Daniel Otero, PhD Candidate
Department of Applied Mathematics, University of Waterloo
Function-valued mappings and SSIM-based optimization: two alternative approaches to imaging
In this talk we present two novel approaches to carry out image processing tasks, namely, function-valued mappings (FVMs) and structural similarity index measure (SSIM)-based optimization. With FVMs, also known as Banach-valued functions in the literature, we propose a different way of representing complex datasets, e.g., hyperspectral and diffusion magnetic resonance images, which are usually represented as vector-valued functions. The infinite dimensionality of the range of FVMs offers interesting possibilities for modelling different kinds of datasets, as well as making possible the generalization of the classical fractal and Fourier transforms. As for SSIM-based optimization, we present a general framework for solving optimization problems in which the SSIM is employed as a fidelity term. This framework allows us to solve optimization problems involving the SSIM that had not been addressed before, and also provides an alternative way of performing some of the well known Euclidian-based image processing tasks: e.g., sparse reconstruction, denoising, zooming, etc.. Potential and current developed applications of these two approaches to imaging are also discussed.