Bonfert-Taylor Petra, Leblond Frederic, Holt Robert W, Tichauer Kenneth, Pogue Brian W, Taylor Edward C
Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459, USA.
J Opt Soc Am A Opt Image Sci Vis. 2012 Mar 1;29(3):321-30. doi: 10.1364/JOSAA.29.000321.
This paper is a theoretical exploration of spatial resolution in diffuse fluorescence tomography. It is demonstrated that, given a fixed imaging geometry, one cannot-relative to standard techniques such as Tikhonov regularization and truncated singular value decomposition-improve the spatial resolution of the optical reconstructions via increasing the node density of the mesh considered for modeling light transport. Using techniques from linear algebra, it is shown that, as one increases the number of nodes beyond the number of measurements, information is lost by the forward model. It is demonstrated that this information cannot be recovered using various common reconstruction techniques. Evidence is provided showing that this phenomenon is related to the smoothing properties of the elliptic forward model that is used in the diffusion approximation to light transport in tissue. This argues for reconstruction techniques that are sensitive to boundaries, such as L1-reconstruction and the use of priors, as well as the natural approach of building a measurement geometry that reflects the desired image resolution.
本文是对扩散荧光层析成像中空间分辨率的理论探索。结果表明，在固定成像几何条件下，相对于诸如蒂霍诺夫正则化和截断奇异值分解等标准技术，无法通过增加用于模拟光传输的网格节点密度来提高光学重建的空间分辨率。利用线性代数技术表明，当节点数量增加到超过测量数量时，正向模型会丢失信息。结果表明，使用各种常见的重建技术无法恢复此信息。有证据表明，这种现象与在组织光传输扩散近似中使用的椭圆正向模型的平滑特性有关。这表明需要采用对边界敏感的重建技术，如L1重建和先验的使用，以及构建反映所需图像分辨率的测量几何的自然方法。
