scholarly journals A Modified Split Bregman Algorithm for Computing Microstructures Through Young Measures

2021 ◽  
Vol 19 (2) ◽  
pp. 886-920
Author(s):  
Gabriela Jaramillo ◽  
Shankar C. Venkataramani
Keyword(s):  
Young Measures ◽  
Split Bregman ◽  
Split Bregman Algorithm

Multiple Aerosol Unmixing by the Split Bregman Algorithm

2011 ◽  
Author(s):  
Russell Warren ◽  
Stanley Osher ◽  
Richard Vanderbeek
Keyword(s):  
Split Bregman ◽  
Split Bregman Algorithm

scholarly journals Fast Split Bregman Based Deconvolution Algorithm for Airborne Radar Imaging

2020 ◽  
Vol 12 (11) ◽  
pp. 1747 ◽  
Author(s):  
Yin Zhang ◽  
Qiping Zhang ◽  
Yongchao Zhang ◽  
Jifang Pei ◽  
Yulin Huang ◽  
...  
Keyword(s):  
Real Time ◽  
Computing Time ◽  
Real Data ◽  
Radar Imaging ◽  
Matrix Inversion ◽  
Airborne Radar ◽  
Split Bregman ◽  
Regularization Problem ◽  
Azimuth Resolution ◽  
Split Bregman Algorithm

Deconvolution methods can be used to improve the azimuth resolution in airborne radar imaging. Due to the sparsity of targets in airborne radar imaging, an L 1 regularization problem usually needs to be solved. Recently, the Split Bregman algorithm (SBA) has been widely used to solve L 1 regularization problems. However, due to the high computational complexity of matrix inversion, the efficiency of the traditional SBA is low, which seriously restricts its real-time performance in airborne radar imaging. To overcome this disadvantage, a fast split Bregman algorithm (FSBA) is proposed in this paper to achieve real-time imaging with an airborne radar. Firstly, under the regularization framework, the problem of azimuth resolution improvement can be converted into an L 1 regularization problem. Then, the L 1 regularization problem can be solved with the proposed FSBA. By utilizing the low displacement rank features of Toeplitz matrix, the proposed FSBA is able to realize fast matrix inversion by using a Gohberg–Semencul (GS) representation. Through simulated and real data processing experiments, we prove that the proposed FSBA significantly improves the resolution, compared with the Wiener filtering (WF), truncated singular value decomposition (TSVD), Tikhonov regularization (REGU), Richardson–Lucy (RL), iterative adaptive approach (IAA) algorithms. The computational advantage of FSBA increases with the increase of echo dimension. Its computational efficiency is 51 times and 77 times of the traditional SBA, respectively, for echoes with dimensions of 218 × 400 and 400 × 400 , optimizing both the image quality and computing time. In addition, for a specific hardware platform, the proposed FSBA can process echo of greater dimensions than traditional SBA. Furthermore, the proposed FSBA causes little performance degradation, when compared with the traditional SBA.

scholarly journals Using the Split Bregman Algorithm to Solve the Self-repelling Snakes Model

2022 ◽  
Author(s):  
Huizhu Pan ◽  
Jintao Song ◽  
Wanquan Liu ◽  
Ling Li ◽  
Guanglu Zhou ◽  
...  
Keyword(s):  
Evolution Equations ◽  
Active Contour Model ◽  
Operator Splitting ◽  
The Self ◽  
Convergence Time ◽  
Variational Model ◽  
Split Bregman ◽  
Geodesic Active Contour ◽  
Non Local ◽  
Split Bregman Algorithm

AbstractPreserving contour topology during image segmentation is useful in many practical scenarios. By keeping the contours isomorphic, it is possible to prevent over-segmentation and under-segmentation, as well as to adhere to given topologies. The Self-repelling Snakes model (SR) is a variational model that preserves contour topology by combining a non-local repulsion term with the geodesic active contour model. The SR is traditionally solved using the additive operator splitting (AOS) scheme. In our paper, we propose an alternative solution to the SR using the Split Bregman method. Our algorithm breaks the problem down into simpler sub-problems to use lower-order evolution equations and a simple projection scheme rather than re-initialization. The sub-problems can be solved via fast Fourier transform or an approximate soft thresholding formula which maintains stability, shortening the convergence time, and reduces the memory requirement. The Split Bregman and AOS algorithms are compared theoretically and experimentally.

