The Search for a Good Basis

Wednesday, November 13, 1996 - 9:30am - 10:30am
Keller 3-180
Gilbert Strang (Massachusetts Institute of Technology)
An image corresponds to a very long vector, with one component for each pixel (three components for a color image). By a change of basis the long vector is concentrated into a much smaller number of components, ready for compression. We study the block Toeplitz matrix that produces a new basis from a bank of two filters -- lowpass and highpass. The filter coefficients determine the success of the compression. They also determine whether iteration of the lowpass filter (with rescaling) will lead to a useful wavelet basis for function spaces.

Thus the construction of wavelets comes from a problem in matrix analysis. Actual compression uses 4--5 iterations of the basis change.