An inner product space approach to image coding by contractive transformations

Consideration is given to modeling of arbitrary digital gray tone images as the fixed points of contractive transformations on the image space. The transformation is designed to exploit a form of image redundancy called piecewise self-similarity. Results from inner product space theory are used to optimize the transformation within a class of affine transformations. The resulting transformation is described by a small amount of information compared to the original image, and its piecewise self-similar fixed point, found by successively iterating the transformation from any initial image, is close to the original image. Results are improved compared to earlier results with this technique