Implementations of the discrete wavelet transform: complexity, memory, and parallelization issues

The discrete wavelet transform (DWT) has been touted as a very effective tool in many signal processing application, including compression, denoising and modulation. For example, the forthcoming JPEG 2000 image compression standard will be based on the DWT. However, in order for the DWT to achieve the popularity of other more established techniques (e.g., the DCT in compression) a substantial effort is necessary in order to solve some of the related implementation issues. Specific issues of interest include memory utilization, computation complexity and scalability. In this paper we concentrate on wavelet-based image compression and provide examples, based on our recent work, of how these implementation issues can be addressed in three different environments, namely, memory constrained applications, software-only encoding/decoding, and parallel computing engines. Specifically we will discuss (1) a low memory image coding algorithm that employs a line-based transform, (2) a technique to exploit the sparseness of non- zero wavelet coefficients in a software-only image decoder, and (3) parallel implementation techniques that take full advantage of lifting filterbank factorizations.

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