The analysis of different Wavelets including novel Wavelet families based on atomic functions are presented, especially for ultrasound (US) and mammography (MG) images compression. This way we are able to determine with what type of filters Wavelet works better in compression of such images. Key properties: Frequency response, approximation order, projection cosine, and Riesz bounds were determined and compared for the classic Wavelets W9/7 used in standard JPEG2000, Daubechies8, Symlet8, as well as for the complex Kravchenko-Rvachev Wavelets ψ(t) based on the atomic functions up(t), fup (2)(t), and eup(t). The comparison results show significantly better performance of novel Wavelets that is justified by experiments and in study of key properties.