Phase retrieval of bandlimited functions for the wavelet transform
Rima Alaifari, Francesca Bartolucci, Matthias Wellershoff
Abstract
We study the recovery of square-integrable signals from the absolute values of their wavelet transforms, also called wavelet phase retrieval. We present a new uniqueness result for wavelet phase retrieval. To be precise, we show that any wavelet with finitely many vanishing moments allows for the unique recovery of real-valued bandlimited signals up to global sign. Additionally, we present the first uniqueness result for sampled wavelet phase retrieval in which the underlying wavelets are allowed to be complex-valued and we present a uniqueness result for phase retrieval from sampled Cauchy wavelet transform measurements.
Topics & Concepts
WaveletMathematicsPhase retrievalDiscrete wavelet transformStationary wavelet transformWavelet transformBandlimitingHarmonic wavelet transformUniquenessSecond-generation wavelet transformWavelet packet decompositionCascade algorithmMathematical analysisAlgorithmPattern recognition (psychology)Fourier transformArtificial intelligenceComputer scienceSeismic Imaging and Inversion TechniquesAdvanced X-ray Imaging TechniquesImage and Signal Denoising Methods