Example Routine: Plotting the Relationship Curve Between Signal Measurement Count M and Reconstruction Success Probability

In signal processing, the relationship curve between measurement count M and reconstruction success probability serves as a critical tool for evaluating compressed sensing system performance. This curve visually demonstrates how signal reconstruction success rates evolve with increasing sampling points M, providing data-driven support for determining the minimum effective measurement count. The implementation approach involves three main steps: First, set different M values (e.g., ranging from 10 to 100 with increments) and perform Monte Carlo experiments for each M value (typically repeating 1000 trials of random signal generation and reconstruction). Then, count successful reconstructions for each M and calculate corresponding probabilities. Finally, connect data points using smoothing curves. Key parameters include signal sparsity, observation matrix type (e.g., Gaussian random matrix), and reconstruction algorithm selection (such as OMP or Basis Pursuit). The curve typically exhibits an S-shaped characteristic: success probability remains near zero when M falls below a critical threshold, then rapidly increases to 100% once exceeding a certain value. The inflection point corresponds to the theoretical lower bound of minimum measurements, though practical applications require 20%-30% additional margin to account for noise interference. By adjusting sparsity parameters, comparative analysis can reveal how signal complexity affects measurement requirements across different scenarios. Code implementation notes: - Use vectorized operations for efficient Monte Carlo simulations - Implement OMP algorithm with orthogonal projections for sparse recovery - Apply moving average or spline interpolation for curve smoothing - Utilize matrix multiplication functions for observation matrix operations - Configure random seed for reproducible实验结果