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1. 发明授权

US07556602B2 Breast cancer screening with adjunctive ultrasound mammography 有权
标题翻译：乳腺癌筛查与辅助超声乳房X线照相术
公开(公告)号：US07556602B2
公开(公告)日：2009-07-07
申请号：US10160836
申请日：2002-05-31
申请人： Shih-Ping Wang , Donald Chin , Fangyi Rao
发明人： Shih-Ping Wang , Donald Chin , Fangyi Rao
IPC分类号： A61B8/00
CPC分类号： A61B6/463 , A61B6/4423 , A61B6/502 , A61B6/5247 , A61B6/563 , A61B8/0825 , A61B8/406 , A61B8/462 , A61B8/463 , A61B8/464 , A61B8/465 , A61B8/467 , A61B8/469 , A61B8/5238 , A61B8/565 , G06F19/00
摘要： Ultrasound mammography in which an automated transducer scans the patient's breast to generate many images of thin slices that are processed into few images of thick slices that can be displayed simultaneously for practical rapid assessment of the breast. The thin-slice images can be acquired by a technician so that a physician need only spend time in assessing the few displayed thick-slice images and, possibly, only a few of the thin-slice images that might match a suspected anomaly indicated in the thick-slice images. Computer-aided detection or diagnosis (CAD) can be performed on the images and resulting mark and/or other information can be displayed as well. Vibration images can be obtained as well and similarly processed and displayed to highlight abnormalities or for other reasons.
摘要翻译：超声乳腺摄影术，其中自动换能器扫描患者的乳房以产生薄片的许多图像，其被加工成可以同时显示以用于乳房的实际快速评估的厚片的少数图像。薄片图像可以由技术人员获取，使得医生仅需要花费时间来评估少数显示的厚片图像，并且可能仅花费少量可能匹配疑似异常的薄片图像厚片图像。可以对图像执行计算机辅助检测或诊断（CAD），并且可以显示所得到的标记和/或其他信息。也可以获得振动图像，并进行相似的处理和显示，以突显异常或其他原因。

2. 发明申请

US20090312640A1 ADJUNCTIVE ULTRASOUND PROCESSING AND DISPLAY FOR BREAST CANCER SCREENING 审中-公开
标题翻译：用于乳腺癌筛查的ADJUNCTIVE ULTRASOUND PROCESSING AND DISPLAY FOR BREAST CANCER SCREENING
公开(公告)号：US20090312640A1
公开(公告)日：2009-12-17
申请号：US12546339
申请日：2009-08-24
申请人： Shih-Ping Wang , Donald Chin , Fangyi Rao , Nico Karssemeijier
发明人： Shih-Ping Wang , Donald Chin , Fangyi Rao , Nico Karssemeijier
IPC分类号： A61B8/14 , G06K9/00 , A61B6/04
CPC分类号： A61B8/5215 , A61B6/463 , A61B6/502 , A61B6/5241 , A61B6/5247 , A61B6/563 , A61B8/0825 , A61B8/406 , A61B8/4281 , A61B8/4405 , A61B8/463 , A61B8/464 , A61B8/465 , A61B8/466 , A61B8/467 , A61B8/5238 , A61B8/565
摘要： An adjunctive ultrasound mammography system and associated methods are described comprising an adjunctive ultrasound display configured for quick, intuitive, interactive viewing of data derived from volumetric ultrasound scans, the data being displayed near a conventional x-ray mammogram display. Preferred embodiments for navigating among a thick-slice image array, a selected enlarged thick-slice image, and planar ultrasound views are described, including a preferred embodiment in which the planar ultrasound views are updated in real time as a cursor is moved across an active thick-slice image. In one preferred embodiment the thick-slice images are inverted prior to display, with non-breast areas of the image preferably segmented out and reset to dark. The inverted thick-slice images are of more familiar significance to radiologists having years of expertise in analyzing conventional x-ray mammograms. For example, the inverted thick-slice images allow benign features to be more easily dismissed as compared to non-inverted thick-slice images. Preferred embodiments for computing thick-slice image values from the volumetric scan data are also described that emphasize larger mass lesions in the resulting thick-slice images, and that compensate for mass lesions that straddle thick-slice region borders.
摘要翻译：描述了一种辅助超声乳腺摄影系统和相关方法，其包括辅助性超声显示器，其配置用于快速，直观，互动地观看从体积超声扫描获得的数据，该数据显示在常规x射线乳房X线照片显示附近。描述了用于在厚片图像阵列，选定的放大的厚片图像和平面超声波视图之间导航的优选实施例，包括优选实施例，其中当光标跨越活动的时候，平面超声波视图被实时地更新厚片图像。在一个优选实施例中，厚片图像在显示之前被反转，其中图像的非乳房区域优选地被分割出并且重新设置为暗。倒置的厚片图像对于在分析常规x射线乳房X线照片方面具有多年专业知识的放射科医师更为重要。例如，与非倒置厚片图像相比，反向厚片图像允许更容易地解除良性特征。还描述了用于从体积扫描数据计算厚片图像值的优选实施例，其强调所得厚片图像中的较大质量损伤，并补偿跨越厚片区域边界的质量损伤。

