Iterative Wedgelet Transform: An efficient algorithm for computing wedgelet representation and approximation of images

• We relax discrete wedgelet with a continuous edge model.
• We use non-linear least squares to iteratively estimate parameters of relaxed model.
• We use M-term image approximation as a test bed.
• Our method is fast and provides better quality comparing to moments-based approach.

The most common method to compute wedgelet transform is based on exhaustive search which requires assessment of all wedgelet atoms and hence is prohibitively slow. In this paper, the discontinuous edge model of the wedgelet is replaced by a continuous differentiable model to make gradient based estimation of the edge parameters possible. The proposed estimation based approach contributes to a surprisingly fast algorithm called Iterative Wedgelet Transform, which leads to a better tradeoff between quality and computation speed compared to the existing approaches.Performance of the proposed method is studied in the image approximation task and the results are compared with two other major algorithms, namely classical Wedgelet Transform and Moments-based Wedgelet Transform  . The iterative algorithm is shown to be much faster than classical wedgelet transform, O(N2log2N)O(N2log2N) given an N×NN×N image; and compared to the moments-based method exhibits higher precision.