Speckle removal in variable density ESPI fringe patterns with TGV–Hilbert–Shearlet algorithm

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.