Multiresolution representation of data: a general framework
SIAM Journal on Numerical Analysis
Adaptive Multivariate Approximation Using Binary Space Partitions and Geometric Wavelets
SIAM Journal on Numerical Analysis
Image compression by linear splines over adaptive triangulations
Signal Processing
Rate-distortion optimized tree-structured compression algorithms for piecewise polynomial images
IEEE Transactions on Image Processing
The contourlet transform: an efficient directional multiresolution image representation
IEEE Transactions on Image Processing
Wavelet-domain approximation and compression of piecewise smooth images
IEEE Transactions on Image Processing
Directional multiscale modeling of images using the contourlet transform
IEEE Transactions on Image Processing
Directionlets: anisotropic multidirectional representation with separable filtering
IEEE Transactions on Image Processing
A New Hybrid Method for Image Approximation Using the Easy Path Wavelet Transform
IEEE Transactions on Image Processing
Full length article: Lp Bernstein inequalities and inverse theorems for RBF approximation on Rd
Journal of Approximation Theory
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The Easy Path Wavelet Transform (EPWT) (Plonka, 2009) [26] has recently been proposed by one of the authors as a tool for sparse representations of bivariate functions from discrete data, in particular from image data. The EPWT is a locally adaptive wavelet transform. It works along pathways through the array of function values and it exploits the local correlations of the given data in a simple appropriate manner. In this paper, we aim to provide a theoretical understanding of the performance of the EPWT. In particular, we derive conditions for the path vectors of the EPWT that need to be met in order to achieve optimal N-term approximations for piecewise Holder smooth functions with singularities along curves.