Recent studies have demonstrated that the phase recovery from a single fringe pattern with closed fringes can be properly performed if the modulo 2pi fringe orientation is estimated. For example, the fringe pattern in quadrature can be efficiently obtained in terms of the orientational phase spatial operator using fast Fourier transformations and a spiral phase spectral operator in the Fourier space. The computation of the modulo 2pi fringe orientation, however, is by far the most difficult task in the global process of phase recovery. For this reason we propose the demodulation of fringe patterns with closed fringes through the computation of the modulo 2pi fringe orientation using an orientational vector-field-regularized estimator. As we will show, the phase recovery from a single pattern can be performed in an efficient manner using this estimator, provided that it requires one to solve locally in the fringe pattern a simple linear system to optimize a regularized cost function. We present simulated and real experiments applying the proposed methodology.
A comparison between the Wiener least square solution and the LMS algorithm in the FIR digital filter synthesis by adaptive modeling is presented. In the LMS case, a "cut and try" technique is less appropriate because changes in the weights of the cost function affect the desired frequency points as well as the frequency points where a good approximation of the frequency response was already obtained.
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