用于离散层析成像的快速Mojette变换
Fast Mojette Transform for Discrete Tomography
摘要：
本文提出了一种从一维投影图重建二维物体的新算法，该算法在计算上精确，在实验上实用。该算法对于NxN图像具有O（n log2 n）的计算复杂度，其中n = N^2，在存在噪声的情况下是鲁棒的，并且在重建过程中不产生伪影，如常规层析成像方法的情况。重建过程是近似自由的，因为对象被假定为离散的，并利用完全离散的Radon变换。通过在重建中引入冗余，可以进一步抑制投影数据中的噪声。可以控制精确重建所需的投影数量和对噪声的响应，而不包括算法的数字性质。数字投影是Mojette变换的投影，Mojette变换是离散线性图的一种形式。一个简单的分析映射的开发，这些投影精确地压缩成对称的周期性切片内的离散傅立叶变换。构造了一个新的数字角度集，它允许周期切片完全填充所有对象的离散傅立叶空间。提出了通过实验获得这些数字投影的技术，以实现快速和鲁棒的二维重建。
英文摘要：
A new algorithm for reconstructing a two dimensional object from a set of one dimensional projected views is presented that is both computationally exact and experimentally practical. The algorithm has a computational complexity of O(n log2 n) with n = N^2 for an NxN image, is robust in the presence of noise and produces no artefacts in the reconstruction process, as is the case with conventional tomographic methods. The reconstruction process is approximation free because the object is assumed to be discrete and utilizes fully discrete Radon transforms. Noise in the projection data can be suppressed further by introducing redundancy in the reconstruction. The number of projections required for exact reconstruction and the response to noise can be controlled without comprising the digital nature of the algorithm. The digital projections are those of the Mojette Transform, a form of discrete linogram. A simple analytical mapping is developed that compacts these projections exactly into symmetric periodic slices within the Discrete Fourier Transform. A new digital angle set is constructed that allows the periodic slices to completely fill all of the objects Discrete Fourier space. Techniques are proposed to acquire these digital projections experimentally to enable fast and robust two dimensional reconstructions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
