ORTHOGONAL AND SYMMETRIC HAAR WAVELETS ON THE THREE - DIMENSIONAL BALL by Andy Chow

ORTHOGONAL AND SYMMETRIC HAAR WAVELETS ON THE THREE-DIMENSIONAL BALL Andy Chow Master of Science Graduate Department of Computer Science University of Toronto 2010 Spherical signals can be found in a wide range of fields, including astronomy, computer graphics, medical imaging and geoscience. An efficient and accurate representation of spherical signals is therefore essential for many applications. For this reason, we derive a novel wavelet basis called 3D SOHO. It is the first Haar wavelet basis on the three-dimensional spherical solid that is both orthogonal and symmetric. These theoretical properties allow for a fast wavelet transform, optimal approximation, perfect reconstruction and other practical benefits. Experimental results demonstrate the representation performance of 3D SOHO on a variety of volumetric spherical signals, such as those obtained from medical CT, brain MRI and atmospheric model. The approximation performance of 3D SOHO is also empirically compared, against that of Solid Harmonic, 3D Haar wavelet transform and 3D discrete cosine transform.