The fringe pattern obtained by optical interference is susceptible to speckle noise, which causes the fringes to be blurred to some extent. It is a critical step to achieve fringe smoothness while removing speckle noise. In this paper, we propose a new variable image decomposition model TGV–Hilbert–Shearlet, in which low-density fringes, high-density fringes, and noise are described by the total generalized variation (TGV) space, adaptive Hilbert space, and shearlet space, respectively. By assigning appropriate parameters, the image noise reduction and the fringe structural smoothness can be achieved optimally. We test the proposed method on five computer simulation ESPI fringe patterns and three experimentally obtained ESPI images. In addition, we compare it with BL-Hilbert-L 2 and Window Fourier Filter (WFF), which were proved to be effective in denoising. On the basis of regions marked in different images, the signal-to-noise ratio and the average equivalent number of looks are calculated to better characterize the denoising effect and fringe smoothness. Vast experiments show that the proposed TGV–Hilbert–Shearlet method can effectively reduce speckle noise in ESPI images, protect fringe structural information and improve image quality in all aspects compared with BL-Hilbert-L 2 and WFF methods.

中文翻译：

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使用 TGV–Hilbert–Shearlet 算法去除可变密度 ESPI 条纹图案中的斑点

通过光学干涉获得的条纹图案容易受到散斑噪声的影响，导致条纹在一定程度上变得模糊。这是在去除斑点噪声的同时实现条纹平滑的关键步骤。在本文中，我们提出了一种新的可变图像分解模型 TGV–Hilbert–Shearlet，其中低密度条纹、高密度条纹和噪声由总广义变异 (TGV) 空间、自适应希尔伯特空间和剪切波来描述。空间，分别。通过分配适当的参数，可以最佳地实现图像降噪和条纹结构平滑度。我们在五个计算机模拟 ESPI 条纹图案和三个实验获得的 ESPI 图像上测试了所提出的方法。此外，我们将其与 BL-Hilbert-L 2 和 Window Fourier Filter (WFF) 进行比较，这被证明是有效的去噪。在不同图像中标记的区域的基础上，计算信噪比和平均等效外观数，以更好地表征去噪效果和条纹平滑度。大量实验表明，与BL-Hilbert-L 2 和WFF 方法相比，所提出的TGV-Hilbert-Shearlet 方法可以有效降低ESPI 图像中的散斑噪声，保护条纹结构信息并提高图像质量。