12:30pm
EQuad E415
Title: Multi-layered Signal and Image Representation Application to Image Compression
Abstract: One of the greatest challenges for signal and image processing remains the development of efficient representations of signals and images. An efficient representation should permit to study directly the properties of the signal, and understand its structure. Equivalently, the representation should permit to describe the signal with the minimal amount of data.
The underlying assumption behind standard mathematical representations of signals assume that the basis (e.g. the Fourier basis, or a wavelet basis) is well adapted to most signals or images. Our approach follows a completely different direction: -- instead of forcing all signals to adapt to one single basis, we use a collection of libraries of bases to represent a single signal.
The main contribution of this work is a new paradigm for signal and image representation. We describe a new multi-layered representation technique for images. A signal is encoded as the superposition of one main approximation, and a sequence of residuals. The strength of the multi-layered method comes from the fact that we use different bases to encode the main approximation and the residuals. For instance, we can use: