Compressed Sensing, Sparse Representation: Entry-Level Examples and Code Implementation

Here we provide introductory examples for compressed sensing, compressed sampling, and sparse representation to help readers better understand these concepts. When sampling signals, traditional methods often require collecting massive amounts of data, which consumes substantial storage space and increases computational complexity. Compressed sensing techniques enable significant data reduction while preserving sufficient information for accurate signal reconstruction. Sparse representation methods express signals using limited linear combinations, revealing the essential characteristics of signals. These examples demonstrate practical implementations using key algorithms like L1-minimization and orthogonal matching pursuit (OMP), showing how to achieve signal recovery from under-sampled measurements. Through hands-on MATLAB/Python code examples, learners can understand critical functions such as measurement matrix generation, sparse coding, and reconstruction algorithms that form the foundation of modern signal processing systems.