Sub-Nyquist underwater denoising ghost imaging with a Coiflet-wavelet-order-based Hadamard matrix

Underwater ghost imaging (GI) plays an important role in the marine research, marine environment protection, and engineering applications. However, underwater GI encounters the challenges of numerous measurements and noise interference caused by the scattering lights. To solve these problems, we propose a sub-Nyquist denoising GI method to acquire high-quality images of the underwater objects. The proposed method first uses a Coiflet-wavelet decomposition method to create an index order and then utilizes the order to reorder the Hadamard pattern sequence. Then, a total variation regularization algorithm is designed to restore the object images, and a nuclear-norm-minimization algorithm is developed to remove the noises from the restored images. Finally, an experimental setup is built to simulate the complicated underwater environment that includes the turbulence and bubbles. The numerical and experimental results show that the denoising capability of the proposed method is strong, and the imaging performance of the proposed method is similar (slightly better in some cases) to the recently reported state-of-the-art GI methods in the complicated underwater environment and sub-Nyquist sampling ratio condition (e.g., 0.03). The proposed method may find applications in marine underwater imaging areas.