Image encoding using chaotic maps and strange attractors

We describe an application of nonlinear dynamical systems to image transformation and encoding. Our approach is different from the classical one where affine discrete maps are used. Similarly to classical fractal image compression, nonlinear maps use the redundancy in the image for compression. Furthermore, compression speed is enhanced whenever nonlinear maps have more than one attractor. Nonlinear maps having strange chaotic attractors can also be used to encode the image. In this case, the image will take the shape of the strange attractor when mapped under the nonlinear system. The procedure needs some precautions for chaotic maps, because of the sensitivity to initial conditions. Another possibility is to use strange attractors to hide the initial image using various schemes. For example, it is possible to hide the image using position permutation, value permutation, or both position and value permutations. We develop an algorithm to show that chaotic maps can be used successfully for this purpose. We also show that the sensitivity to initial conditions of chaotic maps forms the basis of the encryption strategy.