Error Detection in 2-D Discrete Wavelet Lifting Transforms

Discrete Wavelet transform is a powerful mathematics technique which is being adopted in different applications including physics, image processing, biomedical signal processing, and communication. Due to its pipelined structure and multirate processing requirements, a single numerical error in one stage can easily affect multiple outputs in final result. In this paper, we propose a weighted checksum code based fault tolerance technique for 2-D discrete wavelet transform. The technique encodes the input array at the 2-D discrete wavelet transform algorithm level, and algorithms are designed to operate on encoded data and produce encoded output data. The proposed encoding technique can perfectly fit into the lifting structure and existing general purpose 2-D discrete wavelet lifting VLSI architectures, without significant modification and overhead. We present the mathematics proof of this coding technique and show this technique can detect the errors in 2-D wavelet transforms. The hardware overhead using this technique is significantly lower than existing methods.