@inproceedings{f666d2c6bae344fcb27a5a6693ba0d96,
title = "Convergence of an inertial proximal method for l1-regularized least-squares",
abstract = "A fast, low-complexity, algorithm for solving the ℓ1-regularized least-squares problem is devised and analyzed. Our algorithm, which we call the Inertial Iterative Soft-Thresholding Algorithm (I-ISTA), incorporates inertia into a forward-backward proximal splitting framework. We show that the iterates of I-ISTA converge linearly to a minimum with a better rate of convergence than the well-known Iterative Shrinkage/Soft-Thresholding Algorithm (ISTA) for solving ℓ1-regularized least-squares. The improvement in convergence rate over ISTA is significant on ill-conditioned problems and is gained with minor additional computations. We conduct numerical experiments which show that I-ISTA converges more quickly than ISTA and two other computationally comparable algorithms on compressed sensing and deconvolution problems.",
keywords = "Inertial forward-backward proximal splitting, compressed sensing, deconvolution, gradient descent with momentum, heavy ball method",
author = "Johnstone, {Patrick R.} and Pierre Moulin",
year = "2015",
month = aug,
day = "4",
doi = "10.1109/ICASSP.2015.7178635",
language = "English (US)",
series = "ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "3566--3570",
booktitle = "2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings",
address = "United States",
note = "40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 ; Conference date: 19-04-2014 Through 24-04-2014",
}