Ten lectures on wavelets
Characterization of Signals from Multiscale Edges
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multifractal formalism for functions part I: results valid for all functions
SIAM Journal on Mathematical Analysis
Journal of Computational Physics
Reconstructing images from their most singular fractal manifold
IEEE Transactions on Image Processing
Reconstruction of speech signals from their unpredictable points manifold
NOLISP'11 Proceedings of the 5th international conference on Advances in nonlinear speech processing
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Recent works show that the determination of singularity exponents in images can be useful to assess their information content, and in some cases they can cast additional information about underlying physical processes. However, the concept of singularity exponent is associated to differential calculus and thus cannot be easily translated to a digital context, even using wavelets. In this work we show that a recently patented algorithm allows obtaining precise, meaningful values of singularity exponents at every point in the image by the use of a discretized combinatorial mask, which is an extension of a particular wavelet basis. This mask is defined under the hypothesis that singularity exponents are a measure not only of the degree of regularity of the image, but also of the reconstructibility of a signal from their points.