Preprint: "Complete-to-Overcomplete Discrete Wavelet Transforms: Theory and Applications" by Y. Andreopoulos et al

[Yiannis Andreopoulos (yandreop@etro.vub.ac.be)]

Title: "Complete-to-Overcomplete Discrete Wavelet Transforms: Theory and Applications"
to appear in IEEE Transactions on Signal Processing

Authors: Y. Andreopoulos, A. Munteanu, G. Van der Auwera, J. Cornelis and P. Schelkens

Abstract: A new transform is proposed that derives the overcomplete discrete wavelet transform (ODWT) subbands from the critically-sampled DWT subbands (complete representation). This complete-to-overcomplete DWT (CODWT) has certain advantages in comparison to the conventional approach that performs the inverse DWT to reconstruct the input signal, followed by the à-trous or the low-band shift algorithm. Specifically, the computation of the input signal is not required. As a result, the minimum number of downsampling operations is performed and the use of upsampling is avoided.
The proposed CODWT computes the ODWT subbands by using a set of prediction-filter matrices and filtering-and-downsampling operators applied to the DWT. This formulation demonstrates a clear separation between the single-rate and multi-rate components of the transform. This can be especially significant when the CODWT is used in resource-constrained environments, such as resolution-scalable image and video codecs. To illustrate the applicability of the proposed transform in these emerging applications, a new scheme for the transform-calculation is proposed and existing coding techniques that benefit from its usage are surveyed. The analysis of the proposed CODWT in terms of arithmetic complexity and delay reveals significant gains as compared to the conventional approach.

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