scholarly journals AN ADAPTIVE VARIATIONAL MODEL FOR MEDICAL IMAGES RESTORATION

2019 ◽  
Vol XLII-2/W12 ◽  
pp. 219-224
Author(s):  
T. T. T. Tran ◽  
C. T. Pham ◽  
A. V. Kopylov ◽  
V. N. Nguyen
Keyword(s):  
Optimization Problem ◽  
Medical Images ◽  
Variational Model ◽  
Imaging Analysis ◽  
Split Bregman Method ◽  
Split Bregman ◽  
Piecewise Constant ◽  
First Order ◽  
Proposed Model ◽  
Staircase Effect

<p><strong>Abstract.</strong> Image denoising is one of the important tasks required by medical imaging analysis. In this work, we investigate an adaptive variation model for medical images restoration. In the proposed model, we have used the first-order total variation combined with Laplacian regularizer to eliminate the staircase effect in the first-order TV model while preserve edges of object in the piecewise constant image. We also propose an instance of Split Bregman method to solve the proposed denoising model as an optimization problem. Experimental results from mixed Poisson-Gaussian noise are given to demonstrate that our proposed approach outperforms the related methods.</p>

scholarly journals A New and Fast Multiphase Image Segmentation Model for Color Images

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Yunyun Yang ◽  
Boying Wu
Keyword(s):  
Image Segmentation ◽  
A Priori ◽  
Color Images ◽  
Triple Junctions ◽  
Segmentation Method ◽  
Split Bregman Method ◽  
Split Bregman ◽  
Piecewise Constant ◽  
Multiple Regions ◽  
Convex Image Segmentation

This paper presents a new and fast multiphase image segmentation model for color images. We propose our model by incorporating the globally convex image segmentation method and the split Bregman method into the piecewise constant multiphase Vese-Chan model for color images. We have applied our model to many synthetic and real color images. Numerical results show that our model can segment color images with multiple regions and represent boundaries with complex topologies, including triple junctions. Comparison with the Vese-Chan model demonstrates the efficiency of our model. Besides, our model does not require a priori denoising step and is robust with respect to noise.

scholarly journals Convex Image Segmentation Model Based on Local and Global Intensity Fitting Energy and Split Bregman Method

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Yunyun Yang ◽  
Boying Wu
Keyword(s):  
Image Segmentation ◽  
Active Contour ◽  
Energy Functional ◽  
Split Bregman Method ◽  
Split Bregman ◽  
Proposed Model ◽  
Variational Level Set ◽  
Convex Image Segmentation ◽  
Level Set Formulation ◽  
Global Fitting

We propose a convex image segmentation model in a variational level set formulation. Both the local information and the global information are taken into consideration to get better segmentation results. We first propose a globally convex energy functional to combine the local and global intensity fitting terms. The proposed energy functional is then modified by adding an edge detector to force the active contour to the boundary more easily. We then apply the split Bregman method to minimize the proposed energy functional efficiently. By using a weight function that varies with location of the image, the proposed model can balance the weights between the local and global fitting terms dynamically. We have applied the proposed model to synthetic and real images with desirable results. Comparison with other models also demonstrates the accuracy and superiority of the proposed model.

A High-Order Model of TV and its Augmented Lagrangian Algorithm

2014 ◽  
Vol 568-570 ◽  
pp. 726-733 ◽  
Author(s):  
Lu Tan ◽  
Wei Bo Wei ◽  
Zhen Kuan Pan ◽  
Wei Zhong Zhang ◽  
Jin Ming Duan
Keyword(s):  
Image Denoising ◽  
High Order ◽  
Order Model ◽  
Split Bregman ◽  
Denoising Method ◽  
Proposed Model ◽  
Total Variation Model ◽  
Staircase Effect ◽  
Variational Image ◽  
Split Bregman Algorithm

