Research on Single-channel Blind Deconvolution Algorithm for Multi-source Signals
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摘要: 传统的单通道盲去卷积的方法存在仅能从混合信号中分离出2路源信号的局限，考虑到以上问题，该文提出一种基于优化的深度卷积生成对抗网络的单通道盲去卷积算法(SCBDC)，能从1路混合信号中分离和解卷积出3路以上的独立源信号和混合矩阵。该文实验在汉字和遮挡图像数据集上进行，随机选择4路信号与混合矩阵进行卷积混合，实验结合峰值信噪比(PSNR)和信号相关性指标来评价分离的效果，结果显示，该算法能够有效地分离出多路源信号并去卷积。Abstract: Traditional single-channel blind deconvolution method has the limitation that it can only separate two sources from a mixture. Considering this problem, a Single-Channel Blind Deconvolution algorithm based on optimized deep Convolutional generative adversarial networks (SCBDC) is proposed to separate and deconvolve more than three independent sources and mixing matrix only from a mixture. The experiments are carried on the occlusion Chinese character image datasets, four sources are randomly selected to be mixed with mixing matrix. Peak Signal to Noise Ratio (PSNR) and signal correlation index are combined to evaluate the separation effect. The result shows that the multiple sources can be effectively separated and deconvolved.
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表 1 SCBDC算法
输出：源信号$ \bar s $和混合矩阵${\bar {\boldsymbol{F}}_{} }$ 1: 选择满足高斯分布N(0,1)的m个100维噪声样本z1, z2, ···, zm; 2: 来自实际数据的m个样本s1, s2, ···, sm; 3: 训练 ODCGAN 一定程度地增加判别器的梯度来更新D: $\nabla {\theta _d}\dfrac{1}{m}\displaystyle\sum\limits_{i = 1}^m {\left[ {\lg D\left( { {{\boldsymbol{s}}_i} } \right) + \lg\left( {1 - D\left( {G\left( { {{\boldsymbol{z}}_i} } \right)} \right)} \right)} \right]}$ 一定程度地降低生成器的梯度来更新G: $\nabla {\theta _g}\dfrac{1}{m}\displaystyle\sum\limits_{i = 1}^m {\lg\left( {1 - D\left( {G\left( { {{\boldsymbol{z}}_i} } \right)} \right)} \right)}$ 4: 选择来自高斯分布N(0,1)的随机m个样本z1, z2, ···, zm和混合
矩阵F1, F2, ···, Fm;5: 迭代 计算$\bar {\boldsymbol{X}}$: $\bar {\boldsymbol{X}} = \displaystyle\sum\limits_{i = 1}^m {\left( { {{\boldsymbol{F}}_m} * G\left( { {{\boldsymbol{z}}_m} } \right)} \right)}$ 按照式(12)计算梯度$\nabla {\boldsymbol{\varPhi}}$ 使用adam优化器更新${\boldsymbol{\varPhi}}$ 
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表 4 目标信号与源信号的互相关性值
${{\boldsymbol{S}}_1}$和$ {\bar {\boldsymbol{S}}_1} $ $ {{\boldsymbol{S}}_2} $和$ {\bar {\boldsymbol{S}}_2} $ $ {{\boldsymbol{S}}_3} $和$ {\bar {\boldsymbol{S}}_3} $ $ {{\boldsymbol{S}}_4} $和$ {\bar {\boldsymbol{S}}_4} $ 平均值 第1行 0.9245 0.9613 0.9523 0.7286 0.8917 第2行 0.7599 0.9698 0.8020 0.9154 0.8618 第3行 0.5835 0.9972 0.9119 0.0470 0.6349 第4行 0.7714 0.9444 0.3641 0.9488 0.7412 第5行 0.3824 0.9456 0.9367 0.7104 0.7437 第6行 0.9254 0.9006 0.9684 0.8249 0.9048
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