High Order Reconstruction Using Spectral Methods

使用谱方法进行高阶重建

• 批准号: 0510813
• 负责人: Anne Gelb
• 金额: --
• 依托单位: Arizona State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-06-15 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0510813&HistoricalAwards=false
• 关键词: Order; Reconstruction; Using; Spectral; Methods

The investigators develop tools and techniques to facilitate the accuratereconstruction of spectral data from compressed images. Such reconstructiontypically aims at recreating gray-scale functions from their Fourier orspectral coefficients, and necessarily requires both precise informationof the location of the jump discontinuities of the images, as wellas an appropriate conversion, usually via projection, so that the imagecan be viewed in the regions of smoothness. Current techniques for edgedetection and projection reconstruction are somewhat successful in avoidingGibbs oscillations without compromising the integrity of the the imagesaround the edges (i.e. smearing). They also can retrieve information of smallscale features which arise in many scientific applications. However, thesuccess is seemingly function dependent, and it is difficult to chooseparameters that are robust to be effective in all cases, especiallywhen noise is present in the given data fields. Furthermore, they aredifficult to extend to higher dimensions. The investigators study newways to improve both edge detection and projection methods and ultimatelycreate an automated robust, user-friendly, computationally efficient, andinherently multi-dimensional image reconstruction method. The study teststhe resulting procedures against current image reconstruction methods on arange of applications.Image reconstruction is of critical importance in many scientific fields.The development of high order reconstruction techniques requires bothmathematical rigor to prove theoretical results and computationalrobustness to ensure practical usage. The proposed activities addresshow to obtain images efficiently and with high accuracy when small scalefeatures are of extreme interest in an increasingly image--oriented society.These methods can, for example, enhance the diagnostic ability in medicalimaging applications. They can also be used to better identify the smallscale features in solar activity such as those in connection with LockheedMartin's Solar Imaging Suite. This research is also useful for weatherforecasting models, earthquake and tsunami prediction, and any otherfields in which visualization is critical. Finally, this study stands tosignificantly enhance the ability to compress data, as it it will bepossible to optimize the reconstruction parameters when particularcompression requirements are proposed.

研究人员开发了工具和技术，以促进来自压缩图像的光谱数据的准确结构。 这样的重建旨在从其傅立叶或谱系系数中重新创建灰度函数，并且必然需要精确的信息，即图像的跳跃不连续性位置的位置，通常是通过投影进行适当的转换，因此在平滑度的区域中可以看到成像can。 当前用于挖出和投影重建的技术在避免振荡的情况下有点成功，而不会损害边缘图像的完整性（即涂抹）。 他们还可以检索许多科学应用中出现的小规模特征的信息。 但是，这些方法似乎取决于功能，并且在所有情况下都很难选择能够有效的选择参数，尤其是在给定的数据字段中存在噪声时。 此外，它们不足以扩展到更高的维度。 研究人员研究了新道路，以改善边缘检测和投影方法，并最终创建一种自动化，用户友好，计算高效且具有智能的多维图像重建方法。 该研究测试了对当前图像重建方法对应用程序的影响的过程。图像重建在许多科学领域至关重要。高级重建技术的开发需要两种严格的严格性才能证明理论结果和计算量，以确保实际使用。 当小规模效果在越来越多的图像中引起人们的极端兴趣时，提出的活动是有效地获得图像的，以高度准确地获得图像。例如，这些方法可以增强医学成像应用中的诊断能力。 它们还可以用来更好地识别太阳能活动中的小规模特征，例如与洛克希德玛丁的太阳成像套件有关的特征。 这项研究对于天气预报模型，地震和海啸预测以及可视化至关重要的任何其他场地也很有用。 最后，这项研究具有很高的意义，可以增强压缩数据的能力，因为在提出特定压迫要求时，可以优化重建参数。