Image Denoising using Haar Wavelets

Author: Mario Medone
Course: Digital Signal & Image Processing

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📖 Project Overview

This repository contains an implementation of image denoising using Haar wavelets.
Wavelet-based denoising is a powerful technique for reducing noise in digital images, particularly Gaussian noise, while preserving important structural details.

The project explores:

• The application of the Haar wavelet transform for image decomposition.
• The role of hard and soft thresholding in noise removal.
• The challenge of selecting an appropriate threshold parameter.
• The use of BayesShrink as a standard method for threshold estimation.

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⚙️ Methodology

1. Introduction We introduce the concept of digital images and the presence of noise, focusing particularly on Gaussian noise. We highlight its statistical properties and emphasize the independence of Gaussian noise with respect to the 2D wavelet transform.
2. Literature Review This section provides a brief overview of the 2D Haar wavelet transform, the denoising procedure, and the different wavelet thresholding methods. A detailed discussion is included on the challenges of selecting the optimal threshold parameter, supported by insights from previous works.
3. Implementation We implement the thresholding methods and the denoising procedure described in the literature, applying them to test images in order to evaluate their effectiveness.
4. Experimental Results The implemented methods are tested and compared. Based on the outcomes, we analyze which thresholding approach and parameter selection strategy yield the most effective denoising performance.
5. Conclusions We summarize the findings and provide final considerations on the overall work, highlighting the strengths and limitations of Haar wavelet-based denoising.

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📊 Results & Conclusions

• Haar wavelets are a useful and powerful tool for clearing images from noise, especially Gaussian noise.
• The choice of threshold parameter is non-trivial; standard methods like BayesShrink help automate this process.
• The best configuration observed:
  • Apply soft thresholding to detail coefficients.
  • Use BayesShrink for threshold definition.
• Denoised images show good quality, though performance decreases as noise increases:
  • Higher Gaussian noise standard deviation leads to grainier and blurrier results.

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🚀 How to Run

1. Clone the repository:

   git clone https://github.com/Brosss98/HaarWavelets.git
   cd HaarWavelets

2. Install dependencies:

   pip install -r requirements.txt

3. Run the notebook

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📚 References

A list of the articles, works, and projects consulted to understand Haar wavelet-based image denoising and to build this laboratory:

1. Yang Qiang, Image denoising based on Haar wavelet transform.
   Proceedings of the 2011 International Conference on Electronics and Optoelectronics, 2011, pp. V3-129–V3-132.
   doi: 10.1109/ICEOE.2011.6013318

2. J. Pang, Improved image denoising based on Haar wavelet transform.
   2017 IEEE SmartWorld, Ubiquitous Intelligence & Computing, Advanced & Trusted Computing, Scalable Computing & Communications, Cloud & Big Data Computing, Internet of People and Smart City Innovation (SmartWorld/SCALCOM/UIC/ATC/CBDCom/IOP/SCI), 2017, pp. 1–6.
   doi: 10.1109/UIC-ATC.2017.8397456

3. S. H. Ismael, F. M. Mustafa, I. T. Okümüs, A New Approach of Image Denoising Based on Discrete Wavelet Transform.
   2016 World Symposium on Computer Applications & Research (WSCAR), 2016, pp. 36–40.
   doi: 10.1109/WSCAR.2016.30

4. Shivani Mupparaju, B. Naga Venkata Satya Durga Jahnavi, Comparison of Various Thresholding Techniques of Image Denoising.
   Department of ECE, VNR VJIET, Hyderabad, A.P, India. International Journal of Engineering Research & Technology (IJERT), Vol. 2 Issue 9, September 2013.
   ISSN: 2278-0181

5. Gregory R. Lee, Ralf Gommers, Filip Wasilewski, Kai Wohlfahrt, Aaron O’Leary, PyWavelets: A Python package for wavelet analysis.
   Journal of Open Source Software, 4(36), 1237, 2019.
   doi: 10.21105/joss.01237