About Me

Dr. Hamdi Braiek

I am an Applied Mathematics researcher and Associate Professor at ESPRIT, Tunisia, where I have been teaching and conducting research since 2020. I received my Ph.D. in Applied Mathematics from the National Engineering School of Tunis (ENIT), University of Tunis El Manar, in 2019. I conducted my Ph.D. research at the LAMSIN Laboratory, under the supervision of Prof. Maher Moakher and Dr. Badreddine Rjaibi. Before joining ESPRIT, I taught at several Tunisian higher-education institutions, including the National School of Advanced Sciences and Technologies of Borj Cedria (ENSTAB), the National Engineering School of Tunis (ENIT), the Higher Institute of Biotechnology of Béja (ISBB), and the Higher Institute of Multimedia Arts of Manouba (ISAMM).

My research lies at the intersection of mathematical analysis, variational methods, partial differential equations, optimization, and scientific computing. My main research interests include image restoration, total variation regularization, fractional-order models, variable-exponent models, nonlinear diffusion, and numerical methods for inverse problems. A particular focus of my work is the development of mathematical models and efficient numerical algorithms for image denoising and restoration, including the treatment of Gaussian, speckle, multiplicative, and Cauchy noise.

More recently, my research has expanded toward machine learning, deep learning, physics-informed neural networks, neural PDE solvers, and their integration with mathematical modeling and optimization.

Academic Positions

Associate Professor (Full-Time)
ESPRIT — École Supérieure Privée d'Ingénierie et de Technologies, Tunis, Tunisia
2020 — Present
Current
Contract Assistant Professor
ENSTAB — Ecole Nationale des Sciences et Technologies Avancées à Borj-Cedria, Tunis, Tunisia
2019 — 2020
Part-time Teacher
ENIT — Ecole Nationale d’Ingénieurs de Tunis, Tunis, Tunisia & ESPRIT
2018 — 2019
Contract Assistant Professor
ISBB — Higher Institute of Biotechnology of Beja, Beja, Tunisia
2017 — 2018
Part-time Teacher
ISAMM — Higher Institute of Arts and Multimedia Manouba, Manouba, Tunisia & ESPRIT
2015 — 2016

Education

Ph.D. in Applied Mathematics
National Engineering School of Tunis (ENIT) University of Tunis El Manar, Tunis, Tunisia
Thesis: "Variational and numerical techniques for medical ultrasound image analysis"
Supervisors: Prof. Maher Moakher & Prof. Badreddine Rjaibi
2014 — 2019
DOCTORATE
M.Sc. Business Analytics & Data Science
Virtual University of Tunis (UVT), Tunis, Tunisia
2023 — 2025
MASTER'S
M.Sc. Research in Mathematics
Faculty of Sciences of Tunis (FST), University of Tunis El Manar, Tunis, Tunisia
Thesis: "Reconstruction of boundary data: the case of Stokes equations"
Supervisor: Prof. Faten Khayat
2012 — 2014
MASTER'S
B.Sc. in Fundamental Mathematics
Faculty of Sciences of Monastir (FSM), University of Monastir, Monastir, Tunisia
2009 — 2011
BACHELOR'S
Baccalaureate — Mathematics
Tunisia
2007 — 2008

Research

My research develops mathematical and computational methods for problems where structure must be modeled, recovered, analyzed, or learned from complex data. The work lies at the intersection of applied mathematics, variational methods, partial differential equations (PDEs), optimization, and modern machine learning.

The research integrates mathematical modeling, numerical and optimization methods, and learning-based approaches to solve inverse problems, analyze structured data, and develop physics-informed computational systems for scientific and data-driven applications.