3. 发明申请

US20090240150A1 BREAST CANCER SCREENING WITH ADJUNCTIVE ULTRASOUND MAMMOGRAPHY 有权
标题翻译：乳腺癌筛查与ADJUNCTIVE超声波手术
公开(公告)号：US20090240150A1
公开(公告)日：2009-09-24
申请号：US12479468
申请日：2009-06-05
申请人： Shih-Ping WANG , Donald Chin , Fangyi Rao
发明人： Shih-Ping WANG , Donald Chin , Fangyi Rao
IPC分类号： A61B8/14
CPC分类号： A61B6/463 , A61B6/4423 , A61B6/502 , A61B6/5247 , A61B6/563 , A61B8/0825 , A61B8/406 , A61B8/462 , A61B8/463 , A61B8/464 , A61B8/465 , A61B8/467 , A61B8/469 , A61B8/5238 , A61B8/565 , G06F19/00
摘要： An adjunctive ultrasound mammography system and associated methods are described, comprising a scanning apparatus for facilitating standardized, repeatable breast ultrasound scans, and further comprising an adjunctive ultrasound display apparatus configured for fast, intuitive viewing of adjunctive ultrasound data concurrently with x-ray mammogram information. In one preferred embodiment, thick-slice ultrasound images are displayed near an x-ray mammogram such that a screening radiologist can quickly view the thick-slice images for assistance in interpreting the x-ray mammogram. Methods for concurrently acquiring and displaying vibrational resonance image (VDI) data are described. Computer-aided diagnosis (CAD) algorithms that incorporate acoustically-based feature vectors are described, the feature vectors including lateral shadow metrics, vertical shadow metrics, posterior enhancement metrics, and VDI-based metrics. Algorithms are also described that combine x-ray mammogram CAD results with adjunctive ultrasound CAD results without requiring complex image registrations therebetween. Many of the practical, economic, and political barriers to acceptance and integration of ultrasound mammography into existing mass breast cancer screening environments are mitigated.
摘要翻译：描述了辅助超声乳腺摄影系统和相关方法，其包括用于促进标准化，可重复的乳房超声扫描的扫描装置，并且还包括辅助超声显示装置，其配置为与X射线乳腺X线照相信息同时快速，直观地观看辅助超声数据。在一个优选实施例中，在x射线乳房X线照片附近显示厚片超声图像，使得筛选放射科医师可以快速查看厚切片图像以辅助解释X射线乳腺X线照片。描述了同时获取和显示振动共振图像（VDI）数据的方法。描述了包含声学特征向量的计算机辅助诊断（CAD）算法，其特征向量包括横向阴影度量，垂直阴影度量，后验增强度量和基于VDI的度量。还描述了将x射线乳房X线照片CAD结果与辅助超声CAD结果相结合的算法，而不需要它们之间的复杂图像注册。超声乳房X线照相术在现有的大规模乳腺癌筛查环境中接受和整合的许多实际，经济和政治障碍得到缓解。

