A constructive approach for computing the proximity operator of the p-th power of the ℓ1 norm

A Prater-Bennette, L Shen, EE Tripp - Applied and Computational Harmonic …, 2023‏ - Elsevier
This note is to study the proximity operator of hp=‖⋅‖ 1 p, the power function of the ℓ 1
norm. For general p, computing the proximity operator requires solving a system of …

A tailor-made 3-dimensional directional Haar semi-tight framelet for pMRI reconstruction

YR Li, L Shen, X Zhuang - Applied and Computational Harmonic Analysis, 2022‏ - Elsevier
In this paper, we propose a model for parallel magnetic resonance imaging (pMRI)
reconstruction, regularized by a carefully designed tight framelet system, that can lead to …

A pruning extreme learning machine with regularization for multi-dimensional output problems

Y Dai, Y Zhang, Q Wu - International Journal of Machine Learning and …, 2024‏ - Springer
As a fast algorithm for training single-hidden layer feedforward neural networks, extreme
learning machine (ELM) has been successfully applied to various classification and …

On Choosing Initial Values of Iteratively Reweighted Algorithms for the Piece-wise Exponential Penalty

R Lin, S Li, Y Liu - arxiv preprint arxiv:2310.17849, 2023‏ - arxiv.org
Computing the proximal operator of the sparsity-promoting piece-wise exponential (PiE)
penalty $1-e^{-| x|/\sigma} $ with a given shape parameter $\sigma> 0$, which is treated as …