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.

研究人员开发工具和技术，以促进从压缩图像中准确重建光谱数据。 这种重建通常旨在从它们的傅立叶或频谱系数中重建灰度函数，并且必然需要图像跳跃不连续性位置的精确信息，以及通常通过投影进行的适当转换，以便可以在平滑区域中查看图像。 目前的边缘检测和投影重建技术在避免吉布斯振荡而不损害边缘周围图像的完整性（即拖尾）方面有些成功。 它们还可以检索在许多科学应用中出现的小尺度特征的信息。 然而，这种成功似乎是函数依赖的，并且很难保证分离器在所有情况下都是有效的，特别是当给定的数据字段中存在噪声时。 此外，它们很难扩展到更高的维度。 研究人员研究了改进边缘检测和投影方法的新方法，并最终创建了一种自动化的鲁棒性，用户友好，计算效率高，固有的多维图像重建方法。 研究结果表明，图像重建在许多科学领域中具有重要意义，高阶重建技术的发展既需要严格的数学证明理论结果，又需要计算的鲁棒性来保证实际应用。 所提出的活动表明，当小尺度特征在日益以图像为导向的社会中非常重要时，可以有效地获得高精度的图像。这些方法可以，例如，提高医学成像应用的诊断能力。 它们还可以用来更好地识别太阳活动中的小尺度特征，例如与洛克希德马丁公司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任何其他可视化至关重要的领域也很有用。 最后，本研究显著提高了压缩数据的能力，因为当提出特定的压缩要求时，可以优化重建参数。