Multiresolution Analysis for the Restoration of Noisy X-ray Topographs

The principles of multiresolution analysis, which is based on wavelet theory, are reviewed, and it is shown that this technique is well adapted to the restoration of noisy images. In the analysis, a Gaussian white noise which propagates at all scales of the decomposition is assumed. In contrast to Fourier filtering, which is well localized in reciprocal space but not in direct space, multiresolution filtering allows one to suppress the noise without damaging the resolution. Using the example of an image recorded by a TV camera, it is shown that the technique allows one to obtain the same quality as when summing up to 64 frames. Multiresolution analysis may be used in all fields of science where images are damaged by a Gaussian noise.