G. Van der Auwera

Complete-to-overcomplete discrete wavelet transforms: theory and applications

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 a/spl grave/-trous or the lowband 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 multirate 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 with the conventional approach.

A new method for complete-to-overcomplete discrete wavelet transforms

Overcomplete discrete wavelet transforms (ODWT) are used in a number of applications because they provide shift invariance, a property extremely useful in wavelet-based image processing and video coding. In this paper, we propose a new construction of the ODWT starting from the subbands of the critically sampled (complete) DWT. The most straightforward application of our theory is scalable video coding with in-band prediction, for which it has been shown that the proposed method achieves lower complexity.

Scalable wavelet video-coding with in-band prediction - implementation and experimental results

In this paper we elaborate on a recently proposed approach for scalable video-coding based on in-band prediction in the overcomplete wavelet domain. It is shown that, through a new calculation scheme for the level-by-level complete to overcomplete discrete wavelet transform (DWT) that exploits certain symmetries, important reductions in the multiplication budget are obtained in comparison to the fastest-known algorithm of the literature. Based on the derived overcomplete transform-domain coefficients, a pixel-accurate motion estimation and compensation (ME/MC) algorithm is proposed, which provides a hybrid-coding framework that supports full scalability in resolution, quality and frame rate. To give an indication of the coding performance of such a system, some preliminary results are reported.

Scalable wavelet video-coding with in-band prediction - the bottom-up overcomplete discrete wavelet transform

A new in-band motion compensation algorithm for wavelet-based video coding is proposed: the bottom-up prediction algorithm (BUP). The BUP algorithm overcomes the periodic shift-invariance of the discrete wavelet transform (DWT) and is formalized into new prediction rules using filtering operations. BUP is based on the relationships between the subbands of the shifted input signal and the subbands of the non-shifted reference signal, whereby the number of shifts is limited by the periodic shift-invariance of the DWT. We derive the algorithm for the 1-D DWT with three decomposition levels. The combination of all prediction rules of the BUP algorithm defines a new transform: the bottom-up overcomplete DWT or BUP ODWT, which is shift-invariant. The BUP ODWT calculates the overcomplete subbands by applying the prediction rules to the critically sampled subbands of a wavelet-transformed image. The envisaged application for the BUP algorithm is spatially scalable video coding.

Video coding based on motion estimation in the wavelet detail images

This work proposes a new block based motion estimation and compensation technique applied on the detail images of the wavelet pyramidal decomposition. The algorithm uses two matching criteria, namely the absolute difference and the absolute sum. For a wavelet decomposed one-dimensional step function, it is shown that for odd translations of the step, the absolute sum reaches a smaller minimum than the absolute difference. We also derive in this case a constraint on the highpass filter coefficients so that a zero prediction error can be reached by using the absolute sum. Although this cannot be easily generalized for an arbitrary signal profile, experimental results obtained with photorealistic image sequences indicate that the prediction error can be reduced with respect to techniques that only use the absolute difference as matching criterion.

Evaluation of a quincunx wavelet filter design approach for quadtree-based embedded image coding

We study the compression performance of the quincunx discrete wavelet transform (DWT) and we compare it with the dyadic DWT in terms of rate-distortion. The 2D non-separable quincunx wavelet filters are designed by making use of the transformations of variables technique of Tay and Kingsbury (1993) starting from the 1D biorthogonal (9,7)-taps filters. The applied transformation functions are respectively based on the Kaiser and Chebyshev windows, and on the Lagrange halfband filters. The novelties of this work are in the evaluation of these filters for image compression and the usage of an embedded coder based on the quadtree approach for coding the quincunx subbands.