In recent twenty years, image denoising method which is based on partial differential equations (PDE) has been developed rapidly. Due to its scientific and strong theoretical foundation, it owns accurate and stable results which can be got by efficient algorithms. But it still leaves some problems which need to be solved. The staircase effect is one of the most basic problems in the classical TV (Total Variation) model. This problem can be effectively solved by high-order model proposed in this paper. A fast and efficient numerical algorithm is designed to solve minimization problems related to the high-order model and its applications to variational image denoising are shown. The performance of the proposed model is compared with TV model and other high-order models. The algorithm used for the proposed model is also compared with Split Bregman algorithm. Some numerical experiments validate the model proposed and the algorithm designed in this paper.

scholarly journals Combined total variation of first and fractional orders for Poisson noise removal in digital images

2021 ◽  
pp. 10-19
Author(s):  
Cong Pham ◽  
Thi Thu Tran ◽  
Minh Pham ◽  
Thanh Cong Nguyen
Keyword(s):  
Image Reconstruction ◽  
Image Restoration ◽  
Total Variation ◽  
Fractional Order ◽  
Optimization Problem ◽  
Poisson Noise ◽  
Experimental Results ◽  
First Order ◽  
Proposed Model ◽  
Total Variation Model

Introduction: Many methods have been proposed to handle the image restoration problem with Poisson noise. A popular approach to Poissonian image reconstruction is the one based on Total Variation. This method can provide significantly sharp edges and visually fine images, but it results in piecewise-constant regions in the resulting images. Purpose: Developing an adaptive total variation-based model for the reconstruction of images contaminated by Poisson noise, and an algorithm for solving the optimization problem. Results: We proposed an effective way to restore images degraded by Poisson noise. Using the Bayesian framework, we proposed an adaptive model based on a combination of first-order total variation and fractional order total variation. The first-order total variation model is efficient for suppressing the noise and preserving the keen edges simultaneously. However, the first-order total variation method usually causes artifact problems in the obtained results. To avoid this drawback, we can use high-order total variation models, one of which is the fractional-order total variation-based model for image restoration. In the fractional-order total variation model, the derivatives have an order greater than or equal to one. It leads to the convenience of computation with a compact discrete form. However, methods based on the fractional-order total variation may cause image blurring. Thus, the proposed model incorporates the advantages of two total variation regularization models, having a significant effect on the edge-preserving image restoration. In order to solve the considered optimization problem, the Split Bregman method is used. Experimental results are provided, demonstrating the effectiveness of the proposed method.  Practical relevance: The proposed method allows you to restore Poissonian images preserving their edges. The presented numerical simulation demonstrates the competitive performance of the model proposed for image reconstruction. Discussion: From the experimental results, we can see that the proposed algorithm is effective in suppressing noise and preserving the image edges. However, the weighted parameters in the proposed model were not automatically selected at each iteration of the proposed algorithm. This requires additional research.

scholarly journals Comparison of minimization methods for nonsmooth image segmentation

2018 ◽  
Vol 9 (1) ◽  
pp. 68-86 ◽  
Author(s):  
L. Antonelli ◽  
V. De Simone
Keyword(s):  
Optimization Problem ◽  
Convex Relaxation ◽  
Numerical Comparison ◽  
Two Phase ◽  
Piecewise Constant ◽  
First Order ◽  
Smoothing Methods ◽  
Minimization Methods ◽  
Basic Approaches ◽  
Nonsmooth Optimization Problem

Abstract Segmentation is a typical task in image processing having as main goal the partitioning of the image into multiple segments in order to simplify its interpretation and analysis. One of the more popular segmentation model, formulated by Chan-Vese, is the piecewise constant Mumford-Shah model restricted to the case of two-phase segmentation. We consider a convex relaxation formulation of the segmentation model, that can be regarded as a nonsmooth optimization problem, because the presence of the l1-term. Two basic approaches in optimization can be distinguished to deal with its non differentiability: the smoothing methods and the nonsmoothing methods. In this work, a numerical comparison of some first order methods belongs of both approaches are presented. The relationships among the different methods are shown, and accuracy and efficiency tests are also performed on several images.

