A fast algorithm for a total variation based phase demodulation model

Abstract

In this paper we introduce fast numerical algorithms for the solution of the model. For each variable, background illumination, amplitude modulation and phase map, we develop a fixed point method. Then, we write all three algorithms in the same framework and analyze their convergence rates, local smoothing factors by means of local Fourier analysis and present experimental evidence of their performance on synthetic and real world problems.

Augmented Lagrangian method for a total variation-based model for demodulating phase discontinuities

“…Recently, a fixed point (FP) method to speed up the numerical solution of this model was proposed. 9 This FP method shows a good performance solving the model presented in Legarda-Saenz et al. ; 8 however, similar to other methods based on the TV approach, the FP method performance is dramatically reduced for problems highly anisotropic.…”

“…The numerical solution proposed in Legarda-Saenz et al 8 was a gradient descent scheme which is very slow and therefore a large number of iterations are necessary to reach an adequate solution. To speed up the convergence, a FP method 10,11 was proposed recently: 9 First, equation (3) is written in the following way…”

“…As can be observed in the first term of equation (6), it is not possible to separate the term ψboldxk+1 from the cosine function. To fix this, the cosine function is linearized in the following way and the proposed FP iteration is given by 9 …”

“…Brito-Loeza et al. 9 provide a detailed explanation of the convergence proof and the numerical performance of this method.…”

Augmented Lagrangian method for a TV-based model for demodulating phase discontinuities

“…Recently, it was proposed a fixed point method to speed up the numerical solution of this model. 9 This fixed point method shows a good performance solving the model presented in reference 8; however, similar to other methods based on the TV approach, the fixed point method performance is dramatically reduced for problems highly anosotropic.…”