Hardware-efficient algorithms for implementation of the GHM discrete multiwavelet transform kernels

In this correspondence, we discuss two efficient algorithms for the execution of forward (FDMWT) and inverse (IDMWT) discrete multiwavelet transform basic operations with reduced computational complexities. We used multiwavelet basis proposed by Geronimo, Hadrin, and Massopust (GHM). The direct implementation of GHM-FDMWT basic operation requires 23 multiplications and 19 additions. The direct implementation of GHM-IDMWT basic operation requires 23 multiplication and 16 additions. At the same time, our solutions allow designing the computation procedures, which take only 10 multiplications plus 15 additions for GHM-FDMWT basic operation and 10 multiplications plus 10 additions for GHM-IDMWT basic operation