Practical design of perfect-translation-invariant real-valued discrete wavelet transform

The real-valued tight wavelet frame having perfect translation invariance (PTI) has already proposed. However, due to the irrational-number distances between wavelets, its calculation amount is very large. In this paper, based on the real-valued tight wavelet frame, a practical design of a real-valued discrete wavelet transform (DWT) having PTI is proposed. In this transform, all the distances between wavelets are multiples of 1/4, and its transform and inverse transform are calculated fast by decomposition and reconstruction algorithms at the sacrifice of a tight wavelet frame. However, the real-valued DWT achieves an approximate tight wavelet frame.