Wavelet Edge Detection

Hi,
I'm trying to find edges in a 1d function using wavelets. In my application
I need to invert a diagonal matrix whose diagonal elements are the time
domain coefficients of the wavelet. I'm using a Gaussian wavelet and the
scale I need is so that it dies down fast. So most of the coefficients are
zero. This makes the diagonal matrix non-invertible. But I need an
invertible matrix(The reason is specific to my application and is not
relevant here) Can anyone help?