Sparse representation and image classification with the shearlet transform
Classical 2D wavelet transforms have suboptimal compression performance due to its inability to generate sparse representation of discontinuities along lines. This thesis contains investigations of the shearlet transform which in contrast to classical 2D wavelet transforms is directional. The shearlet transform has optimal compression performance of so called "cartoon like images" and performs better than wavelet on real images too. Besides image compression the thesis concerns image classification using the shearlet transform as a component of the feature extraction procedure. Images are transformed to symmetric and positive definite (SPD) matrices. The space of SPD matrices is not a linear space but is on the other hand a Riemannian manifold with the structure that provides. For the classification task, a kernel support vector classifier is used that uses the log Euclidean metric on the space of SPD matrices. The thesis was written at Syntronic Software Innovations.