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奈奎斯特采样定律是长久以来具有指导意义的经典信号处理技术,它提出信号在采样过程中,当且仅当采样率大于信号带宽的2倍时,才能精确重构信号。压缩感知理论突破了奈奎斯特采样定理对信号采样率的限制,以更低采样率采样信号,并通过适当的重构算法恢复信号。文中以压缩感知理论为基础,结合目前广泛采用的正交匹配追踪算法,基于矩阵分解思想,提出2种改进算法,在运算复杂度方面取得优化,并且满足信号处理时对重构精度的要求。
Nyquist sampling theorem has long been a guiding principle of classical signal processing, it proposed the signal in the sampling process, and only when the sampling rate is greater than twice the signal bandwidth, the signal can be accurately reconstructed. Compressive sensing theory breaks the limit of the Nyquist sampling theorem on signal sampling rate, samples the signal at a lower sampling rate, and restores the signal through an appropriate reconstruction algorithm. In this paper, based on the compressed sensing theory, combined with the currently widely used orthogonal matching pursuit algorithm, based on the idea of matrix decomposition, two improved algorithms are proposed to optimize the computational complexity and meet the requirements for signal reconstruction accuracy.