4. 发明授权

US07828732B2 Breast cancer screening with adjunctive ultrasound mammography 有权
标题翻译：乳腺癌筛查与辅助超声乳房X线照相术
公开(公告)号：US07828732B2
公开(公告)日：2010-11-09
申请号：US12479468
申请日：2009-06-05
申请人： Shih-Ping Wang , Donald Chin , Fangyi Rao
发明人： Shih-Ping Wang , Donald Chin , Fangyi Rao
IPC分类号： A61B8/00
CPC分类号： A61B6/463 , A61B6/4423 , A61B6/502 , A61B6/5247 , A61B6/563 , A61B8/0825 , A61B8/406 , A61B8/462 , A61B8/463 , A61B8/464 , A61B8/465 , A61B8/467 , A61B8/469 , A61B8/5238 , A61B8/565 , G06F19/00
摘要： An adjunctive ultrasound mammography system and associated methods are described, comprising a scanning apparatus for facilitating standardized, repeatable breast ultrasound scans, and further comprising an adjunctive ultrasound display apparatus configured for fast, intuitive viewing of adjunctive ultrasound data concurrently with x-ray mammogram information. In one preferred embodiment, thick-slice ultrasound images are displayed near an x-ray mammogram such that a screening radiologist can quickly view the thick-slice images for assistance in interpreting the x-ray mammogram. Methods for concurrently acquiring and displaying vibrational resonance image (VDI) data are described. Computer-aided diagnosis (CAD) algorithms that incorporate acoustically-based feature vectors are described, the feature vectors including lateral shadow metrics, vertical shadow metrics, posterior enhancement metrics, and VDI-based metrics. Algorithms are also described that combine x-ray mammogram CAD results with adjunctive ultrasound CAD results without requiring complex image registrations therebetween. Many of the practical, economic, and political barriers to acceptance and integration of ultrasound mammography into existing mass breast cancer screening environments are mitigated.
摘要翻译：描述了辅助超声乳腺摄影系统和相关方法，其包括用于促进标准化，可重复的乳房超声扫描的扫描装置，并且还包括辅助超声显示装置，其配置为与X射线乳腺X线照相信息同时快速，直观地观看辅助超声数据。在一个优选实施例中，在x射线乳房X线照片附近显示厚片超声图像，使得筛选放射科医师可以快速查看厚切片图像以辅助解释X射线乳腺X线照片。描述了同时获取和显示振动共振图像（VDI）数据的方法。描述了包含声学特征向量的计算机辅助诊断（CAD）算法，其特征向量包括横向阴影度量，垂直阴影度量，后验增强度量和基于VDI的度量。还描述了将x射线乳房X线照片CAD结果与辅助超声CAD结果相结合的算法，而不需要它们之间的复杂图像注册。超声乳房X线照相术在现有的大规模乳腺癌筛查环境中接受和整合的许多实际，经济和政治障碍得到缓解。

