Illustrate wavelet "filters"

2019-04-02, Jeff Fessler, University of Michigan

In [30]:
using MIRT
using LinearAlgebra: I
In [31]:
M,N = 16,8
T = Aodwt((M,N), level=1)[1]
T = Matrix(T)
@show isapprox(T'T, I)
jim(T)

isapprox(T' * T, I) = true
Out[31]:
1 128 1 128 - 0.50 - 0.25 0 0.25 0.50
In [32]:
tmp = reshape(T', M, N, :)
jim(tmp, padval=1, ncol=N)
Out[32]:
1 16 1 8 - 0.50 - 0.25 0 0.25 0.50
In [33]:
T2 = Aodwt((M,N), level=2)[1]
T2 = Matrix(T2)
@show isapprox(T2'T2, I)
jim(T2)

isapprox(T2' * T2, I) = true
Out[33]:
1 128 1 128 - 0.50 - 0.25 0 0.25 0.50
In [34]:
tmp = reshape(T2', M, N, :)
jim(tmp, padval=1, ncol=N)
Out[34]:
1 16 1 8 - 0.50 - 0.25 0 0.25 0.50