  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.
