出版日期: 2019-03-25 点击次数： 下载次数： DOI: 10.11834/jrs.201980142019 | Volumn23 | Number 2上一篇  |  下一篇

CX-6(02)微纳卫星超分辨率成像

1. 中国科学院计算光学成像技术重点实验室，北京 100094
2. 中国科学院大学，北京 100049
3. 中国科学院微小卫星创新研究院，上海 201203
 收稿日期: 2018-01-11 基金项目: 国家自然科学基金(编号：61505219)；中国科学院国防科技创新基金(编号：CXJJ-16S045)；青岛市光电智库联合基金资助项目 第一作者简介: 谭政，1982年生，男，工程师，研究方向为计算光学成像、遥感数据增强。E-mail: tanzheng@aoe.ac.cn 通信作者简介: 相里斌，1967年生，男，研究员，研究方向为光学工程、计算光学成像技术。E-mail: xiangli@aoe.ac.cn

# 关键词

CX-6(02)微纳卫星, 超分辨率成像, 亚像元信息, 重建算法, 变分贝叶斯, 先验模型

CX-6(02) micro-nano satellite super-resolution imaging
TAN Zheng1,2 , XIANG Libin1 , LYU Qunbo1,2 , SUN Jianying1 , LI Pingfu3 , GAO Shuang3 , YIN Zengshan3
1.Key Laboratory of Computation Optical Imaging Technology, Chinese Academy of Sciences, Beijing 100094, China
2.University of Chinese Academy of Sciences, Beijing 100049, China
3.Department Innovation Academy for Microsatellites of Chinese Academy of Sciences, Shanghai 201203, China

# Abstract

Micro-nano satellite is one of the developing trends of remote sensing technology with the advantages of light-weight, small size, low cost. However, because of the limitation of the volume and weight, the traditional high resolution optical imaging payload with long focal length and large aperture is difficult to apply to earth observation of micro-nano satellite. In order to solve this problem, a super-resolution imaging scheme is demonstrated in this paper. First, in the mode of images acquisition, to obtain multi frame images of the same region, the velocity of imaging relative to the ground should be controlled by satellite attitude. And because the attitude control deviation of satellite is objective, so subpixel displacement information can be generated by pitching, yaw, and rolling random deviations, without to install any other displacement generators; Secondly, In the super-resolution reconstruction algorithm, aiming at solving the problem of prior constraints on variational bayesian super-resolution reconstruction method, we propose a weighted bi-directional difference prior model to overcome the under-constraint of non-edge regions of image due to total variation prior and L1 norm prior, to further restrain the solving space of the observation equation. The above scheme is applied to the China’s first super-resolution imaging micro-nano satellite:CX-6(02) micro-nano satellite. The imaging results of this satellite show that: our images acquisition method can obtain sufficient subpixel information, which is approximately uniformly distributed with 0.1 pixel magnitude; The result of super-resolution reconstruction is superior to the same variational bayesian method based on L1 norm prior model and total variation prior model, it is hardly to introduce or amplify the computational noise in the iterative process of the algorithm, effectively weakens the ill-posed property of the deconvolution operation. Make the CX-6(02) satellite’s imaging resolution increased from 2.8 to 1.4 meters in the 700 km orbit altitude, and the whole satellite is only 66 kg. Except for micro-nano satellite, the design scheme of this paper can also be applied to medium or large optical imaging satellite, it may provide a certain theoretical and experimental support for high resolution earth-observing remote sensing.

