A gaussian random field with 8mm smoothness representing a pure noise PET image Simulated signal Signal plus noise thresholded. Note that by applying a threshold, the area of change can be detected but not the shape of the signal that is still subject to random fluctuations. Wavelets methods approach the problem of the analysis of statistical fields differently as they estimate the signal at any resolution among the random fluctuations . This is possible because wavelet bases provide adequate representation of the patterns of signal in the field. The application of wavelets to a statistical field is no different from the application of wavelet to images.
Statistical maps are just images with noise with variance equal to unity.
Height of the signal was 1. The result of the multi-scale hypothesis testing approach is a binary image. Pixels found significant at any smoothing are depicted in white. The result of wavelet filtering is the estimated map, i.e. the significant profiles of the image. The computation of the variance wavelet transform is more straightforward for statistical maps than it is for images.