An improved pyramid algorithm for synthesizing 2-D discrete wavelet transforms

The pyramid algorithm (PA) has been shown very suitable for computing 2-D forward and inverse discrete wavelet transforms (DWT). In this paper, we present a new 2-D synthesis PA to improve some defects encountered in the classical PA algorithm that usually requires large latency, long computation time, and big memory space. Unlike the PA algorithm which computes a 2-D IDWT level by level, our proposed algorithm performs a 2-D DWT in word size. Thus, for processing an N×N 2-D IDWT with m levels and L-tap filters, the proposed algorithm needs a latency of 3m+4, computes only in N² clock cycles, and spends 2NL+4(m-1) memory space