Optimization Problem Solving, Compressive Sensing Methods and Their Applications in Sparse Signal and Image Processing

This courseware was developed by Professor Wusheng Lu from the Department of Electrical and Computer Engineering at the University of Victoria, Canada, designed to support short-term intensive courses at domestic universities. The content covers optimization problem solving, compressive sensing methods, and their applications in sparse signal and image processing, including compression, reconstruction, and denoising techniques. The optimization section explores various methods including linear programming (implemented using simplex algorithms), integer programming (branch-and-bound methods), and nonlinear programming (gradient-based optimization techniques). The courseware introduces compressive sensing methodology with practical implementations using L1-norm minimization algorithms and orthogonal matching pursuit (OMP) for signal reconstruction. Students will learn how to apply compressive sensing techniques to process sparse signals and images through practical code examples demonstrating sampling matrix construction and reconstruction algorithms. Additionally, the courseware covers commonly used denoising methods such as wavelet transform (with thresholding implementations) and singular value decomposition (SVD-based noise reduction techniques). Through this courseware, students can gain deep insights into cutting-edge technologies and applications in computer engineering, establishing a solid foundation for future studies and professional work. The material includes MATLAB code snippets and algorithm flowcharts to illustrate practical implementation approaches.