The nature of statistical learning theory
The nature of statistical learning theory
Multiresolution representation of data: a general framework
SIAM Journal on Numerical Analysis
Curvelets and curvilinear integrals
Journal of Approximation Theory
Generalized Principal Component Analysis (GPCA)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image compression based on a family of stochastic models
Signal Processing
Method of optimal directions for frame design
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 05
Image Classification Based on Fuzzy Support Vector Machine
ISCID '08 Proceedings of the 2008 International Symposium on Computational Intelligence and Design - Volume 01
Image compression scheme based on curvelet transform and support vector machine
Expert Systems with Applications: An International Journal
ENO schemes with subcell resolution
Journal of Computational Physics
Double sparsity: learning sparse dictionaries for sparse signal approximation
IEEE Transactions on Signal Processing
Learning-based image restoration for compressed images
Image Communication
Machine learning to design full-reference image quality assessment algorithm
Image Communication
-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
IEEE Transactions on Signal Processing
Embedded image coding using zerotrees of wavelet coefficients
IEEE Transactions on Signal Processing
A learning-based method for image super-resolution from zoomed observations
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Sparse geometric image representations with bandelets
IEEE Transactions on Image Processing
The contourlet transform: an efficient directional multiresolution image representation
IEEE Transactions on Image Processing
Sparse Representation for Color Image Restoration
IEEE Transactions on Image Processing
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In Harten's framework, multiresolution transforms are defined by predicting finer resolution levels of information from coarser ones using an operator, called prediction operator, and defining details (or wavelet coefficients) that are the difference between the exact and predicted values. In this paper we use tools of statistical learning in order to design a more accurate prediction operator in this framework based on a training sample, resulting in multiresolution decompositions with enhanced sparsity. In the case of images, we incorporate edge detection techniques in the design of the prediction operator in order to avoid Gibbs phenomenon. Numerical tests are presented showing that the learning-based multiresolution transform compares favorably with the standard multiresolution transforms in terms of compression capability.