scholarly journals An augmented lagrangian method for solving a new variational model based on gradients similarity measures and high order regulariation for multimodality registration

2019 ◽  
Vol 13 (2) ◽  
pp. 309-335 ◽  
Author(s):  
Anis Theljani ◽  
◽  
Ke Chen
Keyword(s):  
Augmented Lagrangian ◽  
Augmented Lagrangian Method ◽  
Similarity Measures ◽  
Lagrangian Method ◽  
High Order ◽  
Variational Model ◽  
Model Based ◽  
Multimodality Registration

Fast Linearized Augmented Lagrangian Method for Euler's Elastica Model

2017 ◽  
Vol 10 (1) ◽  
pp. 98-115 ◽  
Author(s):  
Jun Zhang ◽  
Rongliang Chen ◽  
Chengzhi Deng ◽  
Shengqian Wang
Keyword(s):  
Augmented Lagrangian ◽  
Complexity Analysis ◽  
Augmented Lagrangian Method ◽  
Saddle Points ◽  
Computational Cost ◽  
Lagrangian Method ◽  
Previous Method ◽  
High Order ◽  
Noise Elimination ◽  
Euler’S Elastica

AbstractRecently, many variational models involving high order derivatives have been widely used in image processing, because they can reduce staircase effects during noise elimination. However, it is very challenging to construct efficient algorithms to obtain the minimizers of original high order functionals. In this paper, we propose a new linearized augmented Lagrangian method for Euler's elastica image denoising model. We detail the procedures of finding the saddle-points of the augmented Lagrangian functional. Instead of solving associated linear systems by FFT or linear iterative methods (e.g., the Gauss-Seidel method), we adopt a linearized strategy to get an iteration sequence so as to reduce computational cost. In addition, we give some simple complexity analysis for the proposed method. Experimental results with comparison to the previous method are supplied to demonstrate the efficiency of the proposed method, and indicate that such a linearized augmented Lagrangian method is more suitable to deal with large-sized images.

scholarly journals An augmented Lagrangian method for solving total variation (TV)-based image registration model

2020 ◽  
Vol 14 ◽  
pp. 174830262097353
Author(s):  
Noppadol Chumchob ◽  
Ke Chen
Keyword(s):  
Image Registration ◽  
Augmented Lagrangian ◽  
Numerical Solutions ◽  
Augmented Lagrangian Method ◽  
Closed Form Solution ◽  
Numerical Algorithms ◽  
Lagrangian Method ◽  
Form Solution ◽  
The Other ◽  
Other Hand

Variational methods for image registration basically involve a regularizer to ensure that the resulting well-posed problem admits a solution. Different choices of regularizers lead to different deformations. On one hand, the conventional regularizers, such as the elastic, diffusion and curvature regularizers, are able to generate globally smooth deformations and generally useful for many applications. On the other hand, these regularizers become poor in some applications where discontinuities or steep gradients in the deformations are required. As is well-known, the total (TV) variation regularizer is more appropriate to preserve discontinuities of the deformations. However, it is difficult in developing an efficient numerical method to ensure that numerical solutions satisfy this requirement because of the non-differentiability and non-linearity of the TV regularizer. In this work we focus on computational challenges arising in approximately solving TV-based image registration model. Motivated by many efficient numerical algorithms in image restoration, we propose to use augmented Lagrangian method (ALM). At each iteration, the computation of our ALM requires to solve two subproblems. On one hand for the first subproblem, it is impossible to obtain exact solution. On the other hand for the second subproblem, it has a closed-form solution. To this end, we propose an efficient nonlinear multigrid (NMG) method to obtain an approximate solution to the first subproblem. Numerical results on real medical images not only confirm that our proposed ALM is more computationally efficient than some existing methods, but also that the proposed ALM delivers the accurate registration results with the desired property of the constructed deformations in a reasonable number of iterations.

scholarly journals An Augmented Lagrangian Method for Sliding Contact of Soft Tissue

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Hongqiang Guo ◽  
Jeffrey C. Nickel ◽  
Laura R. Iwasaki ◽  
Robert L. Spilker
Keyword(s):  
Augmented Lagrangian ◽  
Soft Tissues ◽  
Augmented Lagrangian Method ◽  
Fluid Pressure ◽  
Complex Loading ◽  
Lagrangian Method ◽  
Sliding Contact ◽  
Element Formulation ◽  
Contact Interface ◽  
Diarthrodial Joints

Despite the importance of sliding contact in diarthrodial joints, only a limited number of studies have addressed this type of problem, with the result that the mechanical behavior of articular cartilage in daily life remains poorly understood. In this paper, a finite element formulation is developed for the sliding contact of biphasic soft tissues. The augmented Lagrangian method is used to enforce the continuity of contact traction and fluid pressure across the contact interface. The resulting method is implemented in the commercial software COMSOL Multiphysics. The accuracy of the new implementation is verified using an example problem of sliding contact between a rigid, impermeable indenter and a cartilage layer for which analytical solutions have been obtained. The new implementation’s capability to handle a complex loading regime is verified by modeling plowing tests of the temporomandibular joint (TMJ) disc.

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