scholarly journals Deblurring by Solving a TVp-Regularized Optimization Problem Using Split Bregman Method

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Su Xiao
Keyword(s):  
Minimization Problem ◽  
Optimization Problem ◽  
Unconstrained Minimization ◽  
Image Deblurring ◽  
Constrained Minimization ◽  
Split Bregman Method ◽  
Split Bregman ◽  
Closed Form Solutions ◽  
Constrained Minimization Problem ◽  
New Variables

Image deblurring is formulated as an unconstrained minimization problem, and its penalty function is the sum of the error term and TVp-regularizers with0<p<1. Although TVp-regularizer is a powerful tool that can significantly promote the sparseness of image gradients, it is neither convex nor smooth, thus making the presented optimization problem more difficult to deal with. To solve this minimization problem efficiently, such problem is first reformulated as an equivalent constrained minimization problem by introducing new variables and new constraints. Thereafter, the split Bregman method, as a solver, splits the new constrained minimization problem into subproblems. For each subproblem, the corresponding efficient method is applied to ensure the existence of closed-form solutions. In simulated experiments, the proposed algorithm and some state-of-the-art algorithms are applied to restore three types of blurred-noisy images. The restored results show that the proposed algorithm is valid for image deblurring and is found to outperform other algorithms in experiments.

scholarly journals Unsupervised Texture Segmentation Using Active Contour Model and Oscillating Information

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Guodong Wang ◽  
Zhenkuan Pan ◽  
Qian Dong ◽  
Ximei Zhao ◽  
Zhimei Zhang ◽  
...  
Keyword(s):  
Active Contour ◽  
Active Contour Model ◽  
Image Decomposition ◽  
Smooth Approximation ◽  
Split Bregman ◽  
Piecewise Constant ◽  
Decomposition Model ◽  
Contour Model ◽  
Proposed Model ◽  
Data Term

Textures often occur in real-world images and may cause considerable difficulties in image segmentation. In order to segment texture images, we propose a new segmentation model that combines image decomposition model and active contour model. The former model is capable of decomposing structural and oscillating components separately from texture image, and the latter model can be used to provide smooth segmentation contour. In detail, we just replace the data term of piecewise constant/smooth approximation in CCV (convex Chan-Vese) model with that of image decomposition model-VO (Vese-Osher). Therefore, our proposed model can estimate both structural and oscillating components of texture images as well as segment textures simultaneously. In addition, we design fast Split-Bregman algorithm for our proposed model. Finally, the performance of our method is demonstrated by segmenting some synthetic and real texture images.

An Analytical Transient Tire Model

2001 ◽  
Vol 29 (2) ◽  
pp. 108-132 ◽  
Author(s):  
A. Ghazi Zadeh ◽  
A. Fahim
Keyword(s):  
Transient Behavior ◽  
Stability Control ◽  
Vehicle Stability ◽  
Tire Model ◽  
Steering Angle ◽  
First Order ◽  
Vehicle Stability Control ◽  
Proposed Model ◽  
Depth Study ◽  
And Performance

Abstract The dynamics of a vehicle's tires is a major contributor to the vehicle stability, control, and performance. A better understanding of the handling performance and lateral stability of the vehicle can be achieved by an in-depth study of the transient behavior of the tire. In this article, the transient response of the tire to a steering angle input is examined and an analytical second order tire model is proposed. This model provides a means for a better understanding of the transient behavior of the tire. The proposed model is also applied to a vehicle model and its performance is compared with a first order tire model.

An L1-based variational model for Retinex theory and its application to medical images

CVPR 2011 ◽  
2011 ◽  
Author(s):  
Wenye Ma ◽  
Jean-Michel Morel ◽  
Stanley Osher ◽  
Aichi Chien
Keyword(s):  
Medical Images ◽  
Variational Model ◽  
Retinex Theory
Sign in / Sign up

Export Citation Format

Share Document