Alim, UsmanHoracsek, Joshua2017-09-272017-09-2720172017Horacsek, J. (2017). Compactly Supported Biorthogonal Wavelet Constructions on the A-star Lattice and their Application to Visualization (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/25366http://hdl.handle.net/11023/4146In this dissertation, a family of compact biorthogonal wavelet filter banks that are tailored to the geometry of the A-star lattice are derived. Our application of interest is on the three dimensional A-star or {\em body centered cubic} (BCC) lattice. While the BCC lattice has been shown to have superior approximation properties for volumetric data when compared to the Cartesian cubic (CC) lattice, there has been little work in the way of designing wavelet filter banks that respect the geometry of the BCC lattice. Since wavelets have applications in signal de-noising, compression, and sparse signal reconstruction, these filter banks are an important tool that addresses some of the scalability concerns presented by the BCC lattice. We use these filters in the context of volumetric data compression and reconstruction and qualitatively evaluate our results by rendering images of isosurfaces from compressed data.engUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.Computer ScienceWaveletsVolumetric Datamaster thesishttp://dx.doi.org/10.11575/PRISM/25366