Wavelet decomposition and recomposition of echographic images

The basic elements of the wavelet representation are described. Each step of the decomposition corresponds to a certain scale analysis. It is then possible to select the significative objects before the recomposition of the signal. Thus objects with different sizes can be distinguished. If the speckle of an echographic image and its associated signal-to-noise ratio are known, the speckle can be removed after a comparison with the level of the component corresponding to the speckle size. For different scales, the components may correspond to anatomic objects, texture, or edges. The differentiation of these objects can produce images (after reconstruction) where only the useful information is present. Extended to 2D functions and applied to echographic images, this decomposition-segmentation-recomposition process extracts objects in the axial and transverse directions. The resulting images give a good representation of objects without any loss of resolution, since the speckle is well removed