5. 发明授权

US07597663B2 Adjunctive ultrasound processing and display for breast cancer screening 有权
标题翻译：辅助超声处理和显示乳腺癌筛查
公开(公告)号：US07597663B2
公开(公告)日：2009-10-06
申请号：US10305936
申请日：2002-11-27
申请人： Shih-Ping Wang , Donald Chin , Fangyi Rao , Nico Karssemeijier
发明人： Shih-Ping Wang , Donald Chin , Fangyi Rao , Nico Karssemeijier
IPC分类号： A61B8/00
CPC分类号： A61B8/5215 , A61B6/463 , A61B6/502 , A61B6/5241 , A61B6/5247 , A61B6/563 , A61B8/0825 , A61B8/406 , A61B8/4281 , A61B8/4405 , A61B8/463 , A61B8/464 , A61B8/465 , A61B8/466 , A61B8/467 , A61B8/5238 , A61B8/565 , G06F19/00
摘要： An adjunctive ultrasound mammography system and associated methods are described comprising an adjunctive ultrasound display configured for quick, intuitive, interactive viewing of data derived from volumetric ultrasound scans, the data being displayed near a conventional x-ray mammogram display. Preferred embodiments for navigating among a thick-slice image array, a selected enlarged thick-slice image, and planar ultrasound views are described, including a preferred embodiment in which the planar ultrasound views are updated in real time as a cursor is moved across an active thick-slice image. In one preferred embodiment the thick-slice images are inverted prior to display, with non-breast areas of the image preferably segmented out and reset to dark. The inverted thick-slice images are of more familiar significance to radiologists having years of expertise in analyzing conventional x-ray mammograms. For example, the inverted thick-slice images allow benign features to be more easily dismissed as compared to non-inverted thick-slice images. Preferred embodiments for computing thick-slice image values from the volumetric scan data are also described that emphasize larger mass lesions in the resulting thick-slice images, and that compensate for mass lesions that straddle thick-slice region borders.
摘要翻译：描述了一种辅助超声乳腺摄影系统和相关方法，其包括辅助性超声显示器，其配置用于快速，直观，互动地观看从体积超声扫描获得的数据，该数据显示在常规x射线乳房X线照片显示附近。描述了用于在厚片图像阵列，选定的放大的厚片图像和平面超声波视图之间导航的优选实施例，包括优选实施例，其中当光标移动到活动的时候，平面超声波视图被实时地更新厚片图像。在一个优选实施例中，厚片图像在显示之前被反转，其中图像的非乳房区域优选地被分割出并且重新设置为暗。倒置的厚片图像对于在分析常规x射线乳房X线照片方面具有多年专业知识的放射科医师更为重要。例如，与非倒置厚片图像相比，反向厚片图像允许更容易地解除良性特征。还描述了用于从体积扫描数据计算厚片图像值的优选实施例，其强调所得厚片图像中的较大质量损伤，并补偿跨越厚片区域边界的质量损伤。

6. 发明申请

US20130289405A1 ADJUNCTIVE ULTRASOUND PROCESSING AND DISPLAY FOR BREAST CANCER SCREENING 有权
标题翻译：用于乳腺癌筛查的ADJUNCTIVE ULTRASOUND PROCESSING AND DISPLAY FOR BREAST CANCER SCREENING
公开(公告)号：US20130289405A1
公开(公告)日：2013-10-31
申请号：US13863259
申请日：2013-04-15
申请人： Shih-Ping WANG , Donald Chin , Fangyi Rao , Nico Karssemeijier
发明人： Shih-Ping WANG , Donald Chin , Fangyi Rao , Nico Karssemeijier
IPC分类号： A61B8/08
CPC分类号： A61B8/5215 , A61B6/463 , A61B6/502 , A61B6/5241 , A61B6/5247 , A61B6/563 , A61B8/0825 , A61B8/406 , A61B8/4281 , A61B8/4405 , A61B8/463 , A61B8/464 , A61B8/465 , A61B8/466 , A61B8/467 , A61B8/5238 , A61B8/565 , G06F19/00
摘要： An adjunctive ultrasound mammography system and associated methods use an adjunctive ultrasound display configured for quick, intuitive, interactive viewing of volumetric ultrasound scans, displayed near a conventional x-ray mammogram display. Preferred navigations among a thick-slice image array, a selected enlarged thick-slice image, and planar ultrasound views are described, including a mode in which the planar ultrasound views are updated in real time as a cursor is moved across an active thick-slice image. In one example the thick-slice images are inverted prior to display, with non-breast areas of the image preferably segmented out and reset to dark. The inverted thick-slice images are of more familiar significance to radiologists as they are more like conventional x-ray mammograms and allow benign features to be more easily dismissed as compared to non-inverted thick-slice images. Preferred embodiments emphasize larger mass lesions and that compensate for mass lesions that straddle thick-slice region borders.
摘要翻译：辅助超声乳腺摄影系统和相关方法使用辅助超声显示器来配置用于快速，直观，互动地观看体积超声扫描，显示在常规x射线乳腺X线照片显示附近。描述了厚切片图像阵列，所选放大的厚片图像和平面超声波视图之间的优选导航，包括当光标移动穿过有源厚片时实时更新平面超声波视图的模式图片。在一个示例中，厚片图像在显示之前被反转，图像的非乳房区域优选地被分割出并且重置为暗。倒置的厚片图像对于放射科医师来说更为重要，因为它们更像是常规的x射线乳房X线照相术，并且与非倒置的厚切片图像相比，允许良性特征更容易被消除。优选实施例强调较大的质量损伤并且补偿跨越厚片区域边界的质量损伤。

