Nonlinear wavelet transforms for image coding via lifting

Claypoole, Roger L.; Davis, G.; Sweldens, Wim; Baraniuk, Richard G.

doi:10.1109/tip.2003.817237

Cited by 289 publications

(142 citation statements)

References 21 publications

(34 reference statements)

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“…Applying this process iteratively on the smooth coefficient leads to a multiresolution analysis (MRA) [20] of the original signal. Due to its simplicity, some directional transforms based on lifting have been proposed in the literature for image [21]- [23] and video [24]- [29] representation.…”

Section: B Related Workmentioning

confidence: 99%

Directional Transforms for Video Coding Based on Lifting on Graphs

Martinez-Enriquez

Cid-Sueiro

Díaz-de-María

et al. 2018

IEEE Trans. Circuits Syst. Video Technol.

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Abstract-In this work we describe and optimize a general scheme based on lifting transforms on graphs for video coding. A graph is constructed to represent the video signal. Each pixel becomes a node in the graph and links between nodes represent similarity between them. Therefore, spatial neighbors and temporal motion-related pixels can be linked, while nonsimilar pixels (e.g., pixels across an edge) may not be. Then, a lifting-based transform, in which filterin operations are performed using linked nodes, is applied to this graph, leading to a 3-dimensional (spatio-temporal) directional transform which can be viewed as an extension of wavelet transforms for video. The design of the proposed scheme requires four main steps: (i) graph construction, (ii) graph splitting, (iii) filte design, and (iv) extension of the transform to different levels of decomposition. We focus on the optimization of these steps in order to obtain an effective transform for video coding. Furthermore, based on this scheme, we propose a coefficien reordering method and an entropy coder leading to a complete video encoder that achieves better coding performance than a motion compensated temporal filterin wavelet-based encoder and a simple encoder derived from H.264/AVC that makes use of similar tools as our proposed encoder (reference software JM15.1 configu ed to use 1 reference frame, no subpixel motion estimation, 16 × 16 inter and 4 × 4 intra modes).

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Section: B Related Workmentioning

confidence: 99%

Directional Transforms for Video Coding Based on Lifting on Graphs

Martinez-Enriquez

Cid-Sueiro

Díaz-de-María

et al. 2018

IEEE Trans. Circuits Syst. Video Technol.

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“…The class of lifting scheme that we want to analyze is inspired by Claypoole et al [6], because of its popularity and good performance. In this APLS the adaptivity involves only the prediction step, and in opposition to classic LS, the update step precedes the prediction one.…”

Section: Adaptive Predict Lifting Schemesmentioning

confidence: 99%

“…October 5-7, 2009 The great flexibility of lifting scheme offers the possibility to replace linear filters by nonlinear ones. In particular, LS with adaptive update [2], [3], [4] or adaptive prediction [5], [6], [7] have been proposed in the literature, with the target of avoiding oversmoothing of important features such as borders, and at the same time of exploiting the correlation of homogeneous regions by using long filter on them: different filters are thus used in different parts of image, and so the entire transform can be strongly non-isometric. This can be a serious obstacle, since all most successful coding techniques rely on the distortion estimation in the transform domain, either explicitly like in the EBCOT algorithm [8], or implicitly, like in zero-tree based techniques like SPIHT [9] and EZW [10].…”

Section: Introductionmentioning

confidence: 99%

“…However, since the AULSs have strong constraints (to assure the perfect reconstruction without sending any side information), their absolute RD performances are not satisfying (several dB below popular non-adaptive 9/7 filters). For this reason, we consider in this work adaptive prediction LS (APLS), in particular those inspired by the paper by Claypoole et al [6], because of their good RD performances. After a brief recall on APLS in Section II, we show how to estimate distortion in the transform domain for these LS in Section III.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of quantization noise for adaptive-prediction lifting schemes

Parrilli

Cagnazzo

Pesquet‐Popescu³

2009

2009 IEEE International Workshop on Multimedia Signal Processing

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Abstract-The lifting scheme represents an easy way of implementing the wavelet transform and of constructing new contentadapted transforms. However, the adaptive version of lifting schemes can result in strongly non-isometric transforms. This can be a major limitation, since all most successful coding techniques rely on the distortion estimation in the transform domain. In this paper we focus on the problem of evaluating the reconstruction distortion (due to quantization noise) in the wavelet domain when a non-isometric adaptive-prediction lifting scheme is used. The problem arises since these transforms are nonlinear, and so common techniques for distortion evaluation cannot be used in this case. We circumvent the difficulty by computing an equivalent time-varying linear filter, for which it is possible to generalize the distortion computation technique. In addition to the theoretical formulation of the distortion estimation, in this paper we provide experimental results proving the reliability of this estimation, and the consequent improvement of RD performance, thanks to a more effective resource allocation which can be performed in the transform domain.

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“…Lifting structures provide computationally efficient implementation of the wavelet transform [1][2][3][4][5][6][7] and they found applications in image and video coding and signal and image analysis applications [8,9].…”

Section: Introductionmentioning

confidence: 99%

Directionally Selective Fractional Wavelet Transform Using a 2-D Non-separable Unbalanced Lifting Structure

Keskin

Enis

etin³

2012

Lecture Notes in Computer Science

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Abstract. In this paper, we extend the recently introduced concept of fractional wavelet transform to obtain directional subbands of an image. Fractional wavelet decomposition is based on two-channel unbalanced lifting structures whereby it is possible to decompose a given discretetime signal x[n] sampled with period T into two sub-signals x1 [n] and x2[n] whose average sampling periods are pT and qT , respectively. Fractions p and q are rational numbers satisfying the condition: 1/p+1/q = 1. Filters used in the lifting structure are designed using the Lagrange interpolation formula. 2-d separable and non-separable extensions of the proposed fractional wavelet transform are developed. Using a non-separable unbalanced lifting structure, directional subimages for five different directions are obtained.

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Nonlinear wavelet transforms for image coding via lifting

Cited by 289 publications

References 21 publications

Directional Transforms for Video Coding Based on Lifting on Graphs

Directional Transforms for Video Coding Based on Lifting on Graphs

Estimation of quantization noise for adaptive-prediction lifting schemes

Directionally Selective Fractional Wavelet Transform Using a 2-D Non-separable Unbalanced Lifting Structure

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