A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
Scaling, Fractals and Wavelets
Scaling, Fractals and Wavelets
The monogenic wavelet transform
IEEE Transactions on Signal Processing
A shearlet approach to edge analysis and detection
IEEE Transactions on Image Processing
Multiresolution monogenic signal analysis using the Riesz-Laplace wavelet transform
IEEE Transactions on Image Processing
Steerable wavelet frames based on the Riesz transform
IEEE Transactions on Image Processing
Higher-order Riesz transforms and steerable wavelet frames
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
IEEE Transactions on Signal Processing
Hypercomplex signals-a novel extension of the analytic signal tothe multidimensional case
IEEE Transactions on Signal Processing
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We reconsider the continuous curvelet transform from a signal processing point of view. We show that the analyzing elements of the curvelet transform, the curvelets, can be understood as analytic signals in the sense of the partial Hilbert transform. We then generalize the usual curvelets by the monogenic curvelets, which are analytic signals in the sense of the Riesz transform. They yield a new transform, called the monogenic curvelet transform. This transform has the useful property that it behaves at the fine scales like the usual curvelet transform and at the coarse scales like the monogenic wavelet transform. In particular, the new transform is highly anisotropic at the fine scales and yields a well-interpretable amplitude/phase decomposition of the transform coefficients over all scales. We illustrate the advantage of this new directional multiscale amplitude/phase decomposition for the estimation of directional regularity.