Variational image decomposition for estimation of fringe orientation and density from electronic speckle pattern interferometry fringe patterns with greatly variable density

• We propose a new method for estimating fringe orientation and density.
• We propose a new image decomposition model the BL–HilbertBL–Hilbert model.
• It is easy to select parameters for our decomposed images with uniform density.

Fringe orientation and density are important properties of fringes. The estimation of fringe orientation and density from electronic speckle pattern interferometry (ESPI) fringe patterns with greatly variable density is still a challenging problem faced in this area. We propose an effective method based on variational image decomposition to estimate fringe orientation and density simultaneously. The BL–HilbertBL–Hilbert model is proposed to successfully decompose an ESPI fringe pattern with greatly variable density into two images: one only includes low density fringes and the other high density fringes. The density of the two decomposed images are uniform. We estimate the orientation and density of the two decomposed images by existing methods. The whole fringe orientation and density can be obtained by combining the corresponding results of the two decomposed images. We evaluate the performance of our method via application to the computer-simulated and experimentally obtained ESPI fringe patterns with greatly variable density and comparison with the widely used three methods.