Wavelet Transforms

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Wim Sweldens - One of the best experts on this subject based on the ideXlab platform.

  • nonlinear Wavelet Transforms for image coding via lifting
    IEEE Transactions on Image Processing, 2003
    Co-Authors: Roger L Claypoole, Wim Sweldens, Geoffrey M Davis, Richard G Baraniuk
    Abstract:

    We investigate central issues such as invertibility, stability, synchronization, and frequency characteristics for nonlinear Wavelet Transforms built using the lifting framework. The nonlinearity comes from adaptively choosing between a class of linear predictors within the lifting framework. We also describe how earlier families of nonlinear filter banks can be extended through the use of prediction functions operating on a causal neighborhood of pixels. Preliminary compression results for model and real-world images demonstrate the promise of our techniques.

  • Wavelet Transforms that map integers to integers
    Applied and Computational Harmonic Analysis, 1998
    Co-Authors: A R Calderbank, Ingrid Daubechies, Wim Sweldens
    Abstract:

    Abstract Invertible Wavelet Transforms that map integers to integers have important applications in lossless coding. In this paper we present two approaches to build integer to integer Wavelet Transforms. The first approach is to adapt the precoder of Laroiaet al.,which is used in information transmission; we combine it with expansion factors for the high and low pass band in subband filtering. The second approach builds upon the idea of factoring Wavelet Transforms into so-called lifting steps. This allows the construction of an integer version of every Wavelet transform. Finally, we use these approaches in a lossless image coder and compare the results to those given in the literature.

  • lossless image compression using integer to integer Wavelet Transforms
    International Conference on Image Processing, 1997
    Co-Authors: A R Calderbank, Ingrid Daubechies, Wim Sweldens, Boonlock Yeo
    Abstract:

    Invertible Wavelet Transforms that map integers to integers are important for lossless representations. We present an approach to build integer to integer Wavelet Transforms based upon the idea of factoring Wavelet Transforms into lifting steps. This allows the construction of an integer version of every Wavelet transform. We demonstrate the use of these Transforms in lossless image compression.

  • ICIP (1) - Lossless image compression using integer to integer Wavelet Transforms
    Proceedings of International Conference on Image Processing, 1
    Co-Authors: A R Calderbank, Ingrid Daubechies, Wim Sweldens, Boonlock Yeo
    Abstract:

    Invertible Wavelet Transforms that map integers to integers are important for lossless representations. We present an approach to build integer to integer Wavelet Transforms based upon the idea of factoring Wavelet Transforms into lifting steps. This allows the construction of an integer version of every Wavelet transform. We demonstrate the use of these Transforms in lossless image compression.

C. Sidney Burrus - One of the best experts on this subject based on the ideXlab platform.

  • multidimensional mapping based complex Wavelet Transforms
    IEEE Transactions on Image Processing, 2005
    Co-Authors: F C A Fernandes, Rutger L. C. Van Spaendonck, C. Sidney Burrus
    Abstract:

    Although the discrete Wavelet transform (DWT) is a powerful tool for signal and image processing, it has three serious disadvantages: shift sensitivity, poor directionality, and lack of phase information. To overcome these disadvantages, we introduce multidimensional, mapping-based, complex Wavelet Transforms that consist of a mapping onto a complex function space followed by a DWT of the complex mapping. Unlike other popular Transforms that also mitigate DWT shortcomings, the decoupled implementation of our Transforms has two important advantages. First, the controllable redundancy of the mapping stage offers a balance between degree of shift sensitivity and transform redundancy. This allows us to create a directional, nonredundant, complex Wavelet transform with potential benefits for image coding systems. To the best of our knowledge, no other complex Wavelet transform is simultaneously directional and nonredundant. The second advantage of our approach is the flexibility to use any DWT in the transform implementation. As an example, we exploit this flexibility to create the complex double-density DWT: a shift-insensitive, directional, complex Wavelet transform with a low redundancy of (3/sup M/-1)/(2/sup M/-1) in M dimensions. No other transform achieves all these properties at a lower redundancy, to the best of our knowledge. By exploiting the advantages of our multidimensional, mapping-based complex Wavelet Transforms in seismic signal-processing applications, we have demonstrated state-of-the-art results.

  • ICASSP - Shiftable, projection-based complex Wavelet Transforms
    IEEE International Conference on Acoustics Speech and Signal Processing, 2002
    Co-Authors: F C A Fernandes, Rutger L. C. Van Spaendonck, C. Sidney Burrus
    Abstract:

    Shift sensitivity, poor directional selectivity and lack of phase information are three major disadvantages of the discrete Wavelet transform, In earlier research, we demonstrated that projection-based complex Wavelet Transforms have excellent directional selectivity and explicit phase information, In this paper, we discuss the theory of projection-based complex Wavelet Transforms and we prove that these Transforms can have reduced shift sensitivity with low transform redundancy. We also provide experimental results to demonstrate the reduced shift sensitivity of our Transforms.