# Key words

CX-6(02) micro-nano satellite, super-resolution imaging, images acquisition, reconstruction algorithm, variational Bayes, prior model

# 2 基本原理

## 2.1 图像序列获取方式

 ${\theta _k} = {D_{{\textit{z}}k}} - {D_{{\textit{z}}1}}$ (1)

 ${c_k} = H\left( {\tan ({D_{{\rm{x}}k}}) - \tan ({D_{{\rm{x}}1}})} \right)/GSD$ (2)

 ${d_K} = \frac{{(K - 1)v/R}}{{GSD \cdot {f_{\rm{p}}}}} + \frac{H}{{GSD}}\left( {\sum\limits_{k = 2}^K {\tan ({D_{yk}})} - \tan ({D_{y1}})} \right)$ (3)

 ${m_{{\rm{OY}}}} = {m_Y} - {d_K}$ (4)

XY方向的位移可以表示为 $[m({b / a})]$ 个像元，其中分数部分 $({b / a})$ 即为亚像元位移。对于超分辨率重建来说，如果分数部分 $({b / a}) = 0$ ，整数部分 $m$ 无论如何变化都是无效的；而如果几帧图像相对于基准图像位移的分数部分都相等，那么即便它们的整数部分不同，也相当于只有一个有效的亚像元位移值，因此，为了提高计算效率，可通过配准结果对无效亚像元位移图像进行剔除，考虑到配准本身的误差，在实际执行时剔除的阈值选为0.05像元。

## 2.2 超分辨率重建算法

 ${{{y}}_k} = {{A}} {{HC}}({{{s}}_k}) {{x}} + {{{n}}_k}$ (5)

 $p({{x}}|{{{y}}_k}) = {{p({{{y}}_k}|{{x}})p({{x}})} / {p({{{y}}_k})}}$ (6)

 $p({{{y}}_k}{\rm{|}}{{x}},{{{s}}_k},{\beta _k}) \propto \beta _k^{N/2}\exp \left( { - \frac{{{\beta _k}}}{2}{{\left\| {{{{y}}_k} - {{AHC}}({{{s}}_k}){{x}}} \right\|}^2}} \right)$ (7)

 $p({{{y}}_k}{{|x}}) \propto p({{{y}}_k}|{{x}}, {{{s}}_k}, \alpha, {\beta _k})p({{{s}}_k})p(\,{\beta _k})$ (8)

 $p({{x}}|\alpha ) = Z(\alpha )\exp \left( { - \alpha U({{x}})} \right)$ (9)

 $p({ x}|\alpha ) = {(\alpha )^{\frac{P}{2}}}\exp \left( { - \alpha \sum\limits_{i = 1}^P {\left( {\sqrt {{\Lambda _i}({{x}})} } \right)} } \right)$ (10)
 $\begin{split} {\Lambda _i}({{x}}) = & {\left( {\Delta _{hi}^ \leftarrow ({{x}})} \right)^2} + {\left( {\Delta _{vi}^ \uparrow ({{x}})} \right)^2} + \\ & {\textit{λ}} \left( {{{\left( {\Delta _{hi}^ \to ({{x}})} \right)}^2} + {{\left( {\Delta _{vi}^ \downarrow ({{x}})} \right)}^2}} \right) \end{split}$ (11)

 $p({{x}}) = p({{x}}|\alpha)p(\alpha)$ (12)

 $\begin{split} p({{x}},{{{s}}_k},\alpha ,{\beta _k}|{{{y}}_k}) = & p({{{y}}_k}|{{x}},{{{s}}_k},{\beta _k})p({{{s}}_k}) \times \\ & p({\beta _k})p({{x}}|\alpha )p(\alpha )/p({{{y}}_k}) \end{split}$ (13)

 $\begin{split} \hat q(\Theta ) = & \arg \min {C_{{\rm{KL}}}}(q(\Theta )\left\| {p(\Theta |{{y}})} \right.)\approx \\ & \arg \min \left( {\int q(\Theta )\log (\frac{{q(\Theta )}}{{p(\Theta ,{{y}})}}){\rm{d}}\Theta } \right) \end{split}$ (14)

 $\max \left( {\inf \left( {p({{{y}}_k}|{{x}},{{{s}}_k},{\beta _k})p({{{s}}_k})p({\beta _k})p({{x}}|\alpha )p(\alpha )} \right)} \right)$ (15)

