Related papers: FAASTA: A fast solver for total-variation regulari…
The ``fast iterative shrinkage-thresholding algorithm'', a.k.a. FISTA, is one of the most widely used algorithms in the literature. However, despite its optimal theoretical $O(1/k^2)$ convergence rate guarantee, oftentimes in practice its…
The L1-regularized maximum likelihood estimation problem has recently become a topic of great interest within the machine learning, statistics, and optimization communities as a method for producing sparse inverse covariance estimators. In…
We propose several deep-learning accelerated optimization solvers with convergence guarantees. We use ideas from the analysis of accelerated forward-backward schemes like FISTA, but instead of the classical approach of proving convergence…
In [19], a general, inexact, efficient proximal quasi-Newton algorithm for composite optimization problems has been proposed and a sublinear global convergence rate has been established. In this paper, we analyze the convergence properties…
Despite the rise to fame of incremental variance-reduced methods in recent years, their use in nonsmooth optimization is still limited to few simple cases. This is due to the fact that existing methods require to evaluate the proximity…
Although recent years have witnessed significant advancements in medical image segmentation, the pervasive issue of domain shift among medical images from diverse centres hinders the effective deployment of pre-trained models. Many…
Compressed sensing has shown great potentials in accelerating magnetic resonance imaging. Fast image reconstruction and high image quality are two main issues faced by this new technology. It has been shown that, redundant image…
Forward-only learning algorithms have recently gained attention as alternatives to gradient backpropagation, replacing the backward step of this latter solver with an additional contrastive forward pass. Among these approaches, the…
We propose a first order algorithm, a modified version of FISTA, to solve an optimization problem with an objective function that is a sum of a possibly nonconvex function, with Lipschitz continuous gradient, and a convex function which can…
The boom of non-uniform sampling and compressed sensing techniques dramatically alleviates the lengthy data acquisition problem of magnetic resonance imaging. Sparse reconstruction, thanks to its fast computation and promising performance,…
The adaptive Iterative Soft-Thresholding Algorithm (ISTA) has been a popular algorithm for finding a desirable solution to the LASSO problem without explicitly tuning the regularization parameter $\lambda$. Despite that the adaptive ISTA is…
Focus of this work is solving a non-smooth constraint minimization problem by a primal-dual splitting algorithm involving proximity operators. The problem is penalized by the Bregman divergence associated with the non-smooth total variation…
In this paper, we propose a novel sparse signal recovery algorithm called Trainable ISTA (TISTA). The proposed algorithm consists of two estimation units such as a linear estimation unit and a minimum mean squared error (MMSE)…
Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…
The accelerated composite optimization method FISTA (Beck, Teboulle 2009) is suboptimal by a constant factor, and we present a new method OptISTA that improves FISTA by a constant factor of 2. The performance estimation problem (PEP) has…
Imaging inverse problems are commonly addressed by minimizing measurement consistency and signal prior terms. While huge attention has been paid to developing high-performance priors, even the most advanced signal prior may lose its…
The most popular first-order accelerated black-box methods for solving large-scale convex optimization problems are the Fast Gradient Method (FGM) and the Fast Iterative Shrinkage Thresholding Algorithm (FISTA). FGM requires that the…
This paper proposes a new backtracking strategy based on the FISTA accelerated algorithm for multiobjective optimization problems. The strategy focuses on solving the problem of Lipschitz constant being unknown. It allows estimate parameter…
Non-Local Total Variation (NLTV) has emerged as a useful tool in variational methods for image recovery problems. In this paper, we extend the NLTV-based regularization to multicomponent images by taking advantage of the Structure Tensor…
Analyzing the worst-case performance of deep neural networks against input perturbations amounts to solving a large-scale non-convex optimization problem, for which several past works have proposed convex relaxations as a promising…