Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Log-similarity for turbulent flows?
Physica D
Image processing and data analysis: the multiscale approach
Image processing and data analysis: the multiscale approach
Meaningful MRA intitialization for discrete time series
Signal Processing - Special issue on current topics in adaptive filtering for hands-free acoustic communication and beyond
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
A Projective Invariant for Textures
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2
Multiple Resolution Texture Analysis and Classification
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multifractality Tests Using Bootstrapped Wavelet Leaders
IEEE Transactions on Signal Processing
Wavelet leader multifractal analysis for texture classification
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Virtual Super Resolution of Scale Invariant Textured Images Using Multifractal Stochastic Processes
Journal of Mathematical Imaging and Vision
Wavelet-based multifractal analysis of 1-D and 2-D signals: New results
Analog Integrated Circuits and Signal Processing
A 2D wavelet-based multiscale approach with applications to the analysis of digital mammograms
Computational Statistics & Data Analysis
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Multifractal analysis is considered a promising tool for image processing, notably for texture characterization. However, practical operational estimation procedures based on a theoretically well established multifractal analysis are still lacking for image (as opposed to signal) processing. Here, a wavelet leader based multifractal analysis, known to be theoretically strongly grounded, is described and assessed for 2D functions (images). By means of Monte Carlo simulations conducted over both self-similar and multiplicative cascade synthetic images, it is shown here to benefit from much better practical estimation performances than those obtained from a 2D discrete wavelet transform coefficient analysis. Furthermore, this is complemented by the original analysis and design of procedures aiming at practically assessing and handling the theoretical function space embedding requirements faced by multifractal analysis. In addition, a bootstrap based statistical approach developed in the wavelet domain is proposed and shown to enable the practical computation of accurate confidence intervals for multifractal attributes from a given image. It is based on an original joint time and scale block non-parametric bootstrap scheme. Performances are assessed by Monte Carlo simulations. Finally, the use and relevance of the proposed wavelet leader and bootstrap based tools are illustrated at work on real-world images.