Research Architecture

Applied Mathematics
Mathematical
Modeling
PDEs Variational Methods Fractional Models Regularization
Computational
Methods
Optimization Numerical Methods Solvers Scientific Computing
Learning
Systems
Machine Learning Deep Learning Generative Models
Structured Problems
Image & Data
Analysis
Restoration Segmentation Edge Detection
Inverse
Problems
Recovery Regularization
Scientific
Computing
Modeling Simulation
Physics + Data Structure-Preserving Learning
GNNs Graph
Learning
PINNs Physics-Informed
Networks
Neural PDE Learning
Solvers

Research Directions

01
Mathematical & Variational Modeling
PDEs · Variational Methods · Fractional Models · Nonlinear Diffusion
Developing mathematical models and regularization methods for nonlinear and inverse problems, with emphasis on structural preservation and well-posed formulations.
02
Image Restoration & Analysis
Denoising · Deblurring · Inpainting · Segmentation · Edge Detection
Developing mathematical and computational methods for restoring degraded images and extracting meaningful structures from visual data.
03
Inverse Problems & Scientific Computing
Optimization · Numerical Methods · Iterative Solvers · PDE Solvers
Designing efficient numerical and optimization methods for inverse problems, mathematical models, and PDE-based computations.
04
Machine Learning & Structured Data
Machine Learning · Deep Learning · GNNs · Generative Models
Exploring learning-based approaches for complex, structured, and high-dimensional data, including graph-based and generative models.
05
Physics-Informed Learning
PINNs · Neural PDE Solvers · Physics-Informed Methods
Combining mathematical and physical constraints with neural networks to develop data-driven models that retain known scientific structure.

Research Evolution

Early Research
Mathematical Imaging
Variational methods Computer vision
Subsequent
Inverse Problems
Image restoration Fractional models Computer vision
Recent
Computational Intelligence
Deep learning Generative models Computer vision
Current
Physics + Learning
Graph networks PINNs Computer vision

Research Collaborations & Projects

PHC–Utique NAMRED Project (2018 — 2019)
Participant
Participant in the Franco-Tunisian research project NAMRED, funded through the Hubert Curien Partnership (PHC–Utique) between Université Côte d'Azur (France) and the University of Tunis El Manar (Tunisia) — joint research activities, scientific exchange and researcher mobility in applied mathematics and image processing.

Publications

Journal Articles

  1. A Fractional-Order Total Variation Regularization for Speckle Noise Removal and Its Numerical Algorithm
    H. Braiek · Journal of Mathematical Sciences, 2026. DOI: 10.1007/s10958-026-08611-z
  2. A new weighted Caputo fractional-order total variation for Cauchy noise removal with Bayesian optimization
    H. Braiek · The Visual Computer, 42(9):364, 2026. DOI: 10.1007/s00371-026-04524-9
  3. Variational Physics-Informed Neural Networks for the p(x)-Laplacian Problem
    H. Braiek · Boletim da Sociedade Paranaense de Matemática, 44(12), 2026. DOI: 10.5269/bspm.79742
  4. A fixed-point iteration for nonlinear PDE involving variable exponent function
    H. Braiek · Advanced Studies: Euro-Tbilisi Mathematical Journal, 19(2):123–140, 2026. DOI: 10.32513/asetmj/193220082619209
  5. Optimal Control Problem with Total Variation for p(x)-Biharmonic Constraint and Approximation
    H. Braiek · Jordan Journal of Mathematics and Statistics, 2026
  6. Primal-Dual Method for Image Denoising with Variable Exponent Sobolev Spaces
    H. Braiek · Moroccan Journal of Pure and Applied Analysis, 11(2):117–133, 2025. DOI: 10.34874/PRSM.mjpaa-vol11iss2.5711
  7. A nonlinear fourth-order PDE for image denoising in Sobolev spaces with variable exponents and its numerical algorithm
    H. Houichet, A. Theljani, M. Moakher · Computational and Applied Mathematics, 40(70), 2021. DOI: 10.1007/s40314-021-01462-1
  8. An adaptive Cahn-Hilliard equation for enhanced edges in binary image inpainting
    A. Theljani, H. Houichet, A. Mohamed · Journal of Algorithms & Computational Technology, 14:1–10, 2020. DOI: 10.1177/1748302620941430
  9. A topological sensitivity method to remove noise and detect edges in ultrasound images
    H. Houichet, M. Moakher, B. Rjaibi · New Trends in Mathematical Sciences, 7(4):421–440, 2019. DOI: 10.20852/ntmsci.2019.383
  10. A nonstandard higher-order variational model for speckle-noise removal and thin-structures detection
    H. Houichet, A. Theljani, M. Moakher, B. Rjaibi · Journal of Mathematical Study, 52(4):394–424, 2019. DOI: 10.4208/jms.v52n4.19.03

