Abstract:

Bernoulli-Gaussian (BG) model in Expectation-Maximization Bernoulli-Gaussian Approximate Message Passing (EM-BG-AMP) algorithm is constrained by its symmetry and restricted in the approximation of the actual signal prior distribution. Gaussian-Mixture (GM) model in Expectation-Maximization Gaussian-Mixture Approximate Message Passing (EM-GM-AMP) algorithm is a high-order model of BG model and has quite high complexity. In order to solve these problems, the Bernoulli-Asymmetric-Gaussian (BAG) model was proposed. Based on the new model, by further derivation, the Expectation-Maximization Bernoulli-Asymmetric-Gaussian Approximate Message Passing (EM-BAG-AMP) algorithm was obtained. The main idea of the proposed algorithm was based on the assumption that the input signal obeyed the BAG model. Then the proposed algorithm used Generalized Approximate Message Passing (GAMP) to reconstruct signal and update the model parameters in iteration. The experimental results show that, when processing different images, compared to EM-BG-AMP,the time and the Peak Signal-to-Noise Ratio (PSNR) values of EM-BAG-AMP are increased respectively by 1.2% and 0.1-0.5 dB, especially in processing images with simple texture and obvious color difference changing, the PSNR values are increased by 0.4-0.5 dB. EM-BAG-AMP is the expansion and extension of EM-BG-AMP and can better adapt to the actual signal.

Key words: compressed sensing, generalized approximate message passing algorithm, expectation maximization, signal model, Bernoulli asymmetric Gaussian

摘要：

期望最大化贝努利高斯(BG)近似信息传递(EM-BG-AMP)算法中的BG模型因为具有对称性,在逼近实际信号先验分布时会受到限制;而期望最大化高斯混合近似信息传递(EM-GM-AMP)算法中的GM模型是BG模型的高阶形式,复杂度较高。为了解决以上问题,提出贝努利不对称高斯模型(BAG),进而推导得到期望最大化贝努利不对称高斯近似信息传递(EM-BAG-AMP)算法。该算法的主要思路是假设输入信号服从BAG模型,然后使用广义近似信息传递(GAMP)重构信号并在算法迭代中同时更新模型参数。实验证明,在处理不同图像数据时,EM-BAG-AMP和EM-BG-AMP相比,时间增加了1.2%,峰值信噪比(PSNR)值提升了0.1~0.5 dB,尤其在处理纹理较少以及色差变化明显的图像时峰值信噪比(PSNR)值提升了0.4~0.5 dB。EM-BAG-AMP是对EM-BG-AMP算法的扩展和延伸,更适合实际信号的处理。

关键词: 压缩感知, 广义近似信息传递算法, 期望最大化, 信号模型, 贝努利不对称高斯