L~1-Based decomposition and reconstruction algorithms and W-matrices

摘要

Mallat's decomposition and reconstruction algorithms are very important in the field of wavelet theory and its application to signal processing. Wavelet theory is based on L~2(R) space and the classical mean square error is employed naturally in many relevant applications. In the recent years, it is understood that the L~2 space is not always the best one for all applications. Therefore, wavelet theory and its approximation properties were also studied in L~1(R) by many researchers. The orthogonality was also developed in L~1 space in our previous work. In this paper, Based on our previous work on L~1 orthogonality, two novel decomposition and reconstruction algorithms, called MAE and ETO algorithms, are discussed in detail. The exact reconstruction algorithms are also established by extending the concept of W-matrices. Experiments are conducted to support these new algorithms.