7. 发明授权

US07313260B2 Controlling thick-slice viewing of breast ultrasound data 有权
标题翻译：控制乳房超声数据的厚切片观察
公开(公告)号：US07313260B2
公开(公告)日：2007-12-25
申请号：US11489371
申请日：2006-07-18
申请人： Shih-Ping Wang , Fangyi Rao
发明人： Shih-Ping Wang , Fangyi Rao
IPC分类号： G06K9/00
CPC分类号： A61B8/0825 , A61B6/463 , A61B6/502 , A61B6/5247 , A61B6/563 , A61B8/406 , A61B8/4281 , A61B8/4405 , A61B8/462 , A61B8/463 , A61B8/464 , A61B8/465 , A61B8/467 , A61B8/5238 , A61B8/565 , G06F19/00 , Y10S128/916
摘要： An adjunctive ultrasound mammography system and associated methods are described in which an ultrasound image being displayed near an x-ray mammogram image may be superimposed thereon or thereunder by a user for facilitating rapid comprehension of breast structures and detection of abnormalities therein. In one preferred embodiment, the x-ray mammogram image corresponds to a standard x-ray mammogram view, and the ultrasound image is a thick-slice image representing a thick-slice or slab-like portion of the breast volume substantially parallel to that standard x-ray mammogram view. In another preferred embodiment, the user is permitted to manually manipulate the registration of the ultrasound image with the x-ray mammogram image. It has been found that the manual registration process, which involves manual vernier adjustments responsive to perceived registration differences, can rapidly increase the radiologist's perception of the breast structures being displayed by both component images. Even though ultrasound images tend to have substantially different textures and feature emphases than x-ray images, the bimodal thick-slice/x-ray image, alone or in conjunction with the vernier registration process, can often expose or clarify tissue structures hidden in the separate component images, and can often obviate or explain certain noticed structures in the component images.
摘要翻译：描述了一种辅助超声乳腺摄影系统及其相关方法，其中在X射线乳房X线照相图像附近显示的超声图像可以由用户叠加在其上或其上，以便于快速理解乳房结构并检测其中的异常。在一个优选实施例中，X射线乳房X线照相图像对应于标准x射线乳房X线照片视图，超声图像是表示基本上平行于该标准的乳房体积的厚切片或板状部分的厚片图像 x射线乳房X线照片视图。在另一个优选实施例中，允许用户用X射线乳腺X线照片图像手动地操作超声图像的登记。已经发现，手动注册过程涉及响应于感知到的注册差异的手动游标调整，可以快速增加放射科医师对由两个分量图像显示的乳房结构的感知。尽管超声图像倾向于具有与x射线图像相比具有显着不同的纹理和特征的重点，但双峰厚片/ X射线图像单独或与游标注册过程一起可以经常暴露或澄清隐藏在单独的组件图像，并且经常可以避免或解释组件图像中的某些注意结构。

