3D Microscopy Deconvolution using Richardson-Lucy Algorithm with Total Variation Regularization
3D Microscopy Deconvolution using Richardson-Lucy Algorithm with Total Variation Regularization
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发表时间：
2004
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通讯作者：
N. Dey;L. Blanc-Féraud;C. Zimmer;P. Roux;Z. Kam;Jean-Christophe Olivo-Marin;J. Zerubia
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作者：
N. Dey;L. Blanc-Féraud;C. Zimmer;P. Roux;Z. Kam;Jean-Christophe Olivo-Marin;J. Zerubia
共焦激光扫描显微镜是一种功能强大且日益流行的生物标本3D成像技术。然而，所获取的图像由于离焦光的模糊和由于光子限制检测的泊松噪声而劣化。已经提出了几种去卷积方法来减少这些退化，包括Richardson-Lucy迭代算法，该算法计算适合泊松统计的最大似然估计。然而，该算法不一定收敛到合适的解决方案，因为它往往会放大噪声。如果它与正则化约束（关于数据的一些先验知识）一起使用，Richardson-Lucy正则化了一个精心选择的约束，总是收敛到一个合适的解决方案。在这里，我们建议将联合收割机的Richardson-Lucy算法与正则化约束的基础上总变分，其平滑避免振荡，同时保持对象的边缘。我们在模拟和真实的图像上表明，这种约束在视觉上和使用定量措施上都改善了反卷积结果。我们比较了几种著名的反卷积方法，如标准的Richardson-Lucy（无正则化），Richardson-Lucy与Tikhonov-Miller正则化，以及基于梯度的加法算法。
Confocal laser scanning microscopy is a powerful and increasingly popular technique for 3D imaging of biological specimens. However the acquired images are degraded by blur from out-of-focus light and Poisson noise due to photon-limited detection. Several deconvolution methods have been proposed to reduce these degradations, including the Richardson-Lucy iterative algorithm, which computes a maximum likelihood estimation adapted to Poisson statistics. However this algorithm does not necessarily converge to a suitable solution, as it tends to amplify noise. If it is used with a regularizing constraint (some prior knowledge on the data), Richardson-Lucy regularized with a well-chosen constraint, always converges to a suitable solution. Here, we propose to combine the Richardson-Lucy algorithm with a regularizing constraint based on Total Variation, whose smoothing avoids oscillations while preserving object edges. We show on simulated and real images that this constraint improves the deconvolution results both visually and using quantitative measures. We compare several well-known deconvolution methods to the proposed method, such as standard Richardson-Lucy (no regularization), Richardson-Lucy with Tikhonov-Miller regularization, and an additive gradient-based algorithm.