3,733 research outputs found
An extension of Chebfun to two dimensions
An object-oriented MATLAB system is described that extends the capabilities of Chebfun to smooth functions of two variables defined on rectangles. Functions are approximated to essentially machine precision by using iterative Gaussian elimination with complete pivoting to form “chebfun2” objects representing low rank approximations. Operations such as integration, differentiation, function evaluation, and transforms are particularly efficient. Global optimization, the singular value decomposition, and rootfinding are also extended to chebfun2 objects. Numerical applications are presented
2-D Prony-Huang Transform: A New Tool for 2-D Spectral Analysis
This work proposes an extension of the 1-D Hilbert Huang transform for the
analysis of images. The proposed method consists in (i) adaptively decomposing
an image into oscillating parts called intrinsic mode functions (IMFs) using a
mode decomposition procedure, and (ii) providing a local spectral analysis of
the obtained IMFs in order to get the local amplitudes, frequencies, and
orientations. For the decomposition step, we propose two robust 2-D mode
decompositions based on non-smooth convex optimization: a "Genuine 2-D"
approach, that constrains the local extrema of the IMFs, and a "Pseudo 2-D"
approach, which constrains separately the extrema of lines, columns, and
diagonals. The spectral analysis step is based on Prony annihilation property
that is applied on small square patches of the IMFs. The resulting 2-D
Prony-Huang transform is validated on simulated and real data.Comment: 24 pages, 7 figure
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