In this paper we present a general framework for the approximation of the volume rendering integral using multiresolution spaces. Instead of solving the integral over the original volume data set we first project it into a wavelet basis. The final integration process is then performed on the resulting coefficients directly. Depending on the used basis functions a large number of coefficients can be neglected while still achieving accurate results. This leads to a drastic reduction in the amount of memory used during the rendering process. Furthermore, this sparse representation can be integrated into the rendering process, which is reflected in the overall rendering times.