Compressed Sensing MATLAB Code Implementation

In modern communication fields, compressed sensing technology represents a groundbreaking sampling theory. By exploiting signal sparsity properties, it acquires discrete signal samples through random sampling at rates substantially lower than Nyquist requirements, followed by perfect reconstruction using nonlinear recovery algorithms. Since its proposal, this technology has attracted extensive attention from both academic and industrial communities. Its applications extend beyond information theory, image processing, optics, pattern recognition, and wireless communications to include geosciences, atmospheric studies, and geological research. Consequently, compressed sensing was recognized by Technology Review as one of the top 10 scientific advancements of 2007.

To better understand this technology, MATLAB implementations typically involve generating random sparse signals, applying compressed sensing principles for sampling and reconstruction, and comparing final results with original signals. The implementation generally includes three key components: sparse signal generation using random Bernoulli/Gaussian distributions, measurement matrix creation through random projection operators like Gaussian or Bernoulli matrices, and reconstruction algorithms such as L1-minimization using Basis Pursuit or Orthogonal Matching Pursuit (OMP). This comparative analysis helps demonstrate the technology's practical applications and reconstruction accuracy. In summary, compressed sensing technology provides innovative approaches for communication development, warranting further research and implementation.