6.342 Wavelets, Approximation, and Compression

Spring 2009 (and Spring 2011, Spring 2013, …)

Lectures: MW 11:00-12:30 in 4-145

Credit: 12 (3-0-9) (Grad H)

Instructor: Vivek Goyal, vgoyal@mit.edu

TA: Watcharapan Suwansantisuk, wsk@mit.edu

Prerequisites:	18.06; and 6.341 or 6.450 (high proficiency in 18.06 and 6.011 can be plenty; interested students should inquire with the instructor)
Overview:	Hilbert space formulation of continuous-time and discrete-time signals. Sampling. Orthogonal and biorthogonal signal expansions. Uncertainty principles and the time-frequency plane. Two-channel filter banks, iterated filter banks, and discrete wavelet transforms. Multiresolution analysis. Wavelet bases, regularity, approximation properties, and nonlinear approximation. Basics of quantization and source coding. Compression, denoising, and other image processing using wavelets. Advanced topics from the current research literature.
Projects:	Several term projects from the past two offerings of the course have been very successful.  With additional work, they have led to papers and theses. These include (list still under construction): Beyond Thresholding: Analysis and Improvements for Deterministic Parameter Estimation B. I. Erkmen and V. K. Goyal, arXiv:0801.3490, 23 Jan 2008. Estimation of Channelized Features in Geological Media Using Sparsity Constraints Behnam Jafarpour, S.M. thesis, February 2008. Reconstruction of Channelized Facies Using Sparsity Constraints B. Jafarpour, V. K. Goyal. and W. T. Freeman, Proc. Soc. Exploration Geophysicists Annual Meeting (Las Vegas, NV), November 2008, pp. 1546-1550. Estimating Signals with Finite Rate of Innovation from Noisy Samples: A Stochastic Algorithm V. F. Y. Tan and V. K. Goyal, IEEE Trans. on Signal Processing, vol. 56, no. 10, pp. 5135-5146, October 2008. DOI: 10.1109/TSP.2008.928510 On the Construction of Invertible Filter Banks on the 2-Sphere B. T. T. Yeo, W. Ou and P. Golland, IEEE Trans. on Image Processing, vol. 17, no. 3, pp. 283-300, March 2008. Denoising Hyperspectral Imagery and Recovering Junk Bands using Wavelets and Sparse Approximation A. C. Zelinski, V. K. Goyal, Proc. IEEE Int. Geoscience and Remote Sensing Symp. (IGARSS) (Denver, CO), August 2006, pp. 387-390. DOI: 10.1109/IGARSS.2006.104

More information about the course:

Class Poster
Class Syllabus
Spring 2007 Stellar Website

Spring 2009 Stellar Website (almost empty for now)