We propose a novel denoising algorithm to reduce the Poisson noise that is typically dominant in fluorescence microscopy data. To process large datasets at a low computational cost, we use the unnormalized Haar wavelet transform. Thanks to some of its appealing properties, independent unbiased MSE estimates can be derived for each subband. Based on these Poisson unbiased MSE estimates, we then optimize linearly parametrized interscale thresholding. Correlations between adjacent images of the multidimensional data are accounted for through a sliding window approach. Experiments on simulated and real data show that the proposed solution is qualitatively similar to a state-of-the-art multiscale method, while being orders of magnitude faster.