Iterative gradient projection algorithm for two-dimensional compressive sensing sparse image reconstruction

2014 ◽  
Vol 104 ◽  
pp. 15-26 ◽  
Author(s):  
Gao Chen ◽  
Defang Li ◽  
Jiashu Zhang
Keyword(s):  
Image Reconstruction ◽  
Compressive Sensing ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Two Dimensional ◽  
Gradient Projection Algorithm ◽  
Sparse Image Reconstruction

Rapid Gradient Projection Algorithm for Image Reconstruction

2014 ◽  
Vol 530-531 ◽  
pp. 443-446
Author(s):  
Hai Xia Yan ◽  
Yan Jun Liu
Keyword(s):  
Image Reconstruction ◽  
Compressed Sensing ◽  
Gradient Descent ◽  
Target Function ◽  
Reconstruction Algorithm ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Descent Direction ◽  
Reconstruction Accuracy ◽  
Gradient Projection Algorithm

In order to improve the speed of compressed sensing image reconstruction algorithm, a rapid gradient projection algorithm for image reconstruction is proposed. In traditional Gradient Projection algorithm, the pursuit direction is alternating, in rapid gradient projection algorithm, we use the Newton's method to calculate the gradient descent direction, thus the constraints conditions of gradient projection is satisfied. And the target function is updated in each iteration computing. The effect of approximation matrix to target function is reduced. The iteration computing times is reduced, because the algorithm works in accurate search direction. Experiment results show that, compared with the GPSR algorithm, the RGPSR algorithm improves the signals reconstruction accuracy, improves PSNR of reconstruction signals, and exhibits higher robustness under different noise intensities.

Improved Gradient Projection Algorithm for Compressed Sensing

2014 ◽  
Vol 543-547 ◽  
pp. 2623-2626
Author(s):  
Hai Xia Yan ◽  
Yan Jun Liu
Keyword(s):  
Image Reconstruction ◽  
Compressed Sensing ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Reconstruction Accuracy ◽  
Gradient Projection Algorithm ◽  
Gradient Direction ◽  
Searching Method ◽  
Negative Gradient

In order to improve efficient of compressed sensing image reconstruction, an improved gradient projection algorithm of compressed sensing theory is proposed. In improved Gradient Projection algorithm, the pursuit direction is updated by search at negative gradient direction, thus the gradient direction is a single direction, because the traditional gradient projection algorithm searching at alternating searching method ,the efficient of gradient projection algorithm is higher than the traditional gradient projection algorithm, Experiment results show that, compared with the GPSR algorithm, the IGPSR algorithm improves the signals reconstruction accuracy, improves PSNR of reconstruction signals, and exhibits higher robustness under different noise intensities.

scholarly journals Relaxed gradient projection algorithm for constrained node-based shape optimization

2021 ◽  
Author(s):  
Ihar Antonau ◽  
Majid Hojjat ◽  
Kai-Uwe Bletzinger
Keyword(s):  
Shape Optimization ◽  
Optimization Problems ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Design Parameters ◽  
Active Set ◽  
Physical Constraints ◽  
Original Algorithm ◽  
Gradient Projection Algorithm ◽  
Non Linear

AbstractIn node-based shape optimization, there are a vast amount of design parameters, and the objectives, as well as the physical constraints, are non-linear in state and design. Robust optimization algorithms are required. The methods of feasible directions are widely used in practical optimization problems and know to be quite robust. A subclass of these methods is the gradient projection method. It is an active-set method, it can be used with equality and non-equality constraints, and it has gained significant popularity for its intuitive implementation. One significant issue around efficiency is that the algorithm may suffer from zigzagging behavior while it follows non-linear design boundaries. In this work, we propose a modification to Rosen’s gradient projection algorithm. It includes the efficient techniques to damp the zigzagging behavior of the original algorithm while following the non-linear design boundaries, thus improving the performance of the method.

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