 $\gamma ({{x}},\alpha ,{{w}}) = {(\alpha )^{P/2}}\exp \left( { - \alpha \sum\limits_i {\frac{{{\Lambda _i}({{x}}) + {w_i}}}{{2\sqrt {{w_i}} }}} } \right)$ (16)

 $\hat q(\Theta) = \arg \min \int {{q} (\Theta)\log \frac{{{q} (\Omega)}}{{p(\Omega)\varUpsilon ({ x}, \alpha, { w})}}} {\rm{d}}\Theta$ (17)

 ${q} (\varTheta) = {q} ({ x})\prod\limits_{k = 1}^K {{q} ({\beta _k})} {q} ({{{s}}_k}){q} (\alpha)$ (18)

 $\begin{split} q({{x}}) \propto \exp & \left( { - \frac{1}{2}\left\langle \alpha \right\rangle \sum\limits_{i = 1}^P {\frac{{{\Lambda _i}({{x}}) + {w_i}}}{{\sqrt {{w_i}} }}} - } \right.\\ & \left. {\frac{1}{2}\sum\limits_k {\left\langle {{\beta _k}} \right\rangle {E_{{{{s}}_k}}}\left[ {{{\left\| {{{{y}}_k} - {\bf{AHC}}({{{s}}_k}){{x}}} \right\|}^2}} \right]} } \right) \end{split}$ (19)

 $\begin{split} & {E_{{{{s}}_k}}}\left[ {{{\left\| {{{{y}}_k} - {\bf{AHC}}({{{s}}_k}){{x}}} \right\|}^2}} \right] \approx{\left\| {{{{y}}_k} - {\bf{AHC}}({{{\bar{ s}}}_k}){{x}}} \right\|^2}+\\ & \sum\limits_{i = 1}^3 {\sum\limits_{j = 1}^3 {{\zeta _{kij}}{{{x}}^{\rm{T}}}{{{O}}_{ki}}{{({{{\bar{ s}}}_k})}^{\rm{T}}}{{{O}}_{kj}}({{{\bar{ s}}}_k}){{x}}} } \end{split}$ (20)

 $\begin{split} [{{{N}}_1}({{{\bar{ s}}}_k}){{x}}, &{{{N}}_2}({{{\bar{ s}}}_k}){{x}},{{{N}}_3}({{{\bar{ s}}}_k}){{x}}] = [({{{P}}_1}({{{\bar{ s}}}_k}){{{M}}_1}({{{\bar{ s}}}_k}) + \\ & {{{P}}_2}({{{\bar{ s}}}_k}){{{M}}_2}({{{\bar{ s}}}_k})){{x}},{{{M}}_1}({{{\bar{ s}}}_k}){{x}},{{{M}}_2}({{{\bar{ s}}}_k}){{x}}] \end{split}$ (21)

${{{P}}_1}({{\bar{ s}}_k})$ ${{{P}}_2}({{\bar{ s}}_k})$ ${{{M}}_1}({{\bar{ s}}_k})$ ${{{M}}_2}({{\bar{ s}}_k})$ 分别为

 ${{{P}}_1}({{\bar{ s}}_k}) = diag(- u\sin ({\theta _k}) - v\cos ({\theta _k}))$ (22)
 ${{{P}}_2}({{\bar{ s}}_k}) = diag(u\cos ({\theta _k}) - v\sin ({\theta _k}))$ (23)
 $\begin{split} {{{M}}_1}({{{\bar{ s}}}_k}) = & ({{I}} - {{{V}}_{{{\bar s}_k}}})({{{L}}_{tr({{\bar s}_k})}} - {{{L}}_{tl({{\bar s}_k})}}) + \\ & {{{V}}_{{{\bar s}_k}}}({{{L}}_{br({{\bar s}_k})}} - {{{L}}_{bl({{\bar s}_k})}}) \end{split}$ (24)
 $\begin{split} {{{M}}_2}({{{\bar{ s}}}_k}) = & ({{I}} - {{{U}}_{{{\bar s}_k}}})({{{L}}_{bl({{\bar s}_k})}} - {{{L}}_{tl({{\bar s}_k})}}) + \\ & {{{U}}_{{{\bar s}_k}}}({{{L}}_{br({{\bar s}_k})}} - {{{L}}_{tr({{\bar s}_k})}}) \end{split}$ (25)