Conference Papers

  1. Advanced Spatio-Temporal Modeling of Seagrass Meadows Through Machine Learning Techniques
    H. Braiek, N. Nagati, M. Trabelsi, A. Ben Ayed, N. Mezni and M.-A. Askri · AFRICATEK 2025, LNICST vol. 677, Springer, 216-234, 2026. DOI: 10.1007/978-3-032-16638-8_15
  2. Split-convexity method for image restoration
    H. Braiek, A. Theljani, B. Rjaibi and M. Moakher · African Conference on Research in Computer Science and Applied Mathematics, CARI 2018, 14th-16th Oct 2018, Stellenbosch, South Africa. pp.104-110.
  3. Variable-exponent Kirchhoff model for image restoration and thin-structures detection using the topological gradient method
    H. Braiek, A. Theljani, B. Rjaibi and M. Moakher · Tendances des Applications Mathématiques en Tunisie, Algérie, Maroc, 325-232, 2017.

Under Review & Submitted

  1. A Novel Adaptive Variable-order Fractional Model for Speckle Noise Removal with Bayesian Optimization
    H. Braiek · Under Review
  2. Deep Learning-Based Framework for Plastic Debris Detection in Dynamic Aquatic Ecosystems
    H. Braiek · Under Review
  3. Adaptive Variable Exponent Functional for Multiplicative Noise Removal in Ultrasound Imaging
    H. Braiek · Submitted

Talks & Travel

Conferences & Funded Collaboration

10
1st International Conference on Advances in Operator Theory and Applications (ICAOTA 2026)
A Variable-Order Fractional Total Variation Operator for Image Restoration
Hammamet, Tunisia · 24–26 March 2026
09
International Conference on Recent Advances in Mathematics and Informatics (ICRAMI 2025)
Edge-Aware Image Denoising via Adaptive Weighted Fractional-Order TV under Cauchy Noise
Sousse, Tunisia · 20–23 November 2025
08
8th EAI Int. Conference on Emerging Technologies for Developing Countries (AFRICATEK 2025)
Advanced Spatio-Temporal Modeling of Seagrass Meadows Through ML Techniques
ESPRIT, Tunisia · 11–13 June 2025
07
African Conference on Research in Computer Science and Applied Mathematics (CARI 2018)
Split-convexity for image restoration
Stellenbosch, South Africa · 14–16 October 2018
06
Int. Conference on Inverse Problems, Control, and Shape Optimization (PICOF 2018)
Image restoration based on p(x)-biharmonic operator
Beirut, Lebanon · 18–20 June 2018
05
2nd Int. Conference on Computational Mathematics and Engineering Sciences (CMES 2017)
A Nonstandard Higher-Order PDE for Edge Detection in Medical Imaging Problems
Istanbul, Turkey · 20–22 May 2017
04
8th Trends in Mathematical Applications in Tunisia, Algeria, Morocco (TAMTAM 2017)
Variable-exponent Kirchhoff model for image restoration and edges detection
Hammamet, Tunisia · 10–13 May 2017
03
International Conference of the Euro-Maghreb Laboratory of Mathematics and their Interactions (LEM2I 2016)
Nonlinear variational model for image segmentation problem
Hammamet, Tunisia · 27 April – 1 May 2016
02
International Conference on Advanced Methods in Image Reconstruction (AMIR 2016)
p(·)-Kirchhoff model to speckle-noise removal and thin-structures detection
Tunis, Tunisia · 16 December 2016
01
International Conference on Inverse Problems, Control, and Shape Optimization (PICOF 2016)
Topological gradient approach to speckle noise removal and edge detection in ultrasound images
Autrans, France · 1–3 June 2016

Funded Collaboration

PHC–Utique NAMRED Project (2018 — 2019)
Participant
Participant in the Franco-Tunisian research project NAMRED, funded through the Hubert Curien Partnership (PHC–Utique) between Université Côte d'Azur (France) and the University of Tunis El Manar (Tunisia) — joint research activities, scientific exchange and researcher mobility in applied mathematics and image processing.

