有限新息率采样中Fast Cadzow去噪方法研究

Research on the Fast Cadzow Denoising Method in Finite Rate of Innovation Sampling

摘要: 本文研究了有限新息率(Finite Rate of Innovation, FRI)信号采样中的Fast Cadzow迭代去噪方法。针对传统Cadzow算法在高维数据降噪中计算复杂度高、收敛速度慢的问题，使用了一种基于子空间投影优化的Fast Cadzow算法，通过减少奇异值分解(SVD)的计算量，提升了算法的效率。本文详细分析了Fast Cadzow算法的数学原理和实现过程，并通过数值仿真实验对其在不同信噪比(SNR)条件下的降噪效果和计算效率进行了验证。实验结果表明，与传统Cadzow算法相比，Fast Cadzow算法在PSNR、计算效率上均表现出显著优势，尤其在低信噪比环境中展现出更强的抗噪能力。本文的研究成果为FRI信号重构时的高效降噪提供了一种新的解决方案，对实际信号处理中的稀疏信号重构具有重要的应用价值。

Abstract: This paper investigates the Fast Cadzow iterative denoising method in Finite Rate of Innovation (FRI) signal sampling. Addressing the limitations of the traditional Cadzow algorithm, which exhibits high computational complexity and slow convergence in high-dimensional data denoising, we employ an optimized Fast Cadzow algorithm based on subspace projection. This approach significantly reduces the computational load of singular value decomposition (SVD) operations, improving the algorithm’s efficiency. We thoroughly analyze the mathematical principles and implementation of the Fast Cadzow algorithm and validate its denoising performance and computational efficiency through numerical simulations under different signal-to-noise ratio (SNR) conditions. Experimental results demonstrate that, compared to the traditional Cadzow algorithm, the Fast Cadzow algorithm achieves significant improvements in PSNR and computational efficiency, with stronger noise resistance, especially in low SNR environments. The findings of this study offer an effective solution for efficient denoising in FRI signal reconstruction and hold substantial application value for sparse signal reconstruction in practical signal processing scenarios.