In this work we propose several parallel algorithms to compute the two-dimensional discrete wavelet transform (2D-DWT), exploiting the available hardware resources. In particular, we will explore OpenMP optimized versions of 2D-DWT over a multicore platform and we will also develop CUDA-based 2D-DWT algorithms which are able to run on GPUs (Graphics Processing Unit). The proposed algorithms are based on several 2D-DWT computation approaches as (1) filter-bank convolution, (2) lifting transform and (3) matrix convolution, so we can determine which of them better adapts to our parallel versions. All proposed algorithms are based on the Daubechies 9/7 filter which is widely used in image/video compression.