Chbani, Jalal Fadili +1
In a Hilbert space setting, for convex optimization, we analyze the convergence rate of a class of first-order algorithms involving inertial features. They can be interpreted as di…
Null controllability of degenerate parabolic equations with a time-varying delay
E. L. Mustapha Ait Benhassi, Mohamed Fadili, Lahcen Maniar
This paper is devoted to the null controllability of a one-dimensional linear parabolic equation with a time-varying state delay and a diffusion coefficient that degenerates at one…
Generalized Conditional Gradient with Augmented Lagrangian for Composite Minimization
Antonio Silveti-Falls, Cesare Molinari, Jalal Fadili
In this paper we propose a splitting scheme which hybridizes generalized conditional gradient with a proximal step which we call CGALP algorithm, for minimizing the sum of three pr…
Controllability of a system of degenerate parabolic equations with non-diagonalizable diffusion matrix
E. M. Ait Ben Hassi, M. Fadili, L. Maniar
In this paper we study the null controllability of some non diagonalizable degenerate parabolic systems of PDEs, we assume that the diffusion, coupling and controls matrices are co…
Model Consistency for Learning with Mirror-Stratifiable Regularizers
Jalal Fadili, Guillaume Garrigos, Jérome Malick +1
Low-complexity non-smooth convex regularizers are routinely used to impose some structure (such as sparsity or low-rank) on the coefficients for linear predictors in supervised lea…
Sensitivity Analysis for Mirror-Stratifiable Convex Functions
Jalal Fadili, Jérôme Malick, Gabriel Peyré
This paper provides a set of sensitivity analysis and activity identification results for a class of convex functions with a strong geometric structure, that we coined "mirror-stra…
On Algebraic condition for null controllability of some coupled degenerate systems
E. M. Ait Benhassi, M. Fadili, L. Maniar
In this paper we will generalize the Kalman rank condition for the null controllability to -coupled linear degenerate parabolic systems with constant coefficients, diagonalizabl…
A Multi-step Inertial Forward--Backward Splitting Method for Non-convex Optimization
Jingwei Liang, Jalal Fadili, Gabriel Peyré
In this paper, we propose a multi-step inertial Forward--Backward splitting algorithm for minimizing the sum of two non-necessarily convex functions, one of which is proper lower s…
Activity Identification and Local Linear Convergence of Douglas--Rachford/ADMM under Partial Smoothness
Jingwei Liang, Jalal Fadili, Gabriel Peyré +1
Convex optimization has become ubiquitous in most quantitative disciplines of science, including variational image processing. Proximal splitting algorithms are becoming popular to…
Local Linear Convergence of Forward-Backward under Partial Smoothness
Jingwei Liang, Jalal Fadili, Gabriel Peyré
In this paper, we consider the Forward--Backward proximal splitting algorithm to minimize the sum of two proper convex functions, one of which having a Lipschitz continuous gradien…
Low Complexity Regularization of Linear Inverse Problems
Samuel Vaiter, Gabriel Peyré, Jalal M. Fadili
Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possi…
A quasi-Newton proximal splitting method
Stephen Becker, M. Jalal Fadili
A new result in convex analysis on the calculation of proximity operators in certain scaled norms is derived. We describe efficient implementations of the proximity calculation for…
Risk estimation for matrix recovery with spectral regularization
Charles-Alban Deledalle, Samuel Vaiter, Gabriel Peyré +2
In this paper, we develop an approach to recursively estimate the quadratic risk for matrix recovery problems regularized with spectral functions. Toward this end, in the spirit of…
Generalized Forward-Backward Splitting
Hugo Raguet, Jalal Fadili, Gabriel Peyré
This paper introduces the generalized forward-backward splitting algorithm for minimizing convex functions of the form , where has a Lipschitz-continuous…
Multiplicative Noise Removal Using L1 Fidelity on Frame Coefficients
Sylvain Durand, Jalal Fadili, Mila Nikolova
We address the denoising of images contaminated with multiplicative noise, e.g. speckle noise. Classical ways to solve such problems are filtering, statistical (Bayesian) methods,…