8. 发明授权

US07103205B2 Breast cancer screening with ultrasound image overlays 有权
标题翻译：乳腺癌筛查与超声图像叠加
公开(公告)号：US07103205B2
公开(公告)日：2006-09-05
申请号：US10305661
申请日：2002-11-27
申请人： Shih-Ping Wang , Fangyi Rao
发明人： Shih-Ping Wang , Fangyi Rao
IPC分类号： G06K9/00
CPC分类号： A61B8/0825 , A61B6/463 , A61B6/502 , A61B6/5247 , A61B6/563 , A61B8/406 , A61B8/4281 , A61B8/4405 , A61B8/462 , A61B8/463 , A61B8/464 , A61B8/465 , A61B8/467 , A61B8/5238 , A61B8/565 , G06F19/00 , Y10S128/916
摘要： An adjunctive ultrasound mammography system and associated methods are described in which an ultrasound image being displayed near an x-ray mammogram image may be superimposed thereon or thereunder by a user for facilitating rapid comprehension of breast structures and detection of abnormalities therein. In one preferred embodiment, the x-ray mammogram image corresponds to a standard x-ray mammogram view, and the ultrasound image is a thick-slice image representing a thick-slice or slab-like portion of the breast volume substantially parallel to that standard x-ray mammogram view. In another preferred embodiment, the user is permitted to manually manipulate the registration of the ultrasound image with the x-ray mammogram image. It has been found that the manual registration process, which involves manual vernier adjustments responsive to perceived registration differences, can rapidly increase the radiologist's perception of the breast structures being displayed by both component images. Even though ultrasound images tend to have substantially different textures and feature emphases than x-ray images, the bimodal thick-slice/x-ray image, alone or in conjunction with the vernier registration process, can often expose or clarify tissue structures hidden in the separate component images, and can often obviate or explain certain noticed structures in the component images.
摘要翻译：描述了一种辅助超声乳腺摄影系统及其相关方法，其中在X射线乳房X线照相图像附近显示的超声图像可以由用户叠加在其上或其上，以便于快速理解乳房结构并检测其中的异常。在一个优选实施例中，X射线乳房X线照相图像对应于标准x射线乳房X线照片视图，超声图像是表示基本上平行于该标准的乳房体积的厚切片或板状部分的厚片图像 x射线乳房X线照片视图。在另一个优选实施例中，允许用户用X射线乳腺X线照片图像手动地操作超声图像的登记。已经发现，手动注册过程涉及响应于感知到的注册差异的手动游标调整，可以快速增加放射科医师对由两个分量图像显示的乳房结构的感知。尽管超声图像倾向于具有与x射线图像相比具有显着不同的纹理和特征的重点，但双峰厚片/ X射线图像单独或与游标注册过程一起可以经常暴露或澄清隐藏在单独的组件图像，并且经常可以避免或解释组件图像中的某些注意结构。

