Compressive Sensing Code Implementation Using Orthogonal Matching Pursuit Algorithm

This article presents comprehensive compressive sensing code implementation and explores image reconstruction using the orthogonal Matching Pursuit (OMP) algorithm. Compressive sensing represents a relatively novel signal processing technique that reduces data volume while preserving image quality through sparse signal sampling below the Nyquist rate. The Orthogonal Matching Pursuit algorithm serves as a fundamental compressive sensing signal reconstruction method that iteratively identifies the optimal solution by selecting dictionary atoms most correlated with current residuals. Key implementation steps include: 1. Initializing residual to original signal 2. Identifying highest-correlation atom indices through dot product calculations 3. Solving least-squares problem using pseudoinverse (pinv() in MATLAB) 4. Updating residuals and repeating until convergence We explain these concepts through accessible demonstrations and provide practical code examples to assist newcomers in understanding compressive sensing fundamentals. The article further discusses compressive sensing applications in image processing domains like medical imaging and remote sensing, along with future development directions including deep learning integration and hardware acceleration. This resource aims to help readers develop solid understanding of compressive sensing principles and OMP algorithm implementation through clearly annotated code structures and mathematical foundations.