Phase retrieval using the wavelet transform

The 1-D phase retrieval problem is to reconstruct a signal given the modulus of its Fourier transform. Conventional solution techniques approximate the solution by discretizing this continuous problem. Our solution obviates this approximation by employing basis functions to better represent a continuous signal. In particular, we use wavelet bases because they provide a structure which permits the use of a fast algorithm and because they incorporate a priori knowledge of the signal. This paper develops our algorithm and illustrates its effectiveness with numerical examples