Phase retrieval from fringe pattern with 1-D discrete wavelet transform

This paper proposes a novel method to obtain frequency modulation (FM) signals from a single fringe pattern for phase retrieval. First, a 1D discrete Meyer wavelet is employed to decompose the pattern image signal row by row and the soft-thresholding approach is applied to remove noise. The low frequency coefficients of the wavelet decomposition are then set to 0, and the signal is reconstructed. Moreover, the optimal wavelet decomposition level is adaptively determined using a cost function-based method. The reconstructed signal, which no longer contains a background component, is normalized using a nonlinear and piecewise normalization method. The proposed method is faster and more accurate than some other phase retrieval approaches, which is illustrated with two test cases.

► We reconstruct the signal through setting the approximate coefficients of wavelet decomposition to 0.
► We propose nonlinear and piecewise normalization method, which can normalize the amplitude of signal to 1 without changing phase.
► We use a cost function to determine the optimal wavelet decomposition level adaptively.