基于多尺度PCA控制空间缩减的二值图像重构优化框架
A Multiscale Optimization Framework for Reconstructing Binary Images using Multilevel PCA-based Control Space Reduction
摘要：
提出并验证了一种有效的计算方法，用于生物医学应用中二元型物理性质模型的最优重构参数。该方法包括基于梯度的多尺度优化与多级控制空间减少，通过使用主成分分析（PCA），再加上动态控制空间放大。降维控制在精细和粗略尺度下可互换使用，以累积优化进度并减轻两种尺度下的副作用。通过所提出的用于校准某些参数以增强优化算法的性能的过程来实现灵活性。减小控制空间的大小提供了伴随的梯度在这两个尺度上获得方便的应用程序，该算法的模型更高的复杂性，并在生物医学科学中的广泛的问题。这种技术被证明优于常规的基于梯度的方法，适用于精细尺度的二进制图像的质量和计算时间。完整的计算框架的性能进行了测试，在应用程序中的电阻抗断层扫描（EIT）的癌症检测的2D逆问题。结果表明，新方法的有效性能和它的高潜力，最大限度地减少假阳性筛选的可能性，提高整体质量的EIT为基础的程序。
英文摘要：
An efficient computational approach for optimal reconstructing parameters of binary-type physical properties for models in biomedical applications is developed and validated. The methodology includes gradient-based multiscale optimization with multilevel control space reduction by using principal component analysis (PCA) coupled with dynamical control space upscaling. The reduced dimensional controls are used interchangeably at fine and coarse scales to accumulate the optimization progress and mitigate side effects at both scales. Flexibility is achieved through the proposed procedure for calibrating certain parameters to enhance the performance of the optimization algorithm. Reduced size of control spaces supplied with adjoint-based gradients obtained at both scales facilitate the application of this algorithm to models of higher complexity and also to a broad range of problems in biomedical sciences. This technique is shown to outperform regular gradient-based methods applied to fine scale only in terms of both qualities of binary images and computing time. Performance of the complete computational framework is tested in applications to 2D inverse problems of cancer detection by the electrical impedance tomography (EIT). The results demonstrate the efficient performance of the new method and its high potential for minimizing possibilities for false positive screening and improving the overall quality of the EIT-based procedures.
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