Wavelets, Filter Banks and Applications

The wavelet transform and its applications in image denoising

Overview

In this exercise, we investigate the wavelet transform and its applications in image denoising. For this reason two functions were developed:

j-level wavelet transform of an NxN image
inverse j-level wavelet transform of and NxN array of wavelet coefficients

Implementation Details

Two functions and a script were developed. Two functions were developed: JlevelWaveletTransform and JlevelInverseWaveletTransform, and a script called denoisingExample.

Forward Filter Wavelet Transform on 2d Image: Illustrates how the J-level wavelet transform of an NxN image can be computed (assuming N is a power of 2). The function to calculate wavelet coefficients takes 3 input arguments: an input image, the number of levels J, and low pass filter. It outputs an array of NxN wavelet coefficients.

Inverse Filter Wavelet Transform on 2d Images: Illustrates how the inverse J-level wavelet transform of an NxN image can be computed (assuming N is a power of 2). Also the reconstructed image would be computed from the input coefficients. It takes 3 inputs: array of wavelet coefficients, the number of levels J and low pass filter. It outputs a reconstructed image.

Example

In order to regenerate the results found inf folder Results, the script denoisingExample must be ran.

License

Wavelets, Filter Banks and Applications is released under the MIT License.