Compressed Sensing Algorithm for Reconstructing Lena Image Using Wavelet Transform and OMP Reconstruction

In this project, we implement a compressed sensing algorithm that utilizes wavelet transform and Orthogonal Matching Pursuit (OMP) reconstruction to recover the Lena test image. This algorithm provides an efficient approach for conserving computational resources by reducing the amount of data required for storage and transmission. The implementation involves first applying a discrete wavelet transform (DWT) to decompose the Lena image into multi-resolution coefficients, followed by the OMP algorithm for sparse signal reconstruction. Key implementation aspects include selecting appropriate wavelet bases (such as Haar or Daubechies wavelets) and configuring OMP parameters like sparsity level and tolerance threshold. We will examine both the advantages and limitations of this approach, including its computational efficiency and reconstruction quality, while comparing its performance against other compression algorithms such as JPEG and conventional transform coding methods. The project also explores fundamental compressed sensing concepts and their applications in computer vision and image processing, particularly focusing on lossless compression techniques and distortion-free image recovery. Additionally, we discuss how to extend compressed sensing algorithms to other domains including speech signal processing and biomedical image analysis, with implementation considerations for different signal types. Finally, we address future research directions and potential applications of compressed sensing algorithms in emerging technologies, such as adaptive sensing matrices and deep learning-enhanced reconstruction methods.