Marc Raimondo School of Mathematics and Statistics, University of Sydney Wavelet deconvolution in a periodic setting Wednesday 26th, May 14:05-15:55pm, Carslaw Building Room 359. Deconvolution problems are naturally represented in the Fourier domain, while thresholding in wavelet bases is known to have broad adaptivity properties. We study a method which combines both Fast Fourier and Fast wavelet transforms and can recover a blurred function observed in white noise with $O(n(\log n)^2)$-steps. In the periodic setting, the method applies to most deconvolution problems, including certain ``boxcar'' kernels, important as a model of motion blur, but having poor Fourier characteristics. Asymptotic theory informs choice of tuning parameters, and yields adaptivity properties for the method over a wide class of error measures and function classes. The method is tested on simulated lidar data suggested by underwater remote sensing. Both visual and numerical results show an improvement over competing approaches. Finally, the theory behind our estimation paradigm gives a complete characterisation of the 'Maxiset' of the method: the set of functions where the method attains a near-optimal rate of convergence for a variety of $L^p$ loss functions.