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Conditioning of and algorithms for image reconstruction from irregular frequency domain samples.

机译：从不规则频域样本中重建图像的条件和算法。

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摘要

The problem of reconstructing an image from irregular samples of its 2-D DTFT arises in synthetic aperture radar (SAR), magnetic resonance imaging (MRI), computed tomography (CT), limited angle tomography, and 2-D filter design. The problem of determining a configuration of a limited number of 2-D DTFT samples also arises in magnetic resonance spectroscopic imaging (MRSI) and 3-D MRI.;This work first focuses on the selection of the measurement data. Since there is no 2-D Lagrange interpolation formula, sufficient conditions for the uniqueness and conditioning of the reconstruction problem are both not apparent. Kronecker substitutions, such as the Good-Thomas FFT, the helical scan FFT, and the 45° rotated support, unwrap the 2-D problem into a 1-D problem, resulting in uniqueness and insights into the problem conditioning. The variance of distances between the adjacent unwrapped 1-D DTFT samples was developed as a sensitivity measure to quickly and accurately estimate of the condition number of the system matrix. A well-conditioned configuration of DTFT samples, restricted to radial lines in CT or spirals in MRI, is found by simulated annealing with the variance sensitivity measure as the objective function. The preconditioned conjugate gradient method reconstructs the 1-D solution that is then rewrapped to a 2-D image. In unrestricted cases, 2-D DTFT configurations like a regular hexagonal pattern can be unwrapped to uniformly-spaced and perfectly conditioned 1-D configurations and quickly solved using an inverse 1-D DFT.;The next focus is on developing fast reconstruction algorithms. A non-iterative DFT-based method of reconstructing an image is presented, by first masking the 2-D DTFT samples with the frequency response of a filter that is zeroed at the unknown 2-D DFT locations, and then quickly deconvolving the filtered image using three 2-D DFTs. The masking filter needs to be precomputed only once per DTFT configuration. A divide-and-conquer image reconstruction method is also presented using subband decomposition and Gabor filters to solve smaller subband problems, leading to a quick unaliased low-resolution image or later to be recombined into the full solution. All methods are applied to actual CT data resulting in faster reconstructions than POCS and FBP with equivalent errors.
机译：从其二维DTFT的不规则样本重建图像的问题出现在合成孔径雷达（SAR），磁共振成像（MRI），计算机断层扫描（CT），有限角度断层扫描和二维过滤器设计中。在磁共振波谱成像（MRSI）和3-D MRI中也会出现确定有限数量的2-D DTFT样品的配置问题。这项工作首先着重于测量数据的选择。由于没有二维Lagrange插值公式，因此唯一性和重构问题的条件都不充分。 Kronecker替代品（例如，Good-Thomas FFT，螺旋扫描FFT和45°旋转支撑）将2D问题分解为1D问题，从而带来了独特性和洞察力。相邻未包装的1-D DTFT样本之间的距离方差被开发为一种灵敏度度量，可以快速而准确地估计系统矩阵的条件数。通过模拟退火（以方差敏感度度量作为目标函数），发现了DTFT样品的良好状态配置，其局限在CT的径向线或MRI的螺旋线中。预处理的共轭梯度方法将重建一维解，然后将其重新包装为二维图像。在不受限制的情况下，可以将2-D DTFT配置（例如规则的六边形图案）解开为均匀间隔且条件良好的1-D配置，并使用反一DFT快速解决;接下来的重点是开发快速重建算法。通过首先用在未知的2-D DFT位置为零的滤波器的频率响应来屏蔽2-D DTFT样本，然后快速对卷积后的图像进行反卷积，提出了一种基于DFT的非迭代方法来重建图像使用三个2-D DFT。每个DTFT配置仅需对屏蔽滤波器进行一次预计算。还提出了使用子带分解和Gabor滤波器解决较小子带问题的分而治之图像重建方法，从而获得快速的无锯齿低分辨率图像，或者稍后将其重新组合为完整解决方案。所有方法均适用于实际CT数据，与POCS和FBP相比，具有更快的重建速度，并且具有同等的误差。

著录项

  • 作者

    Lee, Benjamin Choong.;

  • 作者单位

    University of Michigan.;

  • 授予单位 University of Michigan.;
  • 学科 Engineering Electronics and Electrical.;Health Sciences Radiology.
  • 学位 Ph.D.
  • 年度 2010
  • 页码 175 p.
  • 总页数 175
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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