使用变量分裂和约束优化的乘性噪声去除
Multiplicative Noise Removal Using Variable Splitting and Constrained Optimization
AI总结：
通过对数变换、变量分裂和增广拉格朗日框架，提出MIDAL算法，有效去除乘性噪声并取得速度和去噪性能的领先结果。
摘要：
乘性噪声（也称为散斑噪声）模型是研究相干成像系统（如合成孔径雷达、声纳、超声和激光成像）的核心。与标准高斯加性噪声场景相比，这些模型引入了两个额外的困难：（1）噪声与原始图像相乘（而非相加）；（2）噪声非高斯，常用瑞利和伽马分布。乘性噪声模型的这两个特征阻碍了大多数最先进算法的直接应用，这些算法旨在解决无约束优化问题，其目标函数包含两项：反映噪声加性和高斯性质的二次数据项（对数似然），加上凸（可能非光滑）正则化项（例如全变分或基于小波的正则化/先验）。在本文中，我们通过以下方式解决这些困难：（1）如其他作者所提议，通过取对数将乘性模型转换为加性模型；（2）使用变量分裂获得等价的约束问题；（3）使用增广拉格朗日框架处理该优化问题。一系列实验表明，我们提出的方法（命名为MIDAL，即乘性图像去噪增广拉格朗日法）在速度和去噪性能方面均取得了领先的结果。
英文摘要：
Multiplicative noise (also known as speckle noise) models are central to the study of coherent imaging systems, such as synthetic aperture radar and sonar, and ultrasound and laser imaging. These models introduce two additional layers of difficulties with respect to the standard Gaussian additive noise scenario: (1) the noise is multiplied by (rather than added to) the original image; (2) the noise is not Gaussian, with Rayleigh and Gamma being commonly used densities. These two features of multiplicative noise models preclude the direct application of most state-of-the-art algorithms, which are designed for solving unconstrained optimization problems where the objective has two terms: a quadratic data term (log-likelihood), reflecting the additive and Gaussian nature of the noise, plus a convex (possibly nonsmooth) regularizer (e.g., a total variation or wavelet-based regularizer/prior). In this paper, we address these difficulties by: (1) converting the multiplicative model into an additive one by taking logarithms, as proposed by some other authors; (2) using variable splitting to obtain an equivalent constrained problem; and (3) dealing with this optimization problem using the augmented Lagrangian framework. A set of experiments shows that the proposed method, which we name MIDAL (multiplicative image denoising by augmented Lagrangian), yields state-of-the-art results both in terms of speed and denoising performance.
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