Department of Mathematics, University of California, Los Angeles, CA 90095, USA.
IEEE Trans Image Process. 2010 May;19(5):1259-68. doi: 10.1109/TIP.2009.2039660. Epub 2009 Dec 31.
We develop two new algorithms for tomographic reconstruction which incorporate the technique of equally-sloped tomography (EST) and allow for the optimized and flexible implementation of regularization schemes, such as total variation constraints, and the incorporation of arbitrary physical constraints. The founding structure of the developed algorithms is EST, a technique of tomographic acquisition and reconstruction first proposed by Miao in 2005 for performing tomographic image reconstructions from a limited number of noisy projections in an accurate manner by avoiding direct interpolations. EST has recently been successfully applied to coherent diffraction microscopy, electron microscopy, and computed tomography for image enhancement and radiation dose reduction. However, the bottleneck of EST lies in its slow speed due to its higher computation requirements. In this paper, we formulate the EST approach as a constrained problem and subsequently transform it into a series of linear problems, which can be accurately solved by the operator splitting method. Based on these mathematical formulations, we develop two iterative algorithms for tomographic image reconstructions through EST, which incorporate Bregman and continuative regularization. Our numerical experiment results indicate that the new tomographic image reconstruction algorithms not only significantly reduce the computational time, but also improve the image quality. We anticipate that EST coupled with the novel iterative algorithms will find broad applications in X-ray tomography, electron microscopy, coherent diffraction microscopy, and other tomography fields.
我们开发了两种新的层析重建算法，该算法结合了等斜率层析（EST）技术，允许对正则化方案（如全变差约束）进行优化和灵活实现，并可以纳入任意物理约束。所开发算法的基础结构是 EST，这是 Miao 于 2005 年首次提出的层析采集和重建技术，通过避免直接插值，可以准确地从有限数量的噪声投影中进行层析图像重建。EST 最近已成功应用于相干衍射显微镜、电子显微镜和计算机层析成像，以实现图像增强和减少辐射剂量。然而，EST 的瓶颈在于其由于计算要求较高而导致的速度较慢。在本文中，我们将 EST 方法表述为一个约束问题，并将其转换为一系列线性问题，这些问题可以通过算子分裂方法准确求解。基于这些数学公式，我们通过 EST 开发了两种用于层析图像重建的迭代算法，该算法结合了 Bregman 和连续正则化。我们的数值实验结果表明，新的层析图像重建算法不仅显著减少了计算时间，而且还提高了图像质量。我们预计，EST 与新的迭代算法相结合将在 X 射线层析成像、电子显微镜、相干衍射显微镜和其他层析成像领域得到广泛应用。
