Wavelet Levels With The Ellipse

The following graphs show the same effects of changing the levels as the previous post. These are different in that instead of using just the x points, the whole ellipse is used. The first graph is of the ellipse in green modeled by the wavelets in red using all of the j = 0,...6, levels of resolution. Following that graph is one using just the j = 0, level of resolution and finally one where the higher resolution wavelets are filtered so that they only use ones on one side of the interval.

Another issue is still that finding the coefficients of the wavelets has proved difficult when running the wavelet program on Linux. The problem stems from the inversion of a a matrix to calculate all of the coefficients. The matrix in question is 131x512 with a rank of 131, that I convert to a 512x512 matrix by adding zeros. In windows when it inverts the matrix it probably finds the pseudo matrix so I tried the same thing in Linux by using the vnl_svd::pinverse. However, the results from using the pseudo inverse were the sae as before and Linux might have tried to use the pseudo inverse instead of trying to do the regular one when I called vnl_matrix_inverse(). Another method available was vnl_svd::solve(vnl_vector const& y) to solve a linear system, although use of this just caused a segmentation fault. To remedy the problem now I am going to finish an iterative method that uses the inner product of the point data and the wavelet functions to create the appropriate coefficients.