Redundant Ridgelet Transform and its Application to Image Processing

One of the problems encountered in image transmission is the cut-off or error of a bits chain at the moment of transmission. To protect the transmitted signal, it is necessary to couple quantized transform coding with a redundant transform. Ridgelet transform is a new directional resolution transform and it is more suitable for describing the signals with line or super-plane singularities. Finite ridgelet transform is a discrete orthonormal version of ridgelet transform proposed by Minh N.Do and Martin Vetterli. In this paper, we propose a new conception of redundant ridgelet transform, which we implement it mainly by controlling the ratio of the redundancy at the step of Radon transform in the ridgelet transform. We first briefly introduce the concept of ridgelet transform. Then, we illustrate finite ridgelet transform and the new method. Finally, the main features of the redundant ridgelet transform and its applications for image coding and image analysis are discussed.