Advanced Signal Processing

Throughout my research and various projects, I've harnessed the power of advanced signal processing and optimization techniques to address complex problems in wireless communications, and RF/Microwave remote sensing. A brief overview includes:

Employed Optimization Techniques :

• Majorization-Minimization: Used to iteratively optimize non-convex functions by constructing simpler surrogate functions that are easier to minimize.

• Convex & Non-Convex Programming: used for optimization problems with convex objectives and constraints, as well as non-convex programming methods for more complex, non-convex optimization tasks.

• Regularization-Based Optimization: used to introduce additional information or constraints into optimization problems, often to prevent overfitting or encourage desired properties in solutions.

• Augmented Lagrangian Multipliers (ALM): used to solve constrained optimization problems by iteratively updating Lagrange multipliers and optimizing an augmented Lagrangian function.

• Linear Programming: used to optimize linear objective functions subject to linear constraints, often used in resource allocation problems.

• Gradient Descent: Utilized to optimize functions by iteratively adjusting the solution in the direction of the steepest gradient, seeking the minimum or maximum of the function.

• Proximal Gradient Descent: Employed proximal gradient descent, a variant of gradient descent, often used for optimizing non-smooth and convex functions, particularly in sparse optimization problems.

Addressed Challenges :

• Sparse Representation

• Compressive Sensing

• Low Rank Plus Sparse Matrix Decomposition

• Low-Rank Matrix Completion

• Inverse Problem Methodologies

• Broad Spectrum of Applications:

• Microwave Imaging

• Wireless Communications (Optimal Resource Allocation)

• Radar Signal Processing

• Adaptive Waveform Design

• Robust and Real-Time Enhancement Design