Basis Pursuit Algorithm Simulation for Video Compressed Sensing Systems

Video compressed sensing is a technique that leverages signal sparsity to reduce sampling rates, enabling high-quality signal reconstruction under conditions significantly below the Nyquist sampling rate. The Basis Pursuit algorithm, as a classical reconstruction method in compressed sensing, recovers the original signal by solving a sparse optimization problem through linear programming or convex optimization techniques.

In video compressed sensing systems, the core concept of the Basis Pursuit algorithm involves transforming the sparse representation of video frames into an optimization problem. Video signals typically exhibit temporal and spatial redundancy, which can be represented as a limited number of non-zero coefficients through appropriate sparse transformations (e.g., Discrete Cosine Transform or Wavelet Transform). The Basis Pursuit algorithm reconstructs the original video signal by minimizing the signal's sparse norm while incorporating constraints from the measurement matrix.

Simulation implementation generally includes the following key steps: First, video frames undergo block processing, followed by sparse transformation for each block. Next, compressed sampling is performed on the transformed sparse coefficients using a random measurement matrix (e.g., Gaussian or Bernoulli matrices). Finally, the Basis Pursuit algorithm solves the optimization problem to recover sparse coefficients and reconstruct video frames. Implementation typically involves optimization solvers like CVX or L1-homotopy methods, with key functions including sparse coefficient recovery and inverse transformation operations.

In practical simulations, algorithm performance is influenced by factors such as sparse basis selection, measurement matrix design, and optimization solving methods. By adjusting these parameters, different compression ratios and reconstruction quality trade-offs can be achieved. Additionally, for video sequences, inter-frame correlation must be considered to further enhance compressed sensing efficiency. Basis Pursuit algorithm simulations provide crucial references for optimizing video compression systems and can validate the performance of other improved algorithms through comparative MATLAB or Python implementations.