Patent
Processing or compressing n-dimensional signals with warped wavelet packets and bandelets
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TLDR
In this article, a warped wavelet packet transform was proposed for processing or compressing an n-dimensional digital signal by constructing a sparse representation which takes advantage of the signal geometrical regularity.Abstract:
A method and apparatus for processing or compressing an n-dimensional digital signal by constructing a sparse representation which takes advantage of the signal geometrical regularity. The invention comprises a warped wavelet packet transform which performs a cascade of warped subband filtering along warping grids of sampling points adapted to the signal geometry. It also comprises a bandeletisation which decorrelates the warped wavelet packet coefficients to produce a sparse representation. An inverse warped wavelet packet transform and an inverse bandeletisation reconstruct a signal from its bandelet representation. The invention comprises a compression system which quantizes and codes the bandelet representation, a decompression system, a restoration system which enhances a signal by filtering its bandelet representation, and a feature vector extraction system for pattern recognition applications of a bandelet representation.read more
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References
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A theory for multiresolution signal decomposition: the wavelet representation
TL;DR: In this paper, it is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2 /sup j/ (where j is an integer) can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions.
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Ideal spatial adaptation by wavelet shrinkage
TL;DR: In this article, the authors developed a spatially adaptive method, RiskShrink, which works by shrinkage of empirical wavelet coefficients, and achieved a performance within a factor log 2 n of the ideal performance of piecewise polynomial and variable-knot spline methods.
Book ChapterDOI
Factoring wavelet transforms into lifting steps
Ingrid Daubechies,Wim Sweldens +1 more
TL;DR: In this paper, a self-contained derivation from basic principles such as the Euclidean algorithm, with a focus on applying it to wavelet filtering, is presented, which asymptotically reduces the computational complexity of the transform by a factor two.
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The curvelet transform for image denoising
TL;DR: In this paper, the authors describe approximate digital implementations of two new mathematical transforms, namely, the ridgelet transform and the curvelet transform, which offer exact reconstruction, stability against perturbations, ease of implementation, and low computational complexity.
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Interpolation revisited [medical images application]
TL;DR: Based on the theory of approximation, this paper presents a unified analysis of interpolation and resampling techniques and shows that, contrary to the common belief, those that perform best are not interpolating.