## 1 Introduction  
Digital shearography has the following advantages: full-field, non-contact, high-precision, non-destructive, and real-time measurement [1, 2, 3, 4, 5, 6]. Therefore, it is widely used in aerospace, civil engineering, transportation, machinery, materials, and other non-destructive testing fields [7, 8, 9, 10]. In digital shearography, a beam of coherent light is used to illuminate a rough object. The light beam scattered on the surface of an irregular object is divided into two transversely misplaced beams through the shear element and they interfere with each other in the overlapping area of the detection plane [11, 12, 13]. The wrapped phase pattern with a large amount of noise can be obtained by processing the interferograms recorded before and after the deformation of the object, respectively. Several phase denoising and unwrapping methods are used to obtain the phase information derived from the deformation with high sensitivity. Thus, defect detection and condition monitoring can be realized with the correlation model between the phase information and the physical quantity to be measured. In order to improve the accuracy of phase unwrapping, speckle noise needs to be filtered [14]. Several methods have been proposed to filter the speckle noise of the wrapped phase pattern, which mainly focuses on the spatial and transform domains. Spatial domain denoising uses various smoothing methods to process the value of each pixel to achieve the purpose of filtering. In terms of the spatial domains method, [PERSON], [PERSON] et al. [15]. proposed an average denoising method based on sine-cosine transform,transforming the discontinuous phase of the wrapped phase pattern into a continuous phase. [PERSON] et al. [16] proposed a sine-cosine transform average denoising method based on wavelet packet decomposition to calculate noise energy and determine the cycle threshold, limiting algorithm cycles. Transform domain denoising mainly transforms the noisy wrapped pattern through a particular transformation. It processes it with a specific method in the transform domain and inverse transform to obtain a denoised pattern. [PERSON] et al. [17] proposed a method combining sine-cosine transform with ideal low-pass filtering. [PERSON] et al. [18] proposed an improved adaptive total variation (TV) denoising method based on the block-matching and 3D filtering (BM3D) method for ESPI fringes. [PERSON] et al. [19] proposed that traditional wavelet filtering for shearography fringe patterns of composite materials can reduce noise and preserve details. [PERSON] et al. [20] proposed a sine-cosine transform and stationary wavelet transform method based on the db4 wavelet basis function and high penalty threshold, and it can improve the filtering efficiency. The phase reversal information may be destroyed in several of the above methods and affect the accuracy of defect detection. Several methods are too complex and inefficient for real-time and fast denoising. To the best of our knowledge, the sine-cosine transform average denoising method has been widely used for shearography interferometric patterns and speckle interferometric patterns. Still, the mask and iterations need to be selected according to the direction and fringe density in practical application. This paper proposes a novel and optimized sine-cosine transform wavelet threshold denoising method. In this method, the sym4 wavelet basis function is used according to the characteristics of the laser speckle. Meanwhile, the optimal wavelet decomposition level is ascertained according to the denoising effect. Combined with the speckle characteristics and noise intensity, a soft threshold global denoising method is also proposed to process the wavelet coefficients adaptively and fast. Thus, the complication of the threshold calculation process is decreased, therefore improving the calculation efficiency. This paper provides the filtering differences caused by different decomposition levels, and the optimal decomposition level is obtained through simulation.