Spectral decomposition and progressive reconstruction of scalar volumes

Modern 3D imaging technologies often generate large scale volume datasets that may be represented as 3-way tensors. These volume datasets are usually compressed for compact storage, and interactive visual analysis of the data warrants efficient decompression techniques at real time. Using well known tensor decomposition techniques like CP or Tucker decomposition the volume data can be represented by a few basis vectors, the number of such vectors, called the rank of the tensor, determining the visual quality. However, in such methods, the basis vectors used between successive ranks are completely different, thereby requiring a complete recomputation of basis vectors whenever the visual quality needs to be altered. In this work, a new progressive decomposition technique is introduced for scalar volumes wherein new basis vectors are added to the already existing lower rank basis vectors. Large scale datasets are usually divided into bricks of smaller size and each such brick is represented in a compressed form. The bases used for the different bricks are data dependent and are completely different from one another. The decomposition method introduced here uses the same basis vectors for all the bricks at all hierarchical levels of detail. The basis vectors are data independent thereby minimizing storage and allowing fast data reconstruction.