||The mathematical and computational backgrounds of pattern recognition are the geometries in Hilbert space used for functional analysis and the applied linear algebra used for numerical analysis, respectively. Organs, cells and microstructures in cells dealt with in biomedical image analysis are volumetric data. We are required to process and analyse these data as volumetric data without embedding into higher-dimensional vector spaces from the viewpoint of object-oriented data analysis. Therefore, sampled values of volumetric data are expressed as three-way array data.
The aim of the talk is to develop relaxed closed forms for tensor principal component analysis (PCA) for the recognition, classification, compression and retrieval of volumetric data. The Tucker3-based tensor PCA of a three-mode tensor is used in behaviourmetric study and psychology for the extraction of relations among three entries as an extension of the usual principal component analysis for statistical analysis.
Tensor PCA derives the tensor Karhunen-Loeve transform, which compresses volumetric data, such as organs, cells in organs and microstructures in cells, preserving both the geometric and statistical properties of objects and spatial textures in the space.
Because of high-resolution sampling in the colour channels, images observed by a hyperspectral camera system are expressed by three-mode tensors. Hyperspectral images express spectral information of two- dimensional images on the imaging plane. The tensor PCA decomposition of hyperspectral images extracts statistically dominant information from hyperspectral images.