Comparison of Reconstruction Performance: BP vs OMP vs StOMP on Natural Images

In the field of natural image reconstruction, Basis Pursuit (BP), Orthogonal Matching Pursuit (OMP), and Stagewise Orthogonal Matching Pursuit (StOMP) are three classical reconstruction algorithms based on compressed sensing theory. These methods can recover original signals from limited sampling data. Using the 256×256 Lena image as a case study, this article compares the reconstruction performance of these three methods after compressed sampling and analyzes StOMP's performance variations under different threshold settings. The BP algorithm achieves precise reconstruction of sparse signals by minimizing the L1 norm through convex optimization techniques. Its main advantage lies in achieving global optimal solutions, making it particularly suitable for high-precision applications. However, it involves solving complex optimization problems using methods like linear programming or interior-point algorithms, resulting in higher computational complexity and longer reconstruction times. For natural images, BP preserves edge and texture details effectively, but may produce smoothing effects at lower sampling rates. OMP employs a greedy iterative strategy that progressively selects the most correlated atoms (basis functions) to approximate the target signal. The algorithm implementation typically involves correlation computation, atom selection, and residual updating in each iteration. OMP offers faster reconstruction speed compared to BP, making it suitable for small to medium-scale problems. However, its efficiency decreases with high-dimensional data due to increased iteration counts. For the Lena image, OMP quickly recovers basic structures but may generate artifacts in complex texture regions, particularly when low-frequency components dominate. StOMP represents an improved version of OMP that enhances computational efficiency by batch-selecting atoms through thresholding mechanisms. The implementation involves setting a threshold parameter to determine which atoms to select in each stage, significantly reducing the number of required iterations. The algorithm's performance heavily depends on threshold selection: higher thresholds lead to conservative atom selection, potentially losing image details, while lower thresholds may introduce noise. Experimental results demonstrate that for the Lena image, moderate threshold values achieve a balance between reconstruction speed and accuracy, preserving hair textures while avoiding background noise. In summary, BP is ideal for scenarios demanding strict quality requirements, OMP provides a compromise between efficiency and effectiveness, while StOMP offers flexibility through threshold parameter tuning to adapt to different needs. Practical applications should consider computational resources and image characteristics when selecting the appropriate algorithm.