Low-Memory Wavelet Transforms for Wireless Sensor Networks: A Tutorial

The computational and memory resources of wireless sensor nodes are typically very limited, as the employed low-energy microcontrollers provide only hardware support for 16 bit integer operations and have very limited random access memory (RAM). These limitations prevent the application of modern signal processing techniques to pre-process the collected sensor data for energy and bandwidth efficient transmission over sensor networks. This tutorial introduces communication and networking generalists without a background in wavelet signal processing to low-memory wavelet transform techniques. We first explain the one-dimensional wavelet transform (including the lifting scheme for in-place computation), the two-dimensional wavelet transform, as well as the evaluation of wavelet transforms with fixed-point arithmetic. Then, we explain the fractional wavelet filter technique which computes wavelet transforms with 16 bit integers and requires less than 1.5 kByte of RAM for a 256 x 256 gray scale image. We present case studies illustrating the use of these low-memory wavelet techniques in conjunction with image coding systems to achieve image compression competitive to the JPEG2000 standard on resource-constrained wireless sensor nodes. We make the C-code software for the techniques introduced in this tutorial freely available.