An optimization of the relaxed signal adapted wavelet by semidefinite programming techniques

In this paper, we consider a frequency response optimization of the relaxed signal-adapted wavelet which achieves its coding-gain at arbitrarily specified level (not necessarily achieves the maximal coding gain as seen in the standard signal-adapted wavelet). Thanks to the flexibility generated by the relaxation, we can optimize the frequency response of its filter bank in practically important senses. We propose an efficient approach based on the Kalman-Yakubovich-Popov (KYP) lemma and the semidefinite programming.