Recovering convex edges of an image from noisy tomographic data

Goldenshluger A.; Spokoiny V.

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Recovering convex edges of an image from noisy tomographic data

机译：从嘈杂的层析图像数据中恢复图像的凸边

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摘要

We consider the problem of recovering edges of an image from noisy tomographic data. The original image is assumed to have a discontinuity jump (edge) along the boundary of a compact convex set. The Radon transform of the image is observed with noise, and the problem is to estimate the edge. We develop an estimation procedure which is based on recovering the support function of the edge. It is shown that the proposed estimator is nearly optimal in order in a minimax sense. Numerical examples illustrate reasonable practical behavior of the estimation procedure.

机译：我们考虑了从嘈杂的层析数据中恢复图像边缘的问题。假定原始图像沿紧凸集的边界具有不连续跳跃（边缘）。用噪声观察到图像的Radon变换，问题是估计边缘。我们开发了一种基于恢复边缘支持功能的估计程序。结果表明，所提出的估计器在极小极大意义上在顺序上几乎是最优的。数值例子说明了估计程序的合理实际行为。

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《IEEE Transactions on Information Theory》 |2006年第4期|p.1322-1334|共13页
作者
Goldenshluger A.; Spokoiny V.;
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正文语种 eng
中图分类无线电电子学、电信技术;
关键词
Radon transforms; edge detection; image denoising; image reconstruction; minimax techniques; tomography; Radon transform; convex edge recovery; image reconstruction; minimax estimation; noisy tomographic data; Edge detection; Radon transform; minimax estimation; optim;

机译：Radon变换;边缘检测;图像去噪;图像重建;最小极大值技术;断层扫描;Radon变换;凸边缘恢复;图像重建;最小极大值估计;噪声断层图像;边缘检测;Radon变换;最小极大值估计;最优化;

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专利

1. On the shape-from-moments problem and recovering edges from noisy Radon data [J] . Goldenshluger A., Spokoiny V. Probability Theory and Related Fields . 2004,第1期

机译：关于矩矩问题和从嘈杂的Radon数据中恢复边缘
2. On the shape–from–moments problem and recovering edges from noisy Radon data [J] . A. Goldenshluger, V. Spokoiny Probability Theory and Related Fields . 2004,第1期

机译：关于形变矩问题和从嘈杂的Radon数据中恢复边缘
3. An Adaptive Method for Recovering Image from Mixed Noisy Data [J] . Liu J, Huan ZD, Huang HY, International Journal of Computer Vision . 2009,第2期

机译：一种从混合噪声数据中恢复图像的自适应方法
4. Comparing GA with MART to tomographic reconstruction of ultrasound images with and without noisy input data [C] . Kodali S.P., Deb K., Munshi P., IEEE Congress on Evolutionary Computation;CEC '09 . 2009

机译：将GA和MART进行比较，可以对有无输入数据的超声图像进行层析成像重建
5. Convex and Non-Convex Optimizations for Recovering Structured Data: Algorithms and Analysis [D] . Cho, Myung. 2017

机译：恢复结构化数据的凸优化和非凸优化：算法和分析
6. Dimensionality reduced plug and play priors for improving photoacoustic tomographic imaging with limited noisy data [O] . Navchetan Awasthi, Sandeep Kumar Kalva, Manojit Pramanik, 2021

机译：维数减少了塞子和播放前沿用于改善具有有限噪声数据的光声断层图像
7. Recovering convex edges of an image from noisy tomographic data [O] . Er Goldenshluger, Vladimir Spokoiny 2006

机译：从嘈杂的层析成像数据中恢复图像的凸边
8. Development of a Portable X-Ray Computed Tomographic Imaging System for Drill-Site Investigation of Recovered Core [R] . Freifield, B. M., Kneafsey, T. J., Tomutsa, L., 2003

机译：便携式X射线计算机断层扫描成像系统的开发，用于回收岩心的钻探现场调查

Recovering convex edges of an image from noisy tomographic data

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