30-06-2012, 05:26 PM
Two-Dimensional Wavelets
[attachment=26369]
For image processing applications we need wavelets that are two-dimensional.
This problem reduces down to designing 2D filters.
We will focus on a particular class of 2D filters: separable filters (can be directly designed from their 1D counterparts)
2D Scaling Functions
The theories of multiresolution analysis and wavelets can be generalized to higher dimensions.
In practice the usual choice for a two-dimensional scaling function or wavelet is a product of two one-dimensional functions. For example,
and the dilation equation assumes the form:
Denoising Images
Denoising Daubechies’ face:
Transform the image to the wavelet domain using Coiflets with three vanishing moments
Apply a threshold at two standard deviations
Inverse-transform the image.
Denoising and Enhancement
Apply DWT
Shrink transform coefficients in finer scales to reduce the effect of noise
Emphasize features within a certain range using a nonlinear mapping function
Perform IDWT to reconstruct the image.
[attachment=26369]
For image processing applications we need wavelets that are two-dimensional.
This problem reduces down to designing 2D filters.
We will focus on a particular class of 2D filters: separable filters (can be directly designed from their 1D counterparts)
2D Scaling Functions
The theories of multiresolution analysis and wavelets can be generalized to higher dimensions.
In practice the usual choice for a two-dimensional scaling function or wavelet is a product of two one-dimensional functions. For example,
and the dilation equation assumes the form:
Denoising Images
Denoising Daubechies’ face:
Transform the image to the wavelet domain using Coiflets with three vanishing moments
Apply a threshold at two standard deviations
Inverse-transform the image.
Denoising and Enhancement
Apply DWT
Shrink transform coefficients in finer scales to reduce the effect of noise
Emphasize features within a certain range using a nonlinear mapping function
Perform IDWT to reconstruct the image.