About Me
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
Education
Supervisors: Prof. Maher Moakher & Prof. Badreddine Rjaibi
Supervisor: Prof. Faten Khayat
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
Modeling
Methods
Systems
Analysis
Problems
Computing
Learning
Networks
Solvers
Research Directions
Research Evolution
Research Collaborations & Projects
Publications
Journal Articles
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A Fractional-Order Total Variation Regularization for Speckle Noise Removal and Its Numerical Algorithm
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A new weighted Caputo fractional-order total variation for Cauchy noise removal with Bayesian optimization
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Variational Physics-Informed Neural Networks for the p(x)-Laplacian Problem
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A fixed-point iteration for nonlinear PDE involving variable exponent function
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Optimal Control Problem with Total Variation for p(x)-Biharmonic Constraint and Approximation
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Primal-Dual Method for Image Denoising with Variable Exponent Sobolev Spaces
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A nonlinear fourth-order PDE for image denoising in Sobolev spaces with variable exponents and its numerical algorithm
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An adaptive Cahn-Hilliard equation for enhanced edges in binary image inpainting
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A topological sensitivity method to remove noise and detect edges in ultrasound images
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A nonstandard higher-order variational model for speckle-noise removal and thin-structures detection
Conference Papers
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Advanced Spatio-Temporal Modeling of Seagrass Meadows Through Machine Learning Techniques
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Split-convexity method for image restoration
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Variable-exponent Kirchhoff model for image restoration and thin-structures detection using the topological gradient method
Under Review & Submitted
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A Novel Adaptive Variable-order Fractional Model for Speckle Noise Removal with Bayesian Optimization
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Deep Learning-Based Framework for Plastic Debris Detection in Dynamic Aquatic Ecosystems
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Adaptive Variable Exponent Functional for Multiplicative Noise Removal in Ultrasound Imaging
Talks & Travel
Conferences & Funded Collaboration
Funded Collaboration
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
Academic Positions & Courses
ESPRIT — École Supérieure Privée d'Ingénierie et de Technologies
2021 — Present-
Mathematics Fundamental 1Content:
- Mathematical logic and reasoning
- Arithmetic in Z (integers)
- Function study and analysis
- Real sequences and convergence
- Matrix calculation and operations
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Mathematics Fundamental 2Content:
- Vector spaces and linear applications
- Polynomials and rational fractions
- Riemann integrals and integration techniques
- Limited developments and Taylor series
- Differential equations
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Mathematics Fundamental 3Content:
- Diagonalization of square matrices
- Trigonalization of square matrices
- Bilinear forms and quadratic forms
- Functions of several real variables
- Differentiation and optimization of multivariable functions
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Mathematics Fundamental 4Content:
- 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
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Mathematics for EngineersContent:
- Ordinary differential equations (ODEs)
- Fourier series and transforms
- Laplace transforms and applications
- Complex analysis basics
- Engineering applications and modeling
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Estimation TechniquesContent:
- Point estimation methods
- Maximum likelihood estimation (MLE)
- Bayesian estimation
- Hypothesis testing
- Parameter inference and confidence intervals
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Numerical AnalysisContent:
- Root finding algorithms
- Interpolation methods
- Numerical differentiation
- Numerical integration (quadrature)
- Solving linear and nonlinear systems
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Scientific ComputingContent:
- Algorithm design principles
- Computational complexity analysis
- Numerical stability and error analysis
- Optimization methods
- Large-scale computing techniques
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StatisticsContent:
- Descriptive statistics and measures
- Hypothesis testing and p-values
- ANOVA and variance analysis
- Regression analysis (linear, multiple)
- Data visualization techniques
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ML OptimizationContent:
- Gradient descent variants
- Convex optimization theory
- Stochastic optimization methods
- Hyperparameter tuning strategies
- Second-order methods (Newton, Quasi-Newton)
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Statistical Analysis (CINFO BI)Content:
- Time series analysis and forecasting
- Multivariate analysis
- Data mining techniques
- Dimensionality reduction
- Business intelligence applications
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Machine LearningContent:
- Supervised learning fundamentals
- Regression techniques
- Classification algorithms
- Ensemble methods (Random Forest, Boosting)
- Model evaluation and validation
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Deep LearningContent:
- Neural network architectures
- Convolutional Neural Networks (CNNs)
- Recurrent Neural Networks (RNNs)
- Backpropagation and optimization
- TensorFlow and PyTorch frameworks
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AI ProjectContent:
- Problem formulation and scoping
- Data acquisition and preprocessing
- Model development and training
- Evaluation and testing
- Deployment and production pipelines
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Data Science ProjectContent:
- Data collection and engineering
- Data preprocessing and cleaning
- Exploratory data analysis (EDA)
- Feature engineering and selection
- Reporting and visualization
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Business MissionContent:
- Real-world business problem analysis
- Stakeholder engagement
- Solution design and prototyping
- Project management
- Presentation and delivery
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Natural Language Processing (NLP)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 & ProbabilityContent:
- Measure theory and integration
- Probability distributions
- Random variables
- Law of large numbers
- Central limit theorem
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Numerical AnalysisContent:
- Root finding methods
- Interpolation and approximation
- Numerical integration
- Finite differences
- ODE solvers
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OptimizationContent:
- Linear programming
- Convex optimization theory
- Gradient methods
- Lagrange multipliers
- Engineering applications
ENIT — National Engineering School of Tunis
2018 — 2019-
MATLAB InitiationContent:
- 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 MathematicsContent:
- Differential equations
- Linear algebra
- Optimization techniques
- Mathematical modeling
- Applications in biology
ISAMM — Higher Institute of Multimedia Arts of Manouba
2015 — 2016-
Numerical AnalysisContent:
- 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
Toolbox
A combination of mathematical analysis tools, programming languages, and modern data science frameworks used in my research and teaching.
Skills
Certifications
Research Stays
Jun–Jul 2017
Oct–Nov 2016