  • Approximate moments and regularity of efficiently implemented orthogonal Wavelet Transforms
    1996 IEEE International Symposium on Circuits and Systems. Circuits and Systems Connecting the World. ISCAS 96, 1996
    Co-Authors: Jens Götze, Philipp Rieder, J.e. Odegard, C. Sidney Burrus
    Abstract:

    An efficient implementation of orthogonal Wavelet Transforms is obtained by approximating the rotation angles of the orthonormal rotations used in a lattice implementation of the filters. This approximation preserves the orthonormality of the transform exactly but leads to non-vanishing moments (except of the zeroth moment). The regularity of these Wavelets is analysed by exploiting their finite scale regularity, i.e. "smoothness" only up to a certain finite scale. This finite scale regularity is also related to classical filter banks.

Michael W Marcellin - One of the best experts on this subject based on the ideXlab platform.

  • scalable image coding using reversible integer Wavelet Transforms
    IEEE Transactions on Image Processing, 2000
    Co-Authors: Ali Bilgin, J Sementilli, Fang Sheng, Michael W Marcellin
    Abstract:

    Reversible integer Wavelet Transforms allow both lossless and lossy decoding using a single bitstream. We present a new fully scalable image coder and investigate the lossless and lossy performance of these Transforms in the proposed coder. The lossless compression performance of the presented method is comparable to JPEG-LS. The lossy performance is quite competitive with other efficient lossy compression methods.

Byeongkyu Kang - One of the best experts on this subject based on the ideXlab platform.

  • photorealistic style transfer via Wavelet Transforms
    International Conference on Computer Vision, 2019
    Co-Authors: Jaejun Yoo, Sanghyuk Chun, Byeongkyu Kang
    Abstract:

    Recent style transfer models have provided promising artistic results. However, given a photograph as a reference style, existing methods are limited by spatial distortions or unrealistic artifacts, which should not happen in real photographs. We introduce a theoretically sound correction to the network architecture that remarkably enhances photorealism and faithfully transfers the style. The key ingredient of our method is Wavelet Transforms that naturally fits in deep networks. We propose a Wavelet corrected transfer based on whitening and coloring Transforms (WCT2) that allows features to preserve their structural information and statistical properties of VGG feature space during stylization. This is the first and the only end-to-end model that can stylize a 1024x1024 resolution image in 4.7 seconds, giving a pleasing and photorealistic quality without any post-processing. Last but not least, our model provides a stable video stylization without temporal constraints. Our code, generated images, pre-trained models and supplementary documents are all available at https://github.com/ClovaAI/WCT2.

  • photorealistic style transfer via Wavelet Transforms
    arXiv: Computer Vision and Pattern Recognition, 2019
    Co-Authors: Jaejun Yoo, Sanghyuk Chun, Byeongkyu Kang
    Abstract:

    Recent style transfer models have provided promising artistic results. However, given a photograph as a reference style, existing methods are limited by spatial distortions or unrealistic artifacts, which should not happen in real photographs. We introduce a theoretically sound correction to the network architecture that remarkably enhances photorealism and faithfully transfers the style. The key ingredient of our method is Wavelet Transforms that naturally fits in deep networks. We propose a Wavelet corrected transfer based on whitening and coloring Transforms (WCT$^2$) that allows features to preserve their structural information and statistical properties of VGG feature space during stylization. This is the first and the only end-to-end model that can stylize a $1024\times1024$ resolution image in 4.7 seconds, giving a pleasing and photorealistic quality without any post-processing. Last but not least, our model provides a stable video stylization without temporal constraints. Our code, generated images, and pre-trained models are all available at this https URL.

Richard G Baraniuk - One of the best experts on this subject based on the ideXlab platform.

  • nonlinear Wavelet Transforms for image coding via lifting
    IEEE Transactions on Image Processing, 2003
    Co-Authors: Roger L Claypoole, Wim Sweldens, Geoffrey M Davis, Richard G Baraniuk
    Abstract:

    We investigate central issues such as invertibility, stability, synchronization, and frequency characteristics for nonlinear Wavelet Transforms built using the lifting framework. The nonlinearity comes from adaptively choosing between a class of linear predictors within the lifting framework. We also describe how earlier families of nonlinear filter banks can be extended through the use of prediction functions operating on a causal neighborhood of pixels. Preliminary compression results for model and real-world images demonstrate the promise of our techniques.

  • adaptive Wavelet Transforms via lifting
    International Conference on Acoustics Speech and Signal Processing, 1998
    Co-Authors: Roger L Claypoole, Richard G Baraniuk, Robert Nowak
    Abstract:

    This paper develops two new adaptive Wavelet Transforms based on the lifting scheme. The lifting construction exploits a spatial-domain, prediction-error interpretation of the Wavelet transform and provides a powerful framework for designing customized Transforms. We use the lifting construction to adaptively tune a Wavelet transform to a desired signal by optimizing data-based prediction error criteria. The performances of the new Transforms are compared to existing Wavelet Transforms, and applications to signal denoising are investigated.