9. 发明申请

US20060257009A1 Controlling thick-slice viewing of breast ultrasound data 有权
标题翻译：控制乳房超声数据的厚切片观察
公开(公告)号：US20060257009A1
公开(公告)日：2006-11-16
申请号：US11489371
申请日：2006-07-18
申请人： Shih-Ping Wang , Fangyi Rao
发明人： Shih-Ping Wang , Fangyi Rao
IPC分类号： G06K9/00
CPC分类号： A61B8/0825 , A61B6/463 , A61B6/502 , A61B6/5247 , A61B6/563 , A61B8/406 , A61B8/4281 , A61B8/4405 , A61B8/462 , A61B8/463 , A61B8/464 , A61B8/465 , A61B8/467 , A61B8/5238 , A61B8/565 , G06F19/00 , Y10S128/916
摘要： An adjunctive ultrasound mammography system and associated methods are described in which an ultrasound image being displayed near an x-ray mammogram image may be superimposed thereon or thereunder by a user for facilitating rapid comprehension of breast structures and detection of abnormalities therein. In one preferred embodiment, the x-ray mammogram image corresponds to a standard x-ray mammogram view, and the ultrasound image is a thick-slice image representing a thick-slice or slab-like portion of the breast volume substantially parallel to that standard x-ray mammogram view. In another preferred embodiment, the user is permitted to manually manipulate the registration of the ultrasound image with the x-ray mammogram image. It has been found that the manual registration process, which involves manual vernier adjustments responsive to perceived registration differences, can rapidly increase the radiologist's perception of the breast structures being displayed by both component images. Even though ultrasound images tend to have substantially different textures and feature emphases than x-ray images, the bimodal thick-slice/x-ray image, alone or in conjunction with the vernier registration process, can often expose or clarify tissue structures hidden in the separate component images, and can often obviate or explain certain noticed structures in the component images.
摘要翻译：描述了一种辅助超声乳腺摄影系统及其相关方法，其中在X射线乳房X线照相图像附近显示的超声图像可以由用户叠加在其上或其上，以便于快速理解乳房结构并检测其中的异常。在一个优选实施例中，X射线乳房X线照相图像对应于标准x射线乳房X线照片视图，超声图像是表示基本上平行于该标准的乳房体积的厚切片或板状部分的厚片图像 x射线乳房X线照片视图。在另一个优选实施例中，允许用户用X射线乳腺X线照片图像手动地操作超声图像的登记。已经发现，手动注册过程涉及响应于感知到的注册差异的手动游标调整，可以快速增加放射科医师对由两个分量图像显示的乳房结构的感知。尽管超声图像倾向于具有与x射线图像相比具有显着不同的纹理和特征的重点，但双峰厚片/ X射线图像单独或与游标注册过程一起可以经常暴露或澄清隐藏在单独的组件图像，并且经常可以避免或解释组件图像中的某些注意结构。

10. 发明授权

US07962541B2 Optimization of spectrum extrapolation for causal impulse response calculation using the hilbert transform 有权
标题翻译：使用希尔伯特变换进行因果脉冲响应计算的频谱外推优化
公开(公告)号：US07962541B2
公开(公告)日：2011-06-14
申请号：US11747007
申请日：2007-05-10
申请人： Fangyi Rao
发明人： Fangyi Rao
IPC分类号： G06F17/17
CPC分类号： G06F17/141
摘要： A causal impulse response function is calculated from a truncated spectrum by extending the real part of the spectrum beyond the truncation frequency and computing the imaginary part with the Hilbert transform to enforce causality. The out of band extrapolation is optimized to reduce the discrepancy between the computed and the original imaginary part in the in band frequency range so that the causal impulse response accurately represents the original spectrum. The technique can be applied to spectral with the delay phase subtracted to enforce delay causality. The Hilbert transform may be employed to maintain causality in S-parameter passivity violation correction. At frequencies where violation happens, the S-parameter matrix is scaled down by the inverse of the magnitude of the largest eigenvalue. Magnitudes at other frequencies are unchanged. An additional phase calculated by the magnitude phase Hilbert transform is added to the scaled spectrum to maintain the causality.
摘要翻译：通过将截取的频谱的实部扩展超过截断频率并用希尔伯特变换计算虚部以实施因果关系，从截断频谱计算因果脉冲响应函数。优化带外外推法以减少频带频率范围内计算出的和原始虚部之间的差异，从而使因果脉冲响应准确地表示原始频谱。该技术可以应用于频谱，延迟相位被减去以执行延迟因果。可以采用希尔伯特变换来维持S参数无源违反校正中的因果关系。在发生违规发生的频率下，S参数矩阵按照最大特征值幅度的倒数缩小。其他频率的幅度不变。通过幅度相位Hilbert变换计算的附加相位被加到缩放的频谱上以维持因果关系。

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