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解决方案/重构方法

解决方案/重构方法

 

[[文件:Orthogonal Matching Pursuit.gif|链接=link=Special:FilePath/Orthogonal_Matching_Pursuit.gif|替代=|缩略图|Example of the retrieval of an unknown signal (gray line) from few measurements (black dots) using the knowledge that the signal is sparse in the Hermite polynomials basis (purple dots show the retrieved coefficients).]]

[[File:Orthogonal Matching Pursuit.gif|500px|thumb|right|Example of the retrieval of an unknown signal (gray line) from few measurements (black dots) using the knowledge that the signal is sparse in the Hermite polynomials basis (purple dots show the retrieved coefficients).|链接=Special:FilePath/Orthogonal_Matching_Pursuit.gif]]

 

Example of the retrieval of an unknown signal (gray line) from few measurements (black dots) using the knowledge that the signal is sparse in the Hermite polynomials basis (purple dots show the retrieved coefficients).

Example of the retrieval of an unknown signal (gray line) from few measurements (black dots) using the knowledge that the signal is sparse in the Hermite polynomials basis (purple dots show the retrieved coefficients).

Recent progress on this problem involves using an iteratively directional TV refinement for CS reconstruction.<ref name = "Orientation and directional refinement" /> This method would have 2 stages: the first stage would estimate and refine the initial orientation field – which is defined as a noisy point-wise initial estimate, through edge-detection, of the given image. In the second stage, the CS reconstruction model is presented by utilizing directional TV regularizer. More details about these TV-based approaches – iteratively reweighted l1 minimization, edge-preserving TV and iterative model using directional orientation field and TV- are provided below.

Recent progress on this problem involves using an iteratively directional TV refinement for CS reconstruction.<ref name = "Orientation and directional refinement" /> This method would have 2 stages: the first stage would estimate and refine the initial orientation field – which is defined as a noisy point-wise initial estimate, through edge-detection, of the given image. In the second stage, the CS reconstruction model is presented by utilizing directional TV regularizer. More details about these TV-based approaches – iteratively reweighted l1 minimization, edge-preserving TV and iterative model using directional orientation field and TV- are provided below.

在此问题上的最新进展涉及将迭代方向的电视优化用于CS重构<ref name="Orientation and directional refinement" />。该方法分为两个阶段: 第一阶段对初始方向场进行估计和细化，初始方向场定义为通过边缘检测对给定图像进行有噪点式初始估计。第二阶段，利用定向电视调制器提出了 CS 重构模型。下面详细介绍了这些基于 TV 的方法: 迭代重加权 l1最小化、边缘保持 TV 和使用方向场和 TV 的迭代模型。

在此问题上的最新进展涉及将迭代方向的电视优化用于CS重构<ref name="Orientation and directional refinement" />。该方法分为两个阶段: 第一阶段对初始方向场进行估计和细化，初始方向场定义为通过边缘检测对给定图像进行有噪点式初始估计。第二阶段，利用定向电视调制器提出了 CS 重构模型。下面详细介绍了这些基于 TV 的方法: 迭代重加权 L1最小化、边缘保持 TV 和使用方向场和 TV 的迭代模型。

=====Iteratively reweighted <math>l_{1}</math> minimization =====

=====Iteratively reweighted <math>l_{1}</math> minimization =====

反复重新加权<math>l_{1}</math>最小化

反复重新加权<math>l_{1}</math>最小化

 

[[文件:IRLS.png|链接=link=Special:FilePath/IRLS.png|替代=|缩略图|iteratively reweighted l1 minimization method for CS]]

[[File:IRLS.png|thumb|iteratively reweighted l1 minimization method for CS|链接=Special:FilePath/IRLS.png]]

 

iteratively reweighted l1 minimization method for CS

iteratively reweighted l1 minimization method for CS

=====Edge-preserving total variation (TV) based compressed sensing<ref name ="EPTV">{{cite journal | last1 = Tian | first1 = Z. | last2 = Jia | first2 = X. | last3 = Yuan | first3 = K. | last4 = Pan | first4 = T. | last5 = Jiang | first5 = S. B. | year = 2011 | title = Low-dose CT reconstruction via edge preserving total variation regularization | url = | journal = Phys Med Biol | volume = 56 | issue = 18| pages = 5949–5967 | doi=10.1088/0031-9155/56/18/011| pmid = 21860076 | pmc = 4026331 | arxiv = 1009.2288 | bibcode = 2011PMB....56.5949T }}</ref>=====

=====Edge-preserving total variation (TV) based compressed sensing<ref name ="EPTV">{{cite journal | last1 = Tian | first1 = Z. | last2 = Jia | first2 = X. | last3 = Yuan | first3 = K. | last4 = Pan | first4 = T. | last5 = Jiang | first5 = S. B. | year = 2011 | title = Low-dose CT reconstruction via edge preserving total variation regularization | url = | journal = Phys Med Biol | volume = 56 | issue = 18| pages = 5949–5967 | doi=10.1088/0031-9155/56/18/011| pmid = 21860076 | pmc = 4026331 | arxiv = 1009.2288 | bibcode = 2011PMB....56.5949T }}</ref>=====

基于边缘保留的总变分（TV）的压缩感知<ref name="EPTV" />

基于边缘保留的总变分（TV）的压缩感知<ref name="EPTV" />

 

[[文件:Edge preserving TV.png|链接=link=Special:FilePath/Edge_preserving_TV.png|替代=|缩略图|Flow diagram figure for edge preserving total variation method for compressed sensing]]

[[File:Edge preserving TV.png|thumb|Flow diagram figure for edge preserving total variation method for compressed sensing|链接=Special:FilePath/Edge_preserving_TV.png]]

 

Flow diagram figure for edge preserving total variation method for compressed sensing

Flow diagram figure for edge preserving total variation method for compressed sensing

 

[[文件:Augmented Lagrangian.png|链接=link=Special:FilePath/Augmented_Lagrangian.png|替代=|缩略图|Augmented Lagrangian method for orientation field and iterative directional field refinement models]]

[[File:Augmented Lagrangian.png|thumb|right|Augmented Lagrangian method for orientation field and iterative directional field refinement models|链接=Special:FilePath/Augmented_Lagrangian.png]]

 

Augmented Lagrangian method for orientation field and iterative directional field refinement models

Augmented Lagrangian method for orientation field and iterative directional field refinement models