 ${\left[ {{{{\Sigma }}_{{\hat{ x}}}}} \right]^{ - 1}}{\hat{ x}} = \sum\limits_k {\left\langle {{\beta _k}} \right\rangle {{[{\bf{AHC}}({{{\bar{ s}}}_k})]}^{\rm{T}}}{{{y}}_k}}$ (26)

 $\begin{split} {\left[ {{{{\Sigma }}_{\hat x}}} \right]^{ - 1}} = & \sum\limits_k {\left\langle {{\beta _k}} \right\rangle {{[{\bf{AHC}}({{{\bar{ s}}}_k})]}^{\rm{T}}}} {\bf{AHC}}({{{\bar{ s}}}_k}) + \\ & \sum\limits_k {\sum\limits_{i = 1}^3 {\sum\limits_{j = 1}^3 {\left\langle {{\beta _k}} \right\rangle {\zeta _{kij}}{{{x}}^{\rm{T}}}{{{O}}_{ki}}{{({{{\bar{ s}}}_k})}^{\rm{T}}}{{{O}}_{kj}}({{{\bar{ s}}}_k})} } } + \\ & \left\langle \alpha \right\rangle {[{\Lambda _i}({{x}})]^{\rm{T}}}\sqrt {{w}} [{\Lambda _i}({{x}})] \end{split}$ (27)

 $\begin{split} {\left[ {{{{\bar{ s}}}_k}} \right]_{n + 1}} = & {{{S}}_k}[{({{S}}_k^p)^{ - 1}}{\bar{ s}}_k^p + \\ & \left\langle {{\beta _k}} \right\rangle ({{{\varGamma }}_k}{\left[ {{{{\bar{ s}}}_k}} \right]_n} + {{{\varPsi }}_k}{\left[ {{{{\bar{ s}}}_k}} \right]_n} + {{{Q}}_k} - {{{\varPhi }}_k})] \end{split}$ (28)

 ${{{\varPhi}} _{ki}} = trace[{({\bf{AHC}})^{\rm{T}}}{{{O}}_{ki}}({{\bar{ s}}_k}){{{\Sigma }}_{{\hat{ x}}}}]$ (29)
 ${{{Q}}_{ki}} = {[{y_k}{{ - }}{\bf AHC}({s_k})x]^{\rm{T}}}{{{\psi }}_{ki}}$ (30)
 ${{{\varPsi }}_k} = [{{{O}}_{k1}}({{\bar{ s}}_k}){\hat{ x}}, {{{O}}_{k2}}({{\bar{ s}}_k}){\hat{ x}}, {{{O}}_{k3}}({{\bar{ s}}_k}){\hat{ x}}]$ (31)

${{{\varPsi }}_k}$ ${{{\varGamma }}_k}$ 为3×3维矩阵，元素分别为

 ${{{\varPsi}} _{kij}} = trace[{{{O}}_{ki}}{({{\bar{ s}}_k})^{\rm{T}}}{{{O}}_{kj}}({{\bar{ s}}_k}){\Sigma _{{\hat{ x}}}}]$ (32)
 ${{{\varGamma}} _{kij}} = \psi _{ki}^{\rm{T}}{\psi _{kj}}$ (33)

# 3 超分辨结果与分析

## 3.2 算法对比分析

Table 1 Comparison of A/B/C gray scale target ROI’s signal-to-noise ratio

 区域A 区域B 区域C 原始图像SNR 89.18 47.69 62.08 全变分先验超分辨结果SNR 61.89 44.61 50.84 L1范数先验超分辨结果SNR 43.84 35.69 39.11 本文方法超分辨结果SNR 126.65 62.50 73.91

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