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Optimal, Multiplierless Implementations of the Discrete Wavelet Transform for Image Compression Applications

Amy Bell


The JPEG2000 standard provides significantly better performance than its predecessor, JPEG, for the compression of digital images; algorithmically speaking, JPEG2000 is the ideal choice for real-time image transmission from mobile, wireless sensors. However, the effective implementation of the sophisticated JPEG2000 components–like the discrete wavelet transform (DWT) and EBCOT quantizer–presents both hardware and signal processing challenges. In this presentation, we illustrate our new filter design techniques and hardware architectures for fast, small, high quality implementations of JPEG2000’s DWT component on field programmable gate arrays (FPGAs). This work represents the first step in realizing the future ultimate vision: a wireless, mobile, lightweight, low power, low cost, easily updated, handheld/wearable/embedded device that quickly transmits and receives high quality image and video data with other devices in a wireless network.

The performance of a JPEG2000 hardware codec depends on the precision with which the DWT filter coefficients are approximated in fixed-point representations. Greater precision implies better compression performance, but at the cost of larger, slower hardware that consumes considerable power. We present a new algorithm–called “zero compensation”–for quantizing (i.e. approximating in fixed-point) the filter coefficients in a “convolution” approach to computing the DWT. This method attempts to preserve the DWT filter bank properties; we show that it enables the design of high-performance image compression filter banks with small, fast hardware. Next, we present a new polyphase filter bank structure that doubles the throughput while maintaining the high quality compression performance of zero compensation. However, this higher throughput polyphase structure requires more hardware and power than the non-polyphase structure.

Finally, we compare our best polyphase, convolution structure with the “lifting” approach to computing the DWT. Lifting is also a polyphase scheme and so it offers the same, doubled throughput of our polyphase, convolution implementation. The inherent orthogonality of the lifting structure implies that it has the unique advance of synthesis inverting analysis in the DWT even after filter coeffficient quantization. However, this orthogonal structure cannot exploit our new zero compensation technique. We present several new methods for designing optical lifting filter coefficients and compare their compression and hardware performance with our best polyphase, convolution technique. Our results indicate that the optimal lifting implementation provides the best compression performance and consumes the least energy; however, the polyphase, convolution architecture exhibits the highest throughput and smallest hardware.


Amy Bell is an Assistant Professor in the Department of Electrical and Computer Engineering at Virginia Tech. She received her Ph.D. in Electrical Engineering from the University of Michigan in 1997. Bell conducts research in wavelet image compression algorithms and architectures, embedded systems, systems biology and biomedical signal and image processing, and engineering education. Her work has been recognized with a 1999 NSF CAREER award; most recently, Bell received a 2002 NSF Information Technology Research award and a 2003 VBI Faculty Fellow award. Bell is also the recipient of two awards for teaching excellence.

Amy Bell Headshot
Amy Bell
Virginia Polytechnic Institute and State University
EEB 125
6 May 2004, 12:00am until 12:00am