MATLAB-Based Compressed Sensing with DCT, DWT, and DFT Orthogonal Bases

This article explores MATLAB-based compressed sensing techniques utilizing Discrete Cosine Transform (DCT), Discrete Wavelet Transform (DWT), and Discrete Fourier Transform (DFT) orthogonal bases along with overcomplete dictionaries for sparse signal decomposition and reconstruction. Compressed sensing has extensive applications in signal processing, effectively reducing data redundancy while enhancing sampling efficiency. The implementation typically involves creating measurement matrices using random sampling operators and applying optimization algorithms like L1-norm minimization for signal recovery. Key MATLAB functions include dct(), dwt(), and fft() for basis transformations, along with sparse recovery algorithms such as Orthogonal Matching Pursuit (OMP) implemented through custom scripting. The article delves into the fundamental principles, practical implementation methodologies, and demonstrates both achieved results and future prospects of this technology in real-world applications.