发布时间: 2019-03-16 摘要点击次数: 全文下载次数: DOI: 10.11834/jig.180391 2019 | Volume 24 | Number 3 图像处理和编码

 收稿日期: 2018-07-02; 修回日期: 2018-09-28 基金项目: 广东省自然科学基金项目(2017A030311028, 2016A030313455) 第一作者简介: 戴超, 1993年生, 男, 硕士研究生, 主要研究方向为图像/视频压缩感知。E-mail:dcldforever@163.com;郑钊彪, 男, 硕士研究生, 主要研究方向为图像/视频压缩感知。E-mail:zhengzhaobb@163.com. 中图法分类号: TN919.8 文献标识码: A 文章编号: 1006-8961(2019)03-0357-09

# 关键词

Hierarchical multi-hypothesis prediction algorithm for compressed video sensing
Dai Chao, Yang Chunling, Zheng Zhaobiao
School of Electronic and Information Engineering, South China University of Technology, Guangzhou 510640, China
Supported by: Natural Science Foundation of Guangdong Province, China(2017A030311028, 2016A030313455)

# Key words

compressed video sensing(CVS); multi-hypothesis prediction; block matching; motion estimation; auto regression

# 1 视频压缩感知中多假设预测算法

 $\mathit{\boldsymbol{y}} = \mathit{\boldsymbol{ \boldsymbol{\varPhi} x}}$ (1)

 $w = \mathop {\arg \min }\limits_\mathit{\boldsymbol{w}} \left\| {\mathit{\boldsymbol{x}} - \mathit{\boldsymbol{Hw}}} \right\|_2^2$ (2)

 ${{\hat w}_{t, i}} = \mathop {\arg \min }\limits_\mathit{\boldsymbol{w}} \left\| {{y_{t, i}} - \mathit{\boldsymbol{ \boldsymbol{\varPhi} }}{\mathit{\boldsymbol{H}}_{t, i}}\mathit{\boldsymbol{w}}} \right\|_2^2$ (3)

 ${{\hat w}_{t, i}} = \mathop {\arg \min }\limits_\mathit{\boldsymbol{w}} \left\| {{y_{t, i}} - \mathit{\boldsymbol{ \boldsymbol{\varPhi} }}{\mathit{\boldsymbol{H}}_{t, i}}\mathit{\boldsymbol{w}}} \right\|_2^2 + {\lambda ^2}\left\| {\mathit{\boldsymbol{ \boldsymbol{\varGamma} w}}} \right\|_2^2$ (4)

 ${{\hat w}_{t, i}} = {({(\mathit{\boldsymbol{ \boldsymbol{\varPhi} }}{H_{t, i}})^{\rm{T}}}(\mathit{\boldsymbol{ \boldsymbol{\varPhi} }}{H_{t, i}}) + {\lambda ^2}{\mathit{\boldsymbol{ \boldsymbol{\varGamma} }}^{\rm{T}}}\mathit{\boldsymbol{ \boldsymbol{\varGamma} }})^{ - 1}}{(\mathit{\boldsymbol{ \boldsymbol{\varPhi} }}{H_{t, i}})^{\rm{T}}}{y_{t, i}}$ (5)

 $\mathit{\boldsymbol{\hat w}} = \mathop {\arg \min }\limits_\mathit{\boldsymbol{w}} \left\| {\mathit{\boldsymbol{w}} - \mathit{\boldsymbol{Hw}}} \right\|_2^2 = {({\mathit{\boldsymbol{H}}^{\rm{T}}}\mathit{\boldsymbol{H}})^{ - 1}}\mathit{\boldsymbol{H\tilde x}}$ (6)

# 2 分级多假设预测方案

Table 1 Motion vectors of 4 neighbouring blocks in 45th frame of Hall sequence comparing to key frame

 块序号 1 2 3 4 运动矢量 (0，0) (0，0) (0，0) (0，0)

# 2.1 分级运动估计方案

1) 观测域初级运动估计

$4b×4b$图像块最左上角的$b×b$图像块以观测值绝对误差和SAD为匹配准则在参考帧的相应搜索窗中进行菱形快速搜索，得到最优匹配块和相应的运动矢量$\mathit{\boldsymbol{mv}}1$。对当前$4b×4b$图像块中的每个$b×b$图像子块计算其与运动矢量$\mathit{\boldsymbol{mv}}1$对应的图像块的观测值SAD。若SAD小于阈值$τ_{1}$($τ_{1}$是通过实验得到的经验值。$τ_{1}$越大，运动估计的计算复杂度降低越明显；$τ_{1}$越小，预测精度提升越明显)，则相应子块分为$A$类，使用基于Tikhonov的多假设预测算法进行预测，若SAD大于$τ_{1}$，则该子块进入步骤2)，重新计算运动矢量。

2) 观测域末级运动估计

3) 像素域初级运动估计

4) 像素域末级运动估计

# 2.2 基于自回归模型的多假设预测方案

1) 搜寻相似像素点组

 $\mathit{\boldsymbol{x}} = \left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}}\\ \vdots \\ {{x_k}} \end{array}} \right]$ (7)

 ${\mathit{\boldsymbol{X}}_{{\rm{group}}}} = \left[ {\begin{array}{*{20}{c}} {x_1^1}&{x_1^2}& \cdots &{x_1^8}\\ {x_2^1}&{x_2^2}& \cdots &{x_2^8}\\ \vdots&\vdots &{}& \vdots \\ {x_k^1}&{x_k^2}& \cdots &{x_k^8} \end{array}} \right]$ (8)

2) 求解自回归系数

 $\alpha = \mathop {\arg \min }\limits_\alpha \left\| {\mathit{\boldsymbol{x}} - {\mathit{\boldsymbol{X}}_{{\rm{group}}}}\alpha } \right\|$ (9)

3) 计算当前像素点的预测值

 ${\mathit{\boldsymbol{x}}_{{\rm{pre}}}} = {\mathit{\boldsymbol{x}}_{{\rm{nei}}}} \times \alpha$ (10)

# 3.1 与MH-DS[16]算法仿真结果对比

Table 2 Time complexity comparison between different prediction schemes

 /s 视频序列 MH-DS Hi-MH Foreman 7.24 5.81 Coastguard 7.95 6.22

# 3.2 与PBCR-DCVS算法[11]仿真结果对比

Table 3 Time complexity comparison between two algorithms

 /s 视频序列 重构方法 采样率 0.1 0.2 0.3 0.4 0.5 Soccer PBCR-DCVS 47.82 76.04 87.55 48.16 49.22 Hi-MH 17.93 17.99 17.8 18.31 16.55 Foreman PBCR-DCVS 47.29 76.46 88.27 50.41 51.67 Hi-MH 15.65 16.84 16.11 16.41 15.27 Mother-daughter PBCR-DCVS 45.47 73.17 85.46 54.45 55.49 Hi-MH 14.54 16.84 16.05 15.86 14.24 Coastguard PBCR-DCVS 45.45 73.57 85.07 52.52 53.88 Hi-MH 12.53 16.38 14.88 15.01 14.29 注：加粗字体为最优结果。

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