On the Imaging of Fractal Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Arbitrarily smooth orthogonal nonseparable wavelets in R2
SIAM Journal on Mathematical Analysis
Texture Roughness Analysis and Synthesis via Extended Self-Similar (ESS) Model
IEEE Transactions on Pattern Analysis and Machine Intelligence
Construction of nonseparable multiwavelets for nonlinear image compression
EURASIP Journal on Applied Signal Processing
Characterization of second-order isotropic fractional brownian fields
IEEE Transactions on Signal Processing
Algorithms for designing wavelets to match a specified signal
IEEE Transactions on Signal Processing
A new approach for estimation of statistically matched wavelet
IEEE Transactions on Signal Processing
Nonseparable two- and three-dimensional wavelets
IEEE Transactions on Signal Processing
nth-order fractional Brownian motion and fractional Gaussian noises
IEEE Transactions on Signal Processing
Principal component filter banks for optimal multiresolutionanalysis
IEEE Transactions on Signal Processing
Nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for Rn
IEEE Transactions on Information Theory - Part 2
Spectral representation of fractional Brownian motion in n dimensions and its properties
IEEE Transactions on Information Theory
Fractal-Based Description of Natural Scenes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Wavelet families of increasing order in arbitrary dimensions
IEEE Transactions on Image Processing
Evaluating Kube and Pentland's fractal imaging model
IEEE Transactions on Image Processing
Multidimensional orthogonal filter bank characterization and design using the Cayley transform
IEEE Transactions on Image Processing
Text Extraction and Document Image Segmentation Using Matched Wavelets and MRF Model
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
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This paper presents a new approach for the estimation of 2-channel nonseparable wavelets matched to images in the statistical sense. To estimate a matched wavelet system, first, we estimate the analysis wavelet filter of a 2-channel nonseparable filterbank using the minimum mean square error (MMSE) criterion. The MMSE criterion requires statistical characterization of the given image. Because wavelet basis expansion behaves as Karhunen-Loeve type expansion for fractional Brownian processes, we assume that the given image belongs to a 1st order or a 2nd order isotropic fractional Brownian field (IFBF). Next, we present a method for the design of a 2-channel two-dimensional finite-impulse response (FIR) biorthogonal perfect reconstruction filterbank (PRFB) leading to the estimation of a compactly supported statistically matched wavelet. The important contribution of the paper lies in the fact that all filters are estimated from the given image itself. Several design examples are presented using the proposed theory. Because matched wavelets will have better energy compaction, performance of estimated wavelets is evaluated by computing the transform coding gain. It is seen that nonseparable matched wavelets give better coding gain as compared to nonseparable non-matched orthogonal and biorthogonal wavelets.