Non-separable two dimensional wavelets and their filter banks in polar coordinates

The problems encountered in development and implementation of orthonormal two dimensional wavelet bases and their filter banks in polar coordinates are addressed. These wavelets and filter banks have possible applications in processing signals that are collected by sensors working in the polar coordinate system, such as biomedical and radar generated signals. The relationship between the space of measurable, square-integrable functions on the punctured polar coordinate system L^2(P) and space of measurable, square-integrable functions on the rectangular plane L^2(R^2) is developed. This allows us to develop complete wavelet bases in a more convenient and familiar surrounding of L^2(R^2) and to transport this theory to L^2(P). Corresponding filter banks are also developed. The implementation of wavelet analysis of punctured polar plane is discussed. An example of wavelet bases, filter banks, and implementation is provided.