2D Wavelet Transform for Image Processing with Compression and Compressed Sensing Applications

In this project, we implement a 2D wavelet transform to achieve image compression and compressed sensing objectives. The implementation involves using wavelet transforms to decompose images into frequency and spatial components, where we selectively retain significant coefficients to achieve compression. Through MATLAB's wavelet toolbox functions like wavedec2() for decomposition and waverec2() for reconstruction, we can efficiently process image data. The compressed sensing technique further reduces bandwidth requirements and storage space by leveraging sparse representations in the wavelet domain. This approach utilizes optimization algorithms such as L1-minimization to reconstruct images from fewer measurements. The application of this technology significantly enhances image transmission efficiency and speed while reducing storage requirements and transmission costs. Key implementation aspects include thresholding techniques for coefficient selection, measurement matrix design for compressed sensing, and reconstruction algorithms for accurate image recovery.