Efficient linearized Bregman iteration for sparse adaptive filters and Kaczmarz solvers

2016 ◽  
Author(s):  
Michael Lunglmayr ◽  
Mario Huemer
Keyword(s):  
Adaptive Filters ◽  
Bregman Iteration ◽  
Linearized Bregman Iteration

A chaotic iterative algorithm based on linearized Bregman iteration for image deblurring

2014 ◽  
Vol 272 ◽  
pp. 198-208 ◽  
Author(s):  
Tiantian Qiao ◽  
Weiguo Li ◽  
Boying Wu ◽  
Jichao Wang
Keyword(s):  
Iterative Algorithm ◽  
Image Deblurring ◽  
Bregman Iteration ◽  
Linearized Bregman Iteration

Two-dimensional multiradar ISAR fusion imaging based on fast linearized Bregman iteration algorithm

2021 ◽  
Vol 15 (02) ◽  
Author(s):  
Xiaoxiu Zhu ◽  
Limin Liu ◽  
Baofeng Guo ◽  
Wenhua Hu ◽  
Lin Shi ◽  
...  
Keyword(s):  
Fusion Imaging ◽  
Iteration Algorithm ◽  
Two Dimensional ◽  
Bregman Iteration ◽  
Linearized Bregman Iteration

scholarly journals Convergence of the linearized Bregman iteration for $\ell _1$-norm minimization

2009 ◽  
Vol 78 (268) ◽  
pp. 2127-2136 ◽  
Author(s):  
Jian-Feng Cai ◽  
Stanley Osher ◽  
Zuowei Shen
Keyword(s):  
Bregman Iteration ◽  
Norm Minimization ◽  
Linearized Bregman Iteration

scholarly journals FPGA-embedded Linearized Bregman Iteration algorithm for trend break detection

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Felipe Calliari ◽  
Gustavo Castro do Amaral ◽  
Michael Lunglmayr
Keyword(s):  
Low Complexity ◽  
Gain Factor ◽  
Iteration Algorithm ◽  
Computationally Efficient ◽  
Bregman Iteration ◽  
Sparse Estimation ◽  
Research Fields ◽  
Field Programmable ◽  
Level Shifts ◽  
Linearized Bregman Iteration

Abstract Detection of level shifts in a noisy signal, or trend break detection, is a problem that appears in several research fields, from biophysics to optics and economics. Although many algorithms have been developed to deal with such a problem, accurate and low-complexity trend break detection is still an active topic of research. The Linearized Bregman Iterations have been recently presented as a low-complexity and computationally efficient algorithm to tackle this problem, with a formidable structure that could benefit immensely from hardware implementation. In this work, a hardware architecture of the Linearized Bregman Iteration algorithm is presented and tested on a Field Programmable Gate Array (FPGA). The hardware is synthesized in different-sized FPGAs, and the percentage of used hardware, as well as the maximum frequency enabled by the design, indicate that an approximately 100 gain factor in processing time, concerning the software implementation, can be achieved. This represents a tremendous advantage in using a dedicated unit for trend break detection applications. The proposed architecture is compared with a state-of-the-art hardware structure for sparse estimation, and the results indicate that its performance concerning trend break detection is much more pronounced while, at the same time, being the indicated solution for long datasets.

scholarly journals An Extended Reweighted ℓ1 Minimization Algorithm for Image Restoration

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3224
Author(s):  
Sining Huang ◽  
Yupeng Chen ◽  
Tiantian Qiao
Keyword(s):  
Generalized Inverse ◽  
Signal To Noise Ratio ◽  
Basis Pursuit ◽  
Minimization Algorithm ◽  
Bregman Iteration ◽  
Pursuit Problem ◽  
L1 Minimization ◽  
ℓ1 Minimization ◽  
Linearized Bregman Iteration ◽  
Better Than

This paper proposes an effective extended reweighted ℓ1 minimization algorithm (ERMA) to solve the basis pursuit problem minu∈Rnu1:Au=f in compressed sensing, where A∈Rm×n, m≪n. The fast algorithm is based on linearized Bregman iteration with soft thresholding operator and generalized inverse iteration. At the same time, it also combines the iterative reweighted strategy that is used to solve minu∈Rnupp:Au=f problem, with the weight ωiu,p=ε+ui2p/2−1. Numerical experiments show that this l1 minimization persistently performs better than other methods. Especially when p=0, the restored signal by the algorithm has the highest signal to noise ratio. Additionally, this approach has no effect on workload or calculation time when matrix A is ill-conditioned.

scholarly journals Application of Generalized Split Linearized Bregman Iteration algorithm for Alzheimer's disease prediction

Aging ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 6206-6224 ◽  
Author(s):  
Weimin Zheng ◽  
Bin Cui ◽  
Zeyu Sun ◽  
Xiuli Li ◽  
Xu Han ◽  
...  
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Iteration Algorithm ◽  
Disease Prediction ◽  
Bregman Iteration ◽  
Linearized Bregman Iteration
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