DIRECT RECONSTRUCTION METHOD FOR WAVELET TRANSFORM EXTREMA REPRESENTATION

In contrast to the iterative reconstruction algorithm of projections o nto convex sets (Mallat and coworkers, 1992; Liew and Nguyen, 1995; Cv etkovic and Vetterli, 1995) a noniterative method that completely solv es the problem of reconstructing from the wavelet transform extrema re presentation is presented for the first time. The solution obtained by the proposed method is mathematically consistent and is indistinguish able from the true solution, i.e. both give the same representation. T he proposed method consists of first finding a least-squares solution in the space spanned by the wavelet sampling bases. An orthogonal comp onent that is to be added to the leastsquares solution to form a consi stent solution is then found by solving a set of linear inequalities s pecified by the a pi iori information in the representation using the linear programming technique. Numerical results presented show that th e reconstructions are of good quality.