Reconstruction from 2-D wavelet transform modulus maxima using projection

Wavelet transform modulus maxima can be used to characterise sharp variations such as edges and contours in an image. The authors analyse the a priori constraints present in the wavelet transform modulus maxima representation. A new projection-based algorithm which enforces all the a prior constraints in the representation is proposed. Quadratic programming is used to obtain a sequence which satisfies the maxima constraint. Thus realising the projection onto the maxima constraint space. To save computation, an approximate method to obtain a sequence which satisfies the maxima constraint is given. The new algorithm is shown to provide better solution than the original reconstruction algorithm of Mallat and Zhong (1992). The authors also propose a simple method to accelerate the algorithm. The acceleration is achieved by the incorporation of a momentum term which exploits the high correlation between the difference images between two consecutive iterations. The simulation results show that the proposed algorithm gives good reconstruction and the simple acceleration method can significantly improve the convergence rate