| Versatile coding techniques are required to face the increasing demand of modern digital communication technology for efficient digital image transmission and storage schemes. In this dissertation, a unified framework for iterative image coding is introduced. In this framework, each basic feature of an image is individually encoded into a nonexpansive operator defined on the image space. This operator admits as fixed point set the class of images possessing the feature in question. Consequently, an image is associated with a family of operators which are specified during the encoding process, while the decoding process consists of finding a common fixed point of these operators. Decoding is achieved via a powerful parallel algorithm which proceeds by extrapolated relaxations of weighted averages of variable blocks of operators. This approach generalizes several coding techniques, in particular fractal coding--which employs a single contractive operator--and set theoretic coding--which employs convex projection operators. The effectiveness and the flexibility of the proposed operator theoretic framework is illustrated through numerical simulations on grayscale images. |
