A Comparison of Two SIMD Implementations of the 2D Discrete Wavelet Transform

There are generally two algorithms to traverse an image to implement the 2D Discrete Wavelet Transform (DWT), namely Row-Column Wavelet Transform (RCWT) and Line-Based Wavelet Transform (LBWT). In the RCWT algorithm, the 2D DWT is divided into two 1D DWT: horizontal and vertical filtering. The horizontal filtering processes the rows of the original image and stores the wavelet coefficients in an auxiliary matrix. Thereafter, the vertical filtering phase processes the columns of the auxiliary matrix and stores the results back in the original matrix. In the LBWT algorithm, the vertical filtering is started as soon as a sufficient number of rows, as determined by the filter length, has been horizontally processed. In this paper, we provide answers to the following questions: first, which implementation is easier to vectorize using SIMD instructions? Second, which SIMD implementation provides more performance? Our initial results for Daubechies’ transform with four coefficients show that the SIMD implementation of the LBWT algorithm is more complicated than the SIMD implementation of the RCWT algorithm, while the former algorithm is 1.60 times faster than the latter algorithm for an image of size 4096× 4096.