Teaching

In addition to my research activities, I teach and develop courses in numerical analysis, scientific computing, optimization, machine learning, big data, and related topics. My teaching interests include numerical methods for nonlinear equations, interpolation and approximation, numerical integration, optimization algorithms, and computational methods.

Teaching Overview

20 Modules
3 Cycles
8 Levels
4 Modes

Academic Positions & Courses

ESPRIT — École Supérieure Privée d'Ingénierie et de Technologies

2021 — Present
Engineering Cycle (1st – 3rd Year)
  • Mathematics Fundamental 1
    84 hours
    Content:
    • Mathematical logic and reasoning
    • Arithmetic in Z (integers)
    • Function study and analysis
    • Real sequences and convergence
    • Matrix calculation and operations
  • Mathematics Fundamental 2
    84 hours
    Content:
    • Vector spaces and linear applications
    • Polynomials and rational fractions
    • Riemann integrals and integration techniques
    • Limited developments and Taylor series
    • Differential equations
  • Mathematics Fundamental 3
    84 hours
    Content:
    • Diagonalization of square matrices
    • Trigonalization of square matrices
    • Bilinear forms and quadratic forms
    • Functions of several real variables
    • Differentiation and optimization of multivariable functions
  • Mathematics Fundamental 4
    84 hours
    Content:
    • Numerical series and convergence tests
    • Sequences and series of functions
    • Improper integrals and parameter-dependent integrals
    • Fourier transform and Fourier analysis
    • Introduction to discrete probability theory
  • Mathematics for Engineers
    42 hours
    Content:
    • Ordinary differential equations (ODEs)
    • Fourier series and transforms
    • Laplace transforms and applications
    • Complex analysis basics
    • Engineering applications and modeling
  • Estimation Techniques
    42 hours
    Content:
    • Point estimation methods
    • Maximum likelihood estimation (MLE)
    • Bayesian estimation
    • Hypothesis testing
    • Parameter inference and confidence intervals
  • Numerical Analysis
    42 hours
    Content:
    • Root finding algorithms
    • Interpolation methods
    • Numerical differentiation
    • Numerical integration (quadrature)
    • Solving linear and nonlinear systems
  • Scientific Computing
    42 hours
    Content:
    • Algorithm design principles
    • Computational complexity analysis
    • Numerical stability and error analysis
    • Optimization methods
    • Large-scale computing techniques
Data Science & BI (4th – 5th Year)
  • Statistics
    42 hours
    Content:
    • Descriptive statistics and measures
    • Hypothesis testing and p-values
    • ANOVA and variance analysis
    • Regression analysis (linear, multiple)
    • Data visualization techniques
  • ML Optimization
    30 hours
    Content:
    • Gradient descent variants
    • Convex optimization theory
    • Stochastic optimization methods
    • Hyperparameter tuning strategies
    • Second-order methods (Newton, Quasi-Newton)
  • Statistical Analysis (CINFO BI)
    21 hours
    Content:
    • Time series analysis and forecasting
    • Multivariate analysis
    • Data mining techniques
    • Dimensionality reduction
    • Business intelligence applications
Artificial Intelligence (ALINFO)
  • Machine Learning
    42 hours
    Content:
    • Supervised learning fundamentals
    • Regression techniques
    • Classification algorithms
    • Ensemble methods (Random Forest, Boosting)
    • Model evaluation and validation
  • Deep Learning
    21 hours
    Content:
    • Neural network architectures
    • Convolutional Neural Networks (CNNs)
    • Recurrent Neural Networks (RNNs)
    • Backpropagation and optimization
    • TensorFlow and PyTorch frameworks
  • AI Project
    42 hours
    Content:
    • Problem formulation and scoping
    • Data acquisition and preprocessing
    • Model development and training
    • Evaluation and testing
    • Deployment and production pipelines
  • Data Science Project
    30 hours
    Content:
    • Data collection and engineering
    • Data preprocessing and cleaning
    • Exploratory data analysis (EDA)
    • Feature engineering and selection
    • Reporting and visualization
  • Business Mission
    21 hours
    Content:
    • Real-world business problem analysis
    • Stakeholder engagement
    • Solution design and prototyping
    • Project management
    • Presentation and delivery
  • Natural Language Processing (NLP)
    21 hours
    Content:
    • Text preprocessing and tokenization
    • Word embeddings and representations
    • Transformer models and BERT
    • Language models and GPT
    • Sentiment analysis and classification

