# Denoising of Wrapped Phase in Digital Speckle Shearography Based on Convolutional Neural Network
###### Abstract  
Speckle-shearing technology is widely used in defect detection due to its high precision and non-contact characteristics. However, the wrapped-phase recording defect information is often accompanied by a lot of speckle noise, which affects the evaluation of defect information. To solve the problems of traditional denoising algorithms in suppressing speckle noise and preserving the texture features of wrapped phases, this study proposes a speckle denoising algorithm called a speckle denoising convolutional neural network (SDCNN). The proposed method reduces the loss of texture information and the blurring of details in the denoising process by optimizing the loss function. Different from the previous simple assumption that the speckle noise is multiplicative, this study proposes a more realistic wrapped image-simulation method, which has better training results. Compared with representative algorithms such as BM3D, SDCNN can handle a wider range of speckle noise and has a better denoising effect. Simulated and real speckle-noise images are used to evaluate the denoising effect of SDCNN. The results show that SDCNN can effectively reduce the speckle noise of the speckle-shear wrapping phase and retain better texture details.  
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complexity. The windowed Fourier transform (WTF) [14] has demonstrated efficacy in denoising wrapped phases, albeit requiring substantial adjustments and processing time. The sine/cosine average filter (SCAF) [15] is introduced to address speckle noise by separate denoising of the numerator and denominator of the arctangent, effectively resolving the phase \(2\pi\) discontinuity and noise issues.  
As neural networks progress, more study is focused on speckle-noise reduction. In Reference [16], CNNs are used to denoise DSPI fringe maps in batches, effectively reducing medium-level noise in fringes but potentially causing slight edge blurring. Reference [17], based on DnCNN [18], proposed a method for the speckle suppression of digital holography, which is effective for noise reduction of stripes with different noise levels, but it is not good for edge recovery of stripes. Reference [19] proposed a DBDNet based on dilated blocks, which effectively recovers DSPI-striped images with high noise levels. In Reference [20], a lightweight residual dense neural network, LRDUNet, is proposed for ESPI stripe noise reduction based on U-Net. While effective in noise reduction, a single model is tasked with handling stripe maps of varying noise levels.  
To denoise the wrapped phase, this study introduces a processing approach for denoising interferograms acquired through DSSPI. To address the issues of noise and boundary blurring within the wrapped phase, we propose a deep-learning technique for denoising the sine and cosine fringes. Subsequently, the denoised sine and cosine fringes are processed using the arctangent function to obtain an improved wrapped phase. Simulation and experimental results demonstrate the effectiveness of this method in successfully suppressing speckle noise and eliminating the boundary blurring associated with defects.