To improve the accuracy of fringe projection profilometry for a single deformed pattern, an instantaneous phase retrieval method is proposed using a wavelet ridge section and an adaptive bandpass filter based on dyadic wavelets. First, we present a concept and assumption named wavelet ridge section to depict the instantaneous phases of the deformed fringe signals, which are also degraded by noise, and then introduce a formula to calculate the width of the wavelet ridge section. Furthermore, an adaptive bandpass filter is designed for extracting the wavelet subsignals corresponding to the wavelet ridge sections to reconstruct the analytical signal. Finally, the instantaneous phase of the distorted fringe pattern is effectively retrieved. All parameters of our method are designed to be adaptive for different fringe patterns. Our experiments indicate that the proposed method is effective for measurements and outperforms other existing mainstream wavelet transform profilometry techniques, not only in accuracy but also in noise suppression performance.