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Iterative shrinkage/thresholding algorithm (ISTA) is a well-studied method for finding sparse solutions to ill-posed inverse problems. In this letter, we present a data-driven scheme for learning optimal thresholding functions for ISTA. The…

Machine Learning · Computer Science 2016-05-04 Ulugbek S. Kamilov , Hassan Mansour

In this paper, we propose a novel algorithm for analysis-based sparsity reconstruction. It can solve the generalized problem by structured sparsity regularization with an orthogonal basis and total variation regularization. The proposed…

Computer Vision and Pattern Recognition · Computer Science 2015-04-29 Chen Chen , Junzhou Huang , Lei He , Hongsheng Li

We study $\ell^1$ regularized least squares optimization problem in a separable Hilbert space. We show that the iterative soft-thresholding algorithm (ISTA) converges linearly, without making any assumption on the linear operator into play…

Optimization and Control · Mathematics 2017-12-04 Guillaume Garrigos , Lorenzo Rosasco , Silvia Villa

The linear inverse problem emerges from various real-world applications such as Image deblurring, inpainting, etc., which are still thrust research areas for image quality improvement. In this paper, we have introduced a new algorithm…

Signal Processing · Electrical Eng. & Systems 2022-11-29 Avinash Kumar , Sujit Kumar Sahoo

In high dimensional settings, sparse structures are crucial for efficiency, both in term of memory, computation and performance. It is customary to consider $\ell_1$ penalty to enforce sparsity in such scenarios. Sparsity enforcing methods,…

Machine Learning · Statistics 2017-11-22 Eugene Ndiaye , Olivier Fercoq , Alexandre Gramfort , Vincent Leclère , Joseph Salmon

Soft threshold pruning is among the cutting-edge pruning methods with state-of-the-art performance. However, previous methods either perform aimless searching on the threshold scheduler or simply set the threshold trainable, lacking…

Machine Learning · Computer Science 2023-02-28 Yanqi Chen , Zhengyu Ma , Wei Fang , Xiawu Zheng , Zhaofei Yu , Yonghong Tian

The need for fast sparse optimization is emerging, e.g., to deal with large-dimensional data-driven problems and to track time-varying systems. In the framework of linear sparse optimization, the iterative shrinkage-thresholding algorithm…

Optimization and Control · Mathematics 2025-01-22 Vito Cerone , Sophie M. Fosson , Diego Regruto

The iterative weighted shrinkage-thresholding algorithm (IWSTA) has shown superiority to the classic unweighted iterative shrinkage-thresholding algorithm (ISTA) for solving linear inverse problems, which address the attributes differently.…

Computer Vision and Pattern Recognition · Computer Science 2021-12-23 Bingxue Wu , Jiao Wei , Chen Li , Yudong Yao , Yueyang Teng

Square-root (loss) regularized models have recently become popular in linear regression due to their nice statistical properties. Moreover, some of these models can be interpreted as the distributionally robust optimization counterparts of…

Optimization and Control · Mathematics 2023-10-06 Hong T. M. Chu , Kim-Chuan Toh , Yangjing Zhang

Regularization of ill-posed linear inverse problems via $\ell_1$ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an $\ell_1$ penalized functional is via an…

Numerical Analysis · Mathematics 2013-01-01 I. Daubechies , M. Fornasier , I. Loris

Many machine learning techniques sacrifice convenient computational structures to gain estimation robustness and modeling flexibility. However, by exploring the modeling structures, we find these "sacrifices" do not always require more…

Machine Learning · Computer Science 2019-04-16 Xingguo Li , Haoming Jiang , Jarvis Haupt , Raman Arora , Han Liu , Mingyi Hong , Tuo Zhao

Solving inverse problems with iterative algorithms is popular, especially for large data. Due to time constraints, the number of possible iterations is usually limited, potentially affecting the achievable accuracy. Given an error one is…

Numerical Analysis · Computer Science 2018-02-16 Raja Giryes , Yonina C. Eldar , Alex M. Bronstein , Guillermo Sapiro

Iteratively Re-weighted Least Squares (IRLS) is a method for solving minimization problems involving non-quadratic cost functions, perhaps non-convex and non-smooth, which however can be described as the infimum over a family of quadratic…

Numerical Analysis · Mathematics 2016-02-24 Massimo Fornasier , Steffen Peter , Holger Rauhut , Stephan Worm

Sparsity-constrained optimization underlies many problems in signal processing, statistics, and machine learning. State-of-the-art hard-thresholding (HT) algorithms rely on an appropriately selected continuous step-size parameter to ensure…

Machine Learning · Statistics 2026-05-13 Jin Zhu , Junxian Zhu , Zezhi Wang , Borui Tang , Hongmei Lin , Xueqin Wang

In this note, we consider a special instance of the scaled, inexact and adaptive generalised Fast Iterative Soft-Thresholding Algorithm (SAGE-FISTA) recently proposed in (Rebegoldi, Calatroni, '21) for the efficient solution of strongly…

Optimization and Control · Mathematics 2021-04-02 Luca Calatroni , Simone Rebegoldi

Iteratively reweighted least square (IRLS) is a popular approach to solve sparsity-enforcing regression problems in machine learning. State of the art approaches are more efficient but typically rely on specific coordinate pruning schemes.…

Machine Learning · Statistics 2022-10-03 Clarice Poon , Gabriel Peyré

In this paper, we address the problem of distributed sparse recovery of signals acquired via compressed measurements in a sensor network. We propose a new class of distributed algorithms to solve Lasso regression problems, when the…

Information Theory · Computer Science 2013-10-15 Chiara Ravazzi , Sophie M. Fosson , Enrico Magli

We consider linear inverse problems where the solution is assumed to have a sparse expansion on an arbitrary pre-assigned orthonormal basis. We prove that replacing the usual quadratic regularizing penalties by weighted l^p-penalties on the…

Functional Analysis · Mathematics 2025-10-20 Ingrid Daubechies , Michel Defrise , Christine De Mol

In this paper, we consider an LQR design problem for distributed control systems. For large-scale distributed systems, finding a solution might be computationally demanding due to communications among agents. To this aim, we deal with LQR…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-09-02 Myung Cho

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…

Optimization and Control · Mathematics 2018-07-12 Jingwei Liang , Carola-Bibiane Schönlieb