模糊与泊松噪声下各向异性与各向同性全变差之差用于图像分割
Difference of Anisotropic and Isotropic TV for Segmentation under Blur and Poisson Noise
AI总结：
针对模糊和泊松噪声下的图像分割，提出基于MAP项和AITV正则化的SaT框架，采用ADMM求解，实验证明优于多种方法。
摘要：
本文旨在对受模糊和泊松噪声退化的图像进行分割。我们采用平滑与阈值（SaT）分割框架，该框架先寻找分段平滑解，随后通过$k$-均值聚类对图像进行分割。具体而言，在图像平滑步骤中，我们将Mumford-Shah模型中针对高斯噪声的最小二乘保真项替换为最大后验（MAP）项以处理泊松噪声，并引入各向异性与各向同性全变差（AITV）的加权差作为正则化项，以促进图像梯度的稀疏性。针对这一非凸模型，我们开发了一种特定的分裂方案，并利用近端算子应用交替方向乘子法（ADMM）。我们提供了收敛性分析以验证ADMM方案的有效性。在多种分割场景（灰度/彩色及多相位）上的数值实验表明，我们提出的方法优于包括原始SaT在内的多种分割方法。
英文摘要：
In this paper, we aim to segment an image degraded by blur and Poisson noise. We adopt a smoothing-and-thresholding (SaT) segmentation framework that finds a piecewise-smooth solution, followed by $k$-means clustering to segment the image. Specifically for the image smoothing step, we replace the least-squares fidelity for Gaussian noise in the Mumford-Shah model with a maximum posterior (MAP) term to deal with Poisson noise and we incorporate the weighted difference of anisotropic and isotropic total variation (AITV) as a regularization to promote the sparsity of image gradients. For such a nonconvex model, we develop a specific splitting scheme and utilize a proximal operator to apply the alternating direction method of multipliers (ADMM). Convergence analysis is provided to validate the efficacy of the ADMM scheme. Numerical experiments on various segmentation scenarios (grayscale/color and multiphase) showcase that our proposed method outperforms a number of segmentation methods, including the original SaT.
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。
