Compressed sensing photoacoustic imaging based on the gradient projection Newton pursuit algorithm

Abstract

Photoacoustic imaging (PAI) is a unique non-invasive biomedical imaging technique that illuminates biological tissue with short-pulsed laser light. This process generates acoustic waves, which in turn enable high-resolution and high-contrast imaging of deep tissue. However, the complexity of PAI imaging data presents challenges in achieving rapid and optimal reconstruction results due to the time and resource demands of traditional Nyquist sampling. On the contrary, compressive sensing (CS) overcomes the limitations of Nyquist sampling by recovering the original signal with a lower amount of sampled data, resulting in significant cost savings in signal transmission and processing. Additionally, CS-based hard-thresholding iterative algorithms possess various advantages in sparse optimization, including sparsity control and fast computation. Moreover, the assumptions of the Gradient Projection Newton Pursuit (GPNP) for CS problems are relatively weaker compared to many state-of-the-art algorithms. Therefore, we investigated the performance of the GPNP algorithm in PAI. We compared our algorithm with improved iterative hard thresholding (IIHT), conjugate gradient iterative hard thresholding (CGIHT), compressive sampling matching pursuit (CoSaMP), SPGL1, SALSA and elastic net algorithms using phantom, Vasculature, and SGERF simulation images. The simulation results demonstrate that the GPNP algorithm achieves excellent image reconstruction performance when evaluating both the quality of reconstruction and the reconstruction time. Taking the simulation results of Vasculature with a noise level of 40 dB and 40 channels as an example, the PNSR index of GPNP has improved by 4.09, 11.03, 12.89, 13.14, 13.15, and 11.75 compared to IIHT, CGIHT, elastic net algorithms, SPGL1, SALSA and CoSaMP, respectively.