ENSTAB — National School of Advanced Sciences and Technologies

2019 — 2020
  • Integration & Probability
    42 hours
    Content:
    • Measure theory and integration
    • Probability distributions
    • Random variables
    • Law of large numbers
    • Central limit theorem
  • Numerical Analysis
    42 hours
    Content:
    • Root finding methods
    • Interpolation and approximation
    • Numerical integration
    • Finite differences
    • ODE solvers
  • Optimization
    21 hours
    Content:
    • Linear programming
    • Convex optimization theory
    • Gradient methods
    • Lagrange multipliers
    • Engineering applications

ENIT — National Engineering School of Tunis

2018 — 2019
  • MATLAB Initiation
    16 hours
    Content:
    • MATLAB environment and interface
    • Arrays and matrices
    • Plotting and visualization
    • Functions and scripts
    • Debugging tools

ISBB — Higher Institute of Biotechnology of Beja

2017 — 2018
  • Applied Mathematics
    21 hours
    Content:
    • Differential equations
    • Linear algebra
    • Optimization techniques
    • Mathematical modeling
    • Applications in biology

ISAMM — Higher Institute of Multimedia Arts of Manouba

2015 — 2016
  • Numerical Analysis
    21 hours
    Content:
    • Numerical methods for equations
    • Interpolation techniques
    • Numerical differentiation
    • Numerical integration
    • Optimization methods

Mentoring

I have supervised 20+ final-year engineering projects in Data Science, Artificial Intelligence, Machine Learning and Computer Vision since 2021. Below is a selection of recent project leadership.

Selected Project Leadership

Analysis & Prediction of Fraudulent Job Offers
2023 – 2024 · ESPRIT, Tunisia
End-to-end analytical platform for detecting fraudulent job advertisements — web scraping, data preprocessing, machine-learning modelling and interactive Power BI dashboards.
Analysis & Visualization of Road Traffic Accidents
2023 – 2024 · ESPRIT, Tunisia
Complete data-analytics solution using SQL Server for accident-data management, statistical analysis and interactive visualization.
Mapping Seagrass Meadows with Satellite Imagery & CV
2024 – 2025 · ESPRIT, Tunisia
Machine-learning and computer-vision techniques for detecting and spatio-temporally mapping seagrass ecosystems from remote-sensing data.
ELBankeji — Multilingual Conversational Agent for Banking
2024 – 2025 · ESPRIT
Design and implementation of an AI-powered multilingual conversational agent tailored to banking services and customer support.
Intelligent Medical Prescription Management Using NLP
2025 – 2026 · ESPRIT
Intelligent system for processing and managing medical prescriptions, built on modern natural-language-processing techniques.

Toolbox

A combination of mathematical analysis tools, programming languages, and modern data science frameworks used in my research and teaching.

Skills

Programming & Computing
PythonMATLABFreeFem++R
Data & Machine Learning
Scikit-learnTensorFlowPyTorchPower BIHadoopMongoDB
Languages
Arabic (Native)French (Fluent)English (Advanced)

Certifications

Neural Networks & Deep Learning
DeepLearning.AI · 2022
Convolutional Neural Networks
DeepLearning.AI · 2022
Machine Learning with Python
IBM · 2022
ML in Python with Scikit-learn
France Université Numérique · 2022
Supervised Learning with Scikit-learn
DataCamp · 2022
Data Science & ML Fundamentals
CFI · 2022

Research Stays

Laboratoire J.A. Dieudonné
Université Côte d'Azur (Nice, France)
Jun–Jul 2018
Jun–Jul 2017
Oct–Nov 2016