Optimizing the sparse basis is an effective way to enhance single-pixel imaging performance. Compressed sensing typically employs discrete wavelet basis to map signals into the wavelet domain to achieve approximate sparsity, where wavelet coefficients resemble an exponential decay form. However, in the penalty term of cost function, large lowfrequency wavelet coefficients carry higher weights, while the weights assigned to small high-frequency coefficients are much smaller. This implies that high-frequency coefficients are easily neglected in optimization and are even mistaken as noise and removed, resulting in the loss of image details.We propose an effective method that introduces a diagonal matrix W with exponentially increasing diagonal elements to balance the weights of low-frequency and high-frequency wavelet coefficients, ensuring the weights of high-frequency coefficients are ample to prevent them from being mistakenly treated as noise and discarded.For normalized images of size 256*256 with 25% sampling, proposed method are applied to several common compressed sensing algorithms for single-pixel imaging reconstruction such as L1-minimization, LASSO, and OMP. The simulation results indicate an average improvement of 1.10dB, 1.32dB, and 2.65dB in PSNR, respectively. Even in the presence of strong Gaussian noise with σ =0.2, the method can still partly enhance reconstruction performance.This research provides a novel perspective on optimizing the sparse basis and a practical approach to improving single-pixel imaging performance.
Deformable mirrors are key active components in adaptive optics systems that enable real-time correction of wavefronts. When using lightweight high-coupling deformable mirrors to fit large RMS wavefronts, the best-fitting voltage often exceeds the maximum deformation voltage of the deformable mirror. In such a case, cropping the voltage directly will greatly destroy the wavefront. This will affect the closed-loop effect. In response to the above issues, we propose using the interior point method to fit the wavefront. This method can directly solve the problem in the voltage range allowed by the deformable mirror, which not only simplifies the steps of the original method, but also greatly improves the fitting capability of the deformable mirror. We used the traditional least-squares method and the interior-point method to fit the static aberrations separately in the simulations. Results show that for the original wavefront (RMS = 2059.70 nm), the least squares algorithm can correct the aberrations to 425.35 nm, while the interior point method can correct the aberrations to 248.10 nm. In the experiments, we used a deformable mirror with 294 actuators for closed-loop testing. The experiment results show that for the original wavefront (RMS = 808.53 nm), the least squares algorithm can correct the aberrations to 182.39 nm, while the interior point method can correct the aberrations to 100.95 nm. This method has great significance for giving full exploit to the performance of the deformable mirror and improving the wavefront correction capability of the AO system.
When adaptive optics is applied to target identification, laser high beam quality transmission and other fields, extended object wavefront detection is a technical challenge. And the detection accuracy directly affects the adaptive optics correction effect. To investigate the problem that the focal length of microlens affects the accuracy of extended target wavefront detection. In this paper, a simulation model of extended target wavefront detection based on correlated Hartmann's variable focus was established. The model was based on the commonly used optical system parameters, and it was also established by using the theories of Fresnel diffraction, Newton's imaging equation, the working principle of Shack-Hartmann wavefront detector, and wavefront reconstruction. We analyzed the effect of microlens focal length variation on the wavefront detection accuracy. The relationship curves between the wavefront reconstruction residuals RMS, PV and microlens focal length were obtained. And we further analyzed the intrinsic physical reasons for this relationship.The results show that the variation of the microlens focal length affected the point spread function used in the algorithm.The smaller the focal length, the more accurate the corresponding point spread function calculation results. Therefore, the smaller the calculation error of the subaperture offset, the higher the wavefront detection accuracy.
When adaptive optics is applied to target imaging, laser atmospheric transmission, etc., variable extension target wavefront detection is a technical challenge. And its detection accuracy directly affects the correction effect of adaptive optics.In order to explore the wavefront detection accuracy problem of variable extension targets. In this paper, a simulation model for wavefront detection of variable extension targets with correlated Hartmann was developed. The model was based on the commonly used optical system parameters, and it was also established by using the theories of Fresnel diffraction, Newton's imaging equation, the working principle of Shack-Hartmann wavefront detector, and wavefront recovery.We analyzed the effects of target distance and attitude variations on wavefront detection accuracy. The relationship curves between RMS and PV of wavefront recovered residuals and target distance and different attitudes were obtained in the simulation. And we further carried out the analysis for the intrinsic physical reasons of forming this relationship. The results show that target distance and attitude changes affected the extension of targets within the Hartmann subaperture. When the wavefront was recovered using the correlation algorithm, we obtained that the smaller the extension, the higher the wavefront detection accuracy within the relevant Hartmann detection accuracy. Therefore, it could be summarized that the smaller the extension of the target, the more similar it was to the point target, then the detection error introduced by the extension became smaller.
In this paper, we address the multiframe super resolution problem from a set of degraded, under-sampled, shifted and rotated low resolution images to obtain a high resolution image using the variational Bayesian methods. In the Bayesian framework a prior model on the high resolution image need to be specified, its aim is to summarize our knowledge of the image and to constraint the ill-posed image reconstruction problem. Appropriate prior model selection according to the super resolution scenario is a critical issue. Here we propose the one-parameter l1 prior. Experimental results demonstrate that the proposed method is very effective and compared favorably to state-of-the-art super resolution algorithms.
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