Dual-Domain Optimization-Based Denoising Compressed Sensing Ghost Imaging Reconstruction Algorithm

周阳 Zhou Yang

doi:10.3788/AOS251519

Dual-Domain Optimization-Based Denoising Compressed Sensing Ghost Imaging Reconstruction Algorithm

2025-12-01

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DOI：10.3788/AOS251519

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Objective We aim to address the critical challenges in ghost imaging (GI), including poor image quality, excessive measurement counts, and long imaging time, which limit its practical applications. GI, which reconstructs unknown objects through spatial intensity correlations between two detectors, offers distinct advantages over traditional imaging techniques, such as non-locality, single-pixel imaging, and lens-free operation. However, issues related to reconstruction quality, noise sensitivity, and slow processing speed remain significant barriers. To overcome these challenges, we proposed an anti-noise fast compressed sensing GI target reconstruction algorithm. This algorithm integrates wavelet threshold denoising with preconditioned conjugate gradient dual-domain optimization. Based on generalized orthogonal matching pursuit, the preconditioned conjugate gradient method improved the accuracy of linear system solutions. Additionally, wavelet denoising technology was utilized to mitigate noise interference during the reconstruction process. By applying image reordering and transposition strategies, we effectively removed noise across various dimensions and enhanced background noise suppression in the reconstructed image. We intend to improve the performance of GI in practical applications, particularly in fields such as remote sensing, optical encryption, and biomedical imaging, advancing the use of high-quality and efficient reconstruction. Methods In the target reconstruction process, the residuals, recovery vector, and column index set were first initialized, and some columns were selected for updates. In each iteration, the inner product between the residual and the columns of the sensing matrix was computed. The columns were sorted based on the absolute values of the inner products, and the top 100 columns with the largest inner products were selected. A submatrix was constructed using these columns, and the linear least squares problem was solved using the preconditioned conjugate gradient method to obtain the recovery vector. Next, a wavelet threshold denoising method was applied to remove noise and improve the quality of the recovered signal. The process involved a maximum overlapping discrete wavelet transform (MODWT) to decompose the signal, estimate the noise standard deviation, and compute the threshold. Soft thresholding was used to process the wavelet coefficients, and the inverse wavelet transform was applied to recover the target information. To accelerate the computation, wavelet threshold denoising was applied only in some iterations, reducing the computational load. Finally, through processes such as transposition, reordering, and noise reduction, a clear target image was obtained. Results and Discussions The wavelet threshold denoising and preconditioned conjugate gradient dual-domain optimization-based noise-robust fast compressed sensing ghost imaging (WPCGI) method proposed in this paper has achieved significant progress in both target reconstruction quality and algorithm efficiency. Through experiments on the binary image Airplane, the influence of different S values on the reconstruction signal-to-noise (SNR) is investigated (Table 2). The experimental results show that as the S value increases from 3 to 100, the SNR reaches 12.7147 dB, demonstrating the best reconstruction performance. However, further increasing the S value leads to a decrease in SNR, with SNR values of 11.7431 dB and 11. 6351 dB at S=120 and S=150, respectively, indicating that an appropriately selected S value can improve reconstruction quality and algorithm speed. In comparison to other algorithms, the WPCGI method also shows advantages in runtime, with the runtime for S=100 being 8.28 s, which is significantly better than the 14.15 s for S=3. Moreover, when the least squares algorithm is adopted, the WPCGI method achieves an SNR of 12.3522 dB and a reconstruction time of 9.17 s. This is worse than the PCG method, which has an SNR of 12.7147 dB and a reconstruction time of 8.28 s. Under different measurement times, the reconstruction results of the WPCGI method show clear differences compared to OMP and GOMP methods (Fig. 3). In 1500 measurements, the SNR of WPCGI is 14.8211 dB, significantly outperforming OMP (13.2530 dB) and GOMP (12.6252 dB) (Table 3). Further quantitative comparison analysis of different WPCGI reconstruction strategies and the original image pixel values demonstrates the effective enhancement of image quality through transpose tiling and denoising, particularly in suppressing background noise in the reconstructed image (Fig. 4). The performance of different reconstruction methods on various target images (Fig. 5) shows that WPCGI achieves better reconstruction results and higher SNR values across all images, further confirming its superiority. Furthermore, in environments with different noise intensities, the robustness of the WPCGI method is more prominent (Fig. 6 and Fig. 7). Especially in lower SNR, WPCGI effectively suppresses background noise and improves reconstruction quality. OMP and GOMP methods perform poorly under noise interference, failing to restore target information effectively, with GOMP showing significant background noise at high noise levels. Finally, in an actual imaging system, the WPCGI method successfully reconstructs the target GI at different measurement times, further validating the method's effectiveness and robustness in practical applications (Fig. 8). Conclusions We introduce an innovative target reconstruction algorithm for GI that integrates wavelet threshold denoising with preconditioned conjugate gradient bi-domain optimization, aiming to overcome the limitations of conventional GI techniques, particularly in terms of image quality, noise robustness, and reconstruction speed. By leveraging generalized orthogonal matching pursuit in conjunction with the preconditioned conjugate gradient method, the proposed algorithm significantly enhances the precision of solving linear systems, resulting in more accurate reconstructions. Furthermore, the application of wavelet threshold denoising serves as a powerful tool in mitigating noise interference throughout the reconstruction process, which is critical in preserving the fidelity of the final image. The inclusion of image reordering and transposition strategies provides an additional layer of noise reduction, enhancing the algorithm's ability to suppress noise across multiple dimensions. Extensive simulations and experimental results validate the proposed approach, demonstrating its superior performance in noise suppression, image detail restoration, and reconstruction speed. In particular, in low SNR conditions, the imaging quality provided by this method significantly surpasses that of traditional techniques, exhibiting considerable advantages in both clarity and precision. This breakthrough is especially valuable in high-noise environments where traditional imaging methods often struggle to preserve fine image details. The robustness of the algorithm in challenging conditions makes it particularly well-suited for applications in fields such as remote sensing, optical encryption, and biomedical imaging, where high-quality imaging is paramount.

Keywords:

ghost imaging

wavelet threshold denoising

preconditioned conjugate gradient method

compressed sensing

Dual-Domain Optimization-Based Denoising Compressed Sensing Ghost Imaging Reconstruction Algorithm

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