chapter  5
30 Pages

Statistical Analysis of Image Differences by Wave Jet Decomposition

WithUrs Ε. Ruttimann, Michael Unser, Philippe Thévenaz, Chulhee Lee, Daniel Rio, Daniel W. Hommer

The wavelet transform will concentrate the signal into a small number of local coefficients, yielding favorable local signal-to-noise ratio (SNR) conditions and thus increased statistical signal detection power. The wavelet transform was implemented by the recursive method of Mallat using dyadic scale factors. The correlation structure of the coefficients depends on the autocorrelation of the process and the wavelet prototype. Orthogonality of the wavelets with respect to resolution enables an orthogonal partitioning of the signal space in terms of oriented blob sizes, and orthogonality with respect to discrete wavelet locations permits spatial localization of the signal within the resolution channels. Wavelet analysis is a flexible tool that is well-suited for the detection of weak signals in noisy images, as they typically arise in the biomedical field. The decomposition of the image spectrum into a set of minimally overlapping frequency bands permits taking advantage of the high SNR at low frequencies.