摘要：

泊松去噪是一个典型的病态逆问题，其变分模型需要反复迭代和调节参数且计算效率低下，而纯深度学习模型往往依据经验设计网络且可解释性差。针对以上问题，在泊松噪声去噪变分模型的交替方向乘子法展开的基础上，设计端到端深度卷积神经网络，结合泊松噪声分布统计量与Bayesian最大后验概率估计推导出改进的泊松去噪变分模型。为了求解泊松去噪能量函数极值问题，采用交替方向乘子法，引入辅助变量、拉格朗日乘子和惩罚参数，将该问题分解为高斯去噪和图像重建两类交替优化子问题，先采用先验驱动的深度卷积神经网络实现高斯去噪，再通过解析迭代求解完成图像重建。实验结果表明，与基于非线性主成分分析、VST+BM3D、I+VST+BM3D和TRDPD的泊松去噪模型相比，改进模型在Set12数据集上的峰值信噪比均值分别提高2.73、0.87、0.57和0.50 dB，结构相似性均值分别提高0.148、0.046、0.020和0.047，在彩色图像及正电子发射断层扫描与计算机断层扫描图像上也明显提升了泊松去噪效果。上述实验结果证明了改进模型不仅有效去除了泊松噪声，而且避免了泊松去噪过程中产生的伪影和散斑等问题。

关键词: 泊松去噪, 卷积神经网络, 去噪先验, 变分模型, 交替方向乘子法

Abstract:

The denoising of Poisson noise images is a typical ill-conditioned inverse problem. Its variational model requires repeated iterations and parameter adjustments, which is less computationally efficient. Pure deep learning models often draw on experience to design networks, but they have poor interpretability. Based on the Alternating Direction Method of Multipliers(ADMM) expansion of the Poisson noise denoising variational model, an end-to-end Deep Convolutional Neural Network(DCNN) is designed to derive an improved Poisson denoising variational model by combining the Poisson noise distribution data with the Bayesian maximum a posteriori probability estimation. To solve the Poisson denoising energy function extremum problem, ADMM is used, which introduces auxiliary variables, Lagrange multipliers, and penalty parameters and decomposes the problem into two alternating optimization subproblems of Gaussian denoising and image reconstruction. First, Gaussian denoising is achieved using the priori-driven DCNN to learn the Gaussian denoising. Next, the image reconstruction is completed via analytical iteration. The experimental results show that compared with the NonLinear Principal Component Analysis(NLPCA), VST+BM3D, I+VST+BM3D, and TRDPD-based Poisson denoising models, the mean values of the Peak Signal-to-Noise Ratio(PSNR) of the model on the Set12 dataset are improved by 2.73, 0.87, 0.57, and 0.50 dB, respectively, and the mean values of the Structural SIMilarities(SSIM) are improved by 0.148, 0.046, 0.020, and 0.047, respectively. The Poisson denoising effects on color images and Positron Emission Tomography/Computed Tomography(PET/CT) images are significantly improved. The above experimental results prove that the model effectively removes the Poisson noise and prevents the problems of artifacts and scattering generated during the Poisson denoising process.

Key words: Poisson denoising, Convolutional Neural Network(CNN), denoising prior, variational model, Alternating Direction Method of Multipliers(ADMM)