************************************************************************ COURSE ANNOUNCEMENT FALL 1999 EECS 658 FAST ALGORITHMS FOR SIGNAL PROCESSING Tuesdays & Thursdays 10:30-Noon 3424 EECS INSTRUCTOR: Professor Andrew E. Yagle http://www.eecs.umich.edu/~aey PREREQUISITE: EECS 451 (digital signal processing) or its equivalent. EECS 501 (probability and random processes) is helpful but NOT required. ************************************************************************ WHY SHOULD YOU TAKE THIS COURSE? 1. FAST CONVOLUTIONS (Cook-Toom, Winograd; NOT just using the FFT!): To compute wavelet transforms using Mallat's fast wavelet algorithm. Also to perform digital filtering with maximum efficiency. 2. FAST 2-D CONVOLUTIONS (nesting, splitting, polynomial transforms): Image filtering is where efficiency of these really pays off. Also for some iterative algorithms such as the EM algorithm. 3. FAST FOURIER TRANSFORMS (Good-Thomas, Winograd, split radix, NOT 2^N!): To map 2-D image processing inverse problems to 1-D inverse problems. Very useful for phase retrieval and blind deconvolution. 4. NUMBER THEORETIC TRANSFORMS (NTTs) (Mersenne, Fermat): For VERY fast convolutions of integer-valued digital signals. 5. FAST MATRIX MULTIPLICATION (using divide-and-conquer, NTTs, wavelets): Use for iterative algorithms for solving linear systems of equations. 6. WAVELET-BASED MATRIX INVERSION (sparsification, fast algorithms): Useful in electromagnetics problems (Green's functions). 7. LEVINSON AND SCHUR ALGORITHMS AND GENERALIZATIONS OF THEM: a) 1-sided and 2-sided AR linear prediction; b) correlation and covariance least-squares and ARMA linear prediction; c) spectral factorization and matrix factorization; d) 2-D linear prediction for image coding and restoration; e) inverse scattering (reconstruction of medium from probing impulse); f) inverse scattering with unknown source signal (blind problem). 8. 2-D PHASE RETRIEVAL AND BLIND DECONVOLUTION INVERSE PROBLEMS: To deblur an image when the blurring function is unknown. 9. CURRENT AREAS OF RESEARCH (IEEE Trans. Signal Proc. and Image Proc.): All of the above topics. 10. OFFERED: Last time: Fall 1995. Next time: ??? Don't miss this chance! ************************************************************************ GRADING: Midterm exam: 25% TEXTBOOK: Handouts and papers given in class. Final exam: 25% USEFUL: R.E. Blahut, "Fast Algorithms for Problem sets: 25% Digital Signal Processing," Addison-Wesley. Project: 25% Total: 100% Sign up now, or make wretched your destiny! ************************************************************************