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                       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.
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                 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!
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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!
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