Image decomposition based on wavelet and variational functional
Song Guo-xiang · Systems engineering and electronics · 2007
An algorithm to decompose an image into two components u and v is constructed.The first component u belongs to B11(L1) and it contains geometric information while the second part v is in the dual spaceB-1∞(L∞),which contains signals with oscillatory patterns of zero mean,such as texture and noise.The decomposition by minimizing a variational functional in the wavelet domain which depends on the two variables u and v.To get the minimizer,a new iterative projection algorithm to obtain the sequence of image decomposition components in the wavelet domain and get the final image decomposition components by reconstructing the limit of the sequence.At the same time,the convergence of the algorithm is shown.Numerical results are presented,showing that the new model decomposes better a given image,possible noisy,than the Daubechies-Teschke model.