A Hybrid TV-L1 Model for Noise Removal and Its Split Bregman Algorithm

2013 ◽  
Vol 7 (5) ◽  
pp. 314-322
Author(s):  
Shixiu Zheng ◽  
Zhenkuan Pan ◽  
Jinming Duan ◽  
Guodong Wang
Keyword(s):  
Noise Removal ◽  
Split Bregman ◽  
Split Bregman Algorithm

Anisotropic Total Variation Guided Filtering and Its Split Bregman Algorithm

2017 ◽  
Vol 54 (5) ◽  
pp. 051005
Author(s):  
芦碧波 Lu Bibo ◽  
王乐蓉 Wang Lerong ◽  
王永茂 Wang Yongmao ◽  
郑艳梅 Zheng Yanmei
Keyword(s):  
Total Variation ◽  
Split Bregman ◽  
Guided Filtering ◽  
Split Bregman Algorithm ◽  
Anisotropic Total Variation

scholarly journals A Shearlets-Based Method for Rain Removal from Single Images

2019 ◽  
Vol 9 (23) ◽  
pp. 5137 ◽  
Author(s):  
Guomin Sun ◽  
Jinsong Leng ◽  
Carlo Cattani
Keyword(s):  
Optimal Solution ◽  
Single Image ◽  
Split Bregman ◽  
Global Optimal Solution ◽  
Rain Removal ◽  
Rain Drops ◽  
Global Optimal ◽  
Removal Model ◽  
Split Bregman Algorithm ◽  
Sparse Priors

This work focuses on the problem of rain removal from a single image. The directional multilevel system, Shearlets, is used to describe the intrinsic directional and structure sparse priors of rain streaks and the background layer. In this paper, a Shearlets-based convex rain removal model is proposed, which involves three sparse regularizers: including the sparse regularizer of rain streaks and two sparse regularizers of the Shearlets transform of background layer in the rain drops’ direction and the Shearlets transform of rain streaks in the perpendicular direction. The split Bregman algorithm is utilized to solve the proposed convex optimization model, which ensures the global optimal solution. Comparison tests with three state-of-the-art methods are implemented on synthetic and real rainy images, which suggests that the proposed method is efficient both in rain removal and details preservation of the background layer.

Image Reconstruction Based on Compressed Sensing with Split Bregman Algorithm and Fuzzy Bases

2012 ◽  
Vol 508 ◽  
pp. 80-83
Author(s):  
Jian Jiang Cui ◽  
Xu Jia ◽  
Jing Liu ◽  
Qi Li
Keyword(s):  
Image Reconstruction ◽  
Compressed Sensing ◽  
Reconstruction Algorithm ◽  
Original Data ◽  
Convergence Speed ◽  
Split Bregman ◽  
Reconstruction Image ◽  
Accelerate Convergence ◽  
Split Bregman Algorithm ◽  
Orthogonal Wavelet Transform

When original data is not complete or image degenerates, image reconstruction and recovery will be very important. In order to acquire reconstruction or recovery image with good quality, compressed sensing provides the possibility of achieving, and an image reconstruction algorithm based on compressed sensing with split Bregman method and fuzzy bases sparse representation is proposed, split strategy is applied in split Bregman algorithm in order to accelerate convergence speed; At the same time, discrete cosine transform and dual orthogonal wavelet transform are treated as bases to represent image sparsely, and image is reconstructed by using split Bregman algorithm. Experiments show that the proposed algorithm can improve convergence speed and reconstruction image quality.

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