From Noise to Clarity

A study of frequency-domain and spatial filtering for biomedical images. The project combines Fourier analysis, noise modeling, classical denoising, an adaptive filter, and quantitative evaluation on brain and spine MRI examples.

Analysis pipeline

1. Inspect image spectra and spatial-frequency content.
2. Add controlled Uniform and Gaussian noise.
3. Apply low-pass and high-pass masks in the Fourier domain.
4. Compare mean, Gaussian, bilateral, and adaptive filters.
5. Evaluate reconstruction quality with SNR and PSNR.

Main findings

• Mean filtering reduces noise but introduces the strongest edge blur.
• Gaussian filtering provides stable smoothing at the cost of some fine detail.
• Bilateral filtering better preserves edges by combining spatial and intensity similarity.
• The adaptive method achieved the strongest overall reconstruction quality in the reported experiments by responding to local image statistics.

These findings are based on the images and parameter settings in this repository; they are not clinical validation.

Repository structure

.
├── EngMath.ipynb          # Complete executed analysis
├── Codes Per Part/        # Standalone snippets corresponding to report sections
├── pics/                  # Inputs and generated figures
├── EngMath_Project.pdf    # Full technical report
├── requirements.txt
└── LICENSE

Run locally

git clone https://github.com/moein-yoo/EngMath_Project.git
cd EngMath_Project
python -m venv .venv
python -m pip install -r requirements.txt
jupyter notebook EngMath.ipynb

The scripts in Codes Per Part/ expect to be run from the repository root because they use paths relative to pics/.

Course context

• Course: Engineering Mathematics
• Institution: Sharif University of Technology
• Instructor: Prof. Hamid K. Aghajan
• Term: Fall 2024–Winter 2025

Contributors

• Moein Yousefinia
• Mohammadparsa Ghaderahmadi
• Matin M. Babaei

License

Released under the MIT License.