Application of Compressed Sensing OMP Algorithm in Image Compression and Recovery

This article explores the application of the Orthogonal Matching Pursuit (OMP) algorithm in compressed sensing for image compression and recovery. Compressed sensing technology has gained widespread adoption in image processing due to its ability to maintain high image quality while significantly reducing data volume. The algorithm leverages signal sparsity and computes inner products between signals and measurement matrices to minimize sampling requirements, enabling efficient compression and reconstruction. In implementation, the OMP algorithm iteratively selects the most correlated atoms from a dictionary based on residual signals, with key functions including sparse representation initialization and orthogonal projection calculations. We further examine the algorithm's advantages in computational efficiency and reconstruction accuracy, alongside limitations such as sensitivity to measurement matrix design and sparsity assumptions. The discussion extends to practical implementation challenges and potential applications in resource-constrained environments.