Browsing by Author "Claypoole, Roger L."

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    Adaptive Wavelet Transforms for Image Coding
    (1997-11-01) Claypoole, Roger L.; Davis, Geoffrey; Sweldens, Wim; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
    We introduce a new adaptive transform for wavelet-based image coding. The lifting framework for wavelet construction motivates our analysis and provides new insight into the problem. Since the adaptive transform is non-linear, we examine the central issues of invertibility, stability, and artifacts in its construction. We describe a new type of non-linearity: a set of linear predictors are chosen adaptively using a non-linear selection function. We also describe how earlier families of non-linear filter banks can be extended through the use of prediction functions operating on a causal neighborhood. We present preliminary results for a synthetic test image.
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    Adaptive Wavelet Transforms for Image Coding
    (1997-11-01) Claypoole, Roger L.; Davis, Geoffrey; Sweldens, Wim; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
    We introduce a new adaptive transform for wavelet-based image coding. The lifting framework for wavelet construction motivates our analysis and provides new insight into the problem. Since the adaptive transform is non-linear, we examine the central issues of invertibility, stability, and artifacts in its construction. We describe a new type of non-linearity: a set of linear predictors are chosen adaptively using a non-linear selection function. We also describe how earlier families of non-linear filter banks can be extended through the use of prediction functions operating on a causal neighborhood. We present preliminary results for a synthetic test image.
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    Adaptive Wavelet Transforms for Image Coding using Lifting
    (1998-03-01) Claypoole, Roger L.; Davis, Geoffrey; Sweldens, Wim; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
    Summary form only given. Image compression relies on efficient representations of images, and within smooth image regions, the wavelet transform provides such a representation. However, near edges, wavelet coefficients decay slowly and are expensive to code. We focus on improving the transform by incorporating adaptivity. Construction of nonlinear filter banks has been discussed, but the question of how to utilize the nonlinearities remained. We answer this question by describing our transform via lifting. Lifting provides a spatial domain framework for the wavelet transform. In the lifting formalism, wavelet coefficients are seen as prediction residuals from a linear prediction operation. Wavelet coefficients are large near edges because the linear predictors are built to interpolate low order polynomials. Our goal is to avoid this problem by adapting the predictor based on local image properties. In smooth regions of the image, we use high order polynomial predictors. We adaptively reduce the prediction order to avoid attempting to predict values across discontinuities.
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    Adaptive Wavelet Transforms via Lifting
    (1998) Claypoole, Roger L.; Baraniuk, Richard G.; Nowak, Robert David; Digital Signal Processing (http://dsp.rice.edu/)
    This paper develops new algorithms for adapted multiscale analysis and signal adaptive wavelet transforms. We construct our adaptive transforms with the lifting scheme, which decomposes the wavelet transform into prediction and update stages. We adapt the prediction stage to the signal structure and design the update stage to preserve the desirable properties of the wavelet transform. We incorporate this adaptivity into the redundant and non-redundant transforms; the resulting transforms are scale and spatially adaptive. We study applications to signal estimation; our new transforms show improved denoising performance over existing (non-adaptive) orthogonal transforms.
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    Adaptive Wavelet Transforms via Lifting
    (1999-01-15) Claypoole, Roger L.; Baraniuk, Richard G.; Nowak, Robert David; Digital Signal Processing (http://dsp.rice.edu/)
    This paper develops new algorithms for adapted multiscale analysis and signal adaptive wavelet transforms. We construct our adaptive transforms with the lifting scheme, which decomposes the wavelet transform into prediction and update stages. We adapt the prediction stage to the signal structure and design the update stage to preserve the desirable properties of the wavelet transform. We incorporate this adaptivity into the redundant and non-redundant transforms; the resulting transforms are scale and spatially adaptive. We study applications to signal estimation; our new transforms show improved denoising performance over existing (non-adaptive) orthogonal transforms.
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    Adaptive Wavelet Transforms via Lifting
    (1998-05-01) Claypoole, Roger L.; Baraniuk, Richard G.; Nowak, Robert David; Digital Signal Processing (http://dsp.rice.edu/)
    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.
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    Flexible Wavelet Transforms Using Lifting
    (1998-09-01) Claypoole, Roger L.; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
    We introduce and discuss biorthogonal wavelet transforms using the lifting construction. The lifting construction exploits a spatial-domain, prediction-error interpretation of the wavelet transform and provides a powerful framework for designing customized transforms. We discuss the application of lifting to adaptive and non-linear transforms, transforms of non-uniformly sampled data, and related issues.
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    Lifting Construction of Non-Linear Wavelet Transforms
    (1998-10-01) Claypoole, Roger L.; Baraniuk, Richard G.; Nowak, Robert David; Digital Signal Processing (http://dsp.rice.edu/)
    This paper analyzes non-linear wavelet transforms using the lifting construction. 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 better understand the performance of wavelet transforms that utilize median and Volterra filters.
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    Nonlinear Wavelet Transforms for Image Coding
    (1997-11-01) Claypoole, Roger L.; Davis, Geoffrey; Sweldens, Wim; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
    We examine the central issues of invertibility, stability, artifacts, and frequency-domain characteristics in the construction of nonlinear analogs of the wavelet transform. The lifting framework for wavelet construction motivates our analysis and provides new insight into the problem. We describe a new type of nonlinearity for use in constructing nonlinear transforms: a set of linear predictors that are chosen adaptively using a nonlinear selection function. We also describe how earlier families of nonlinear filter banks can be extended through the use of prediction functions operating on a causal neighborhood. We present preliminary results for a synthetic test image.
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    Nonlinear Wavelet Transforms for Image Coding via Lifting
    (2003-12-01) Claypoole, Roger L.; Davis, Geoffrey; Sweldens, Wim; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
    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.