Consistency proof of two denoising methods and the parameter selection of PDE filtering method for ESPI

Electronic speckle pattern interferometry (ESPI) is a nondestructive, whole-field optical measurement

technique. The removal of speckle noise is fundamental to extract measurement information accurately.

In this letter, two filtering methods based on the oriented feature of ESPI fringes, i.e., the second-order

oriented partial differential equation (SOOPDE) and oriented, regularized quadratic-cost function filtering

methods, are first proven to be consistent. An important question in solving partial differential equation,

i.e., how to select suitable parameters in an adaptive manner, is then discussed. The computer-simulated

and experimentally obtained ESPI fringe patterns and phase map are processed by the SOOPDE filtering

model with adaptive selective parameters. The qualitative and quantitative analyses demonstrate that the

parameters selected by the adaptive method are effective and suitable for the SOOPDE filtering model.