Abstract
According to the theory of compressive sensing, a single-pixel imaging system was built in our laboratory, and imaging scenes are successfully reconstructed by single-pixel imaging, but the quality of reconstructed images in traditional methods cannot meet the demands of further engineering applications. In order to improve the imaging accuracy of our single-pixel camera, some optimization methods of key technologies in compressive sensing are proposed in this paper. First, in terms of sparse signal decomposition, based on traditional discrete wavelet transform and the characteristics of coefficients distribution in wavelet domain, a constraint condition of the exponential decay is proposed and a corresponding constraint matrix is designed to optimize the original wavelet decomposition basis. Second, for the construction of deterministic binary sensing matrices in the single-pixel camera, on the basis of a Gram matrix, a new algorithm model and a new method of initializing a compressed sensing measurement matrix are proposed to optimize the traditional binary sensing matrices via mutual coherence minimization. The gradient projection-based algorithm is used to solve the new mathematical model and train deterministic binary sensing measurement matrices with better performance. Third, the proposed optimization methods are applied to our single-pixel imaging system for optimizing the existing imaging methods. Compared with the conventional methods of single-pixel imaging, the accuracy of image reconstruction and the quality of single-pixel imaging have been significantly improved by our methods. The superior performance of our proposed methods has been fully tested and the effectiveness has also been demonstrated by numerical simulation experiments and practical imaging experiments.
Highlights
According to information theory, one can know that the traditional signal sampling and signal recovery must meet the Shannon-Nyquist theorem [1], which states that to recover the original signal without distortion from a sampled discrete signal, it is required that the signal sampling frequency must be at least twice the bandwidth of the original signal
We describe experiments conducted to test the performance of our optimized wavelet decomposition basis and optimized binary sensing matrix for compressively sensed image reconstruction, compared with the traditional wavelet decomposition basis and the conventional binary measurement matrices that are usually used in single-pixel imaging respectively
These above experiments have well tested the superior performance of our proposed methods in optimizing traditional wavelet decomposition basis and constructing new binary measurement matrices based on the conventional binary sensing matrix
Summary
One can know that the traditional signal sampling and signal recovery must meet the Shannon-Nyquist theorem [1], which states that to recover the original signal without distortion from a sampled discrete signal, it is required that the signal sampling frequency must be at least twice the bandwidth of the original signal. The structure and performance of traditional binary sensing matrices are usually not optimal, which extremely limits the improvement space of expanding compressed sensing measurement matrix and further enhancing imaging quality in single-pixel camera.
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