A Renormalization Group Approach to Image Processing Problems
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ten lectures on wavelets
Adapted wavelet analysis from theory to software
Adapted wavelet analysis from theory to software
Image Processing with Complex Daubechies Wavelets
Journal of Mathematical Imaging and Vision
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
Wavelet-based statistical signal processing using hidden Markovmodels
IEEE Transactions on Signal Processing
Motion estimation using a complex-valued wavelet transform
IEEE Transactions on Signal Processing
Second-order complex random vectors and normal distributions
IEEE Transactions on Signal Processing
Letters: Complex wavelet based texture classification
Neurocomputing
Noise reduction of cDNA microarray images using complex wavelets
IEEE Transactions on Image Processing
Proceedings of the Eighth Indian Conference on Computer Vision, Graphics and Image Processing
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This article presents the construction and various properties of complex Daubechies wavelets with a special emphasis on symmetric solutions. Such solutions exhibit interesting relationships between the real and imaginary components of the complex scaling function and the complex wavelet. We present those properties in the context of image processing. Within the framework of statistical modelling, we focus on the redundant description of real images given by the complex multiresolution representation. A hierarchical Markovian Graphical model is then explored. We present an Expectation Maximization algorithm for optimizing the model with observational complex wavelet data. This model is then applied to image estimation and texture classification. In both applications, we demonstrate the benefit brought by the Markovian hypothesis and the performance of the real images's complex multiscale representation.