EOSC 513: Imaging and Estimation with Wavelets Organizational meeting: time: Wednesday January 5 3, 3:00 PM location: room EOS EAST-302 Boardroom

This course reviews the application of Wavelets and related transforms (Curvelets/Contourlets) to edge-preserved imaging and estimation with applications to (geophysical) data analysis, (seis- mic) imaging, estimation and inversion. These techniques are important for areas in Science and Engineering where data is non-stationary, noisy and contains edges (singularities) that carry important information. Book: Mallat's "A Wavelet tour of signal processing" will be used extensively together with some of the latest papers on non-seperable Wavelets such as Curvelets. Topics: Edge/singularity analysis by the Continuous Wavelet Transform; Construc- tion of orthogonal Wavelet Bases and shift-invariant Frames from Splines Unser (1999a), Coifman and Donoho (1995); Design of non-linear Estimators by (iterative) Thresholding Daubechies et al. (2004); Construction of new non-separable Wavelets such as Curvelets00; Decomposi- tion of images into Redundant Dictionaries with sparseness ('1) constraints (Basis and Match- ing Pursuit Chen et al. (2001), Morphological Componentent Analysis Starck et al. (2004)) Applications: Scaling of Seismic Images Herrmann (2001b, 2005), Herrmann and Bernabe (2004); Sparseness and continuity enhanced Imaging and Estimation Herrmann and Moghad- dam (2005); (Seismic) Deconvolution R. Neelamani and Baraniuk (2002), Daubechies et al. (2004); Image separation Starck et al. (2004), Herrmann and Verschuur (2004) and hands-on examples using Donoho's WaveLab, Chen's Atomizer and CurveLab (to be released early 2005). Prerequisite: Some undergraduate Signal Processing, Linear Algebra, Statistics and some knowledge on Wavelets (e.g. ECE 586) will be useful. For further information please check http://www.eos.ubc.ca/~felix/Teaching/Wavelets/EOSC513/2005/