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1、一种改进的高斯频率域压缩感知稀疏反演方法(英文)AbstractCompressive sensing and sparse inversion methods have gained a significant amount of attention in recent years due to their capability to accurately reconstruct signals from measurements with significantly less data than previously possible. In this paper, a modified
2、Gaussian frequency domain compressive sensing and sparse inversion method is proposed, which leverages the proven strengths of the traditional method to enhance its accuracy and performance. Simulation results demonstrate that the proposed method can achieve a higher signal-to- noise ratio and a bet
3、ter reconstruction quality than its traditional counterpart, while also reducing the computational complexity of the inversion procedure.IntroductionCompressive sensing (CS) is an emerging field that has garnered significant interest in recent years because it leverages the sparsity of signals to re
4、duce the number of measurements required to accurately reconstruct the signal. This has many advantages over traditional signal processing methods, including faster data acquisition times, reduced power consumption, and lower data storage requirements. CS has been successfully applied to a wide rang
5、e of fields, including medical imaging, wireless communications, and surveillance.One of the most commonly used methods in compressive sensing is the Gaussian frequency domain compressive sensing and sparse inversion (GFD-CS) method. In this method, compressive measurements are acquired by multiplyi
6、ng the original signal with a randomly generated sensing matrix. The measurements are then transformed into the frequency domain using the Fourier transform, and the sparse signal is reconstructed using a sparsity promoting algorithm.In recent years, researchers have made numerous improvements to th
7、e GFD-CS method, with the goal of improving its reconstruction accuracy, reducing its computational complexity, and enhancing its robustness to noise. In this paper, we propose a modified GFD-CS method that combines several techniques to achieve these objectives.Proposed MethodThe proposed method bu
8、ilds upon the well-established GFD-CS method, with several key modifications. The first modification is the use of a hierarchical sparsity-promoting algorithm, which promotes sparsity at both the signal level and the transform level. This is achieved by applying the hierarchical thresholding techniq
9、ue to the coefficients corresponding to the higher frequency components of the transformed signal.The second modification is the use of a novel error feedback mechanism, which reduces the impact of measurement noise on the reconstructed signal. Specifically, the proposed method utilizes an iterative
10、 algorithm that updates the measurement error based on the difference between the reconstructed signal and the measured signal. This feedback mechanism effectively increases the signal-to-noise ratio of the reconstructed signal, improving its accuracy and robustness to noise.The third modification i
11、s the use of a low-rank approximation method, which reduces the computational complexity of the inversion algorithm while maintaining reconstruction accuracy. This is achieved by decomposing the sensing matrix into a product of two lower dimensional matrices, which can be subsequently inverted using
12、 a more efficient algorithm.Simulation ResultsTo evaluate the effectiveness of the proposed method, we conducted simulations using synthetic data sets. Three different signal types were considered: a sinusoidal signal, a pulse signal, and an image signal. The results of the simulations were compared
13、 to those obtained using the traditional GFD-CS method.The simulation results demonstrate that the proposed method outperforms the traditional GFD-CS method in terms of signal-to-noise ratio and reconstruction quality. Specifically, the proposed method achieves a higher signal-to-noise ratio and low
14、er mean squared error for all three types of signals considered. Furthermore, the proposed method achieves these results with a reduced computational complexity compared to the traditional method.ConclusionThe results of our simulations demonstrate the effectiveness of the proposed method in enhanci
15、ng the accuracy and performance of the GFD-CS method. The combination of sparsity promotion, error feedback, and low-rank approximation techniques significantly improves the signal-to-noise ratio and reconstruction quality, while reducing the computational complexity of the inversion procedure. Our proposed method has potential applications in a wide range of fields, including medical imaging, wireless communications, and surveillance.