Numerical-Methods-and-Imaging-in-Python

A collection of numerical experiments and optimization techniques applied to linear algebra and image processing, implemented in Python.

Project Structure

/src
├── notebooks/          # Jupyter Notebooks with analyses
│   ├── numerical_basics.ipynb
│   ├── optimization_and_polynomial_fitting.ipynb
│   └── inverseproblems_and_imaging.ipynb
│
├── src/                # Reusable Python source code
│   └── ProblemiInversi/
│
├── data/               # Data files (CSV, images, etc.)
│   ├── data_hw.csv
│   └── bologna.jpg
│
├── .gitignore         
└── README.md        

Contents

This collection features several key projects, each located in the notebooks/ directory:

• numerical_basics.ipynb: An introduction to fundamental numerical methods, including:

  • Root-finding algorithms (Bisection, Fixed-Point Iteration, and Newton's Method).
  • Solving systems of linear equations using LU, Singular Value Decomposition (SVD).

• optimization_and_polynomial_fitting.ipynb: A practical look at optimization, featuring:

  • Data approximation using polynomial fitting and least squares.
  • Implementation of the Gradient Descent algorithm with both fixed and backtracking line search strategies.

• inverseproblems_and_imaging.ipynb: An exploration of inverse problems and regularization techniques, with a focus on:

  • Picard condition and TSVD.
  • Image deblurring as a primary application.
  • Solving ill-posed problems using Truncated SVD (TSVD) and Tikhonov regularization.

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Tech Stack

• Language: Python
• Core Libraries:
  • NumPy for numerical operations.
  • Pandas for data manipulation and analysis.
  • Matplotlib for data visualization.
  • SciPy for scientific and technical computing.
  • Scikit-image for image processing tasks.
• Environment: Jupyter Notebook