Image decomposition model Shearlet–Hilbert–L 2 with better performance for denoising in ESPI fringe patterns

In this paper, we propose an image decomposition model Shearlet–Hilbert–L2 with better performance for denoising in electronic speckle pattern interferometry (ESPI) fringe patterns. In our model, the low-density fringes, high-density fringes, and noise are, respectively, described by shearlet smoothness spaces, adaptive Hilbert space, and L2 space and processed individually. Because the shearlet transform has superior directional sensitivity, our proposed Shearlet–Hilbert–L2 model achieves commendable filtering results for various types of ESPI fringe patterns, including uniform density fringe patterns, moderately variable density fringe patterns, and greatly variable density fringe patterns. We evaluate the performance of our proposed Shearlet–Hilbert–L2 model via application to two computer-simulated and nine experimentally obtained ESPI fringe patterns with various densities and poor quality. Furthermore, we compare our proposed model with windowed Fourier filtering and coherence-enhancing diffusion, both of which are the state-of-the-art methods for ESPI fringe patterns denoising in transform domain and spatial domain, respectively. We also compare our proposed model with the previous image decomposition model BL–Hilbert–L2.