Orthogonal Matching Pursuit (OMP) and CoSaMP Algorithm Implementation in MATLAB

This article explores the implementation of Orthogonal Matching Pursuit (OMP) and Compressive Sampling Matching Pursuit (CoSaMP) algorithms in MATLAB. Both algorithms are fundamental in compressed sensing and are widely used for signal reconstruction, feature selection, and image processing applications. We will provide detailed explanations of their theoretical foundations and implementation approaches, including key MATLAB functions and algorithmic steps. The OMP algorithm operates through iterative selection of the most correlated atoms from a dictionary, followed by orthogonal projection to update the residual. Implementation typically involves correlation calculations using matrix multiplication, least-squares solutions via pseudoinverse operations, and residual updates. Meanwhile, CoSaMP extends this approach by maintaining multiple candidate supports per iteration, requiring advanced matrix operations and support set management. We will demonstrate practical implementation techniques including sparse representation formulation, measurement matrix design, and reconstruction error analysis. The article includes sample MATLAB code showcasing algorithm initialization, iteration control, and performance validation methods. These implementations will help readers understand how to apply these algorithms to real-world problems with proper parameter tuning and optimization considerations.