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Complete-to-overcomplete discrete wavelet transforms: theory and applications This publication appears in: IEEE Transactions on Signal Processing Authors: Y. Andreopoulos, A. Munteanu, G. Van Der Auwera, J. Cornelis and P. Schelkens Volume: 53 Issue: 4 Pages: 1398-1412 Publication Date: Apr. 2005
Abstract: A new transform that derives the overcomplete discrete wavelet transform (ODWT) subbands from the critically-sampled DWT subbands (complete representation) is proposed. This complete-to-overcomplete DWT (CODWT) enjoys 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. In specific, the proposed CODWT does not require the computation of the input signal. As a result, the minimum number of dowsampling operations is performed, while the use of upsampling is avoided altogether. Furthermore, the proposed formulation demonstrates a clear separation between the single-rate and multi-rate components of the transform. The latter is especially significant for recent applications that require the CODWT 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 calculation scheme is proposed and existing coding architectures that benefit from its usage are surveyed. For such applications, the analysis of the proposed CODWT in terms of arithmetic complexity and system delay reveals significant gains as compared to the state-of-the-art implementation of the conventional approach.
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