黃冬梅 戴 亮 魏立斐 魏泉苗 吳國(guó)健
1(上海海洋大學(xué)信息學(xué)院 上海 201306) 2(國(guó)家海洋局東海分局 上海 200136) (dmhuang@shou.edu.cn)
2017-06-10;
2017-07-29
國(guó)家自然科學(xué)基金項(xiàng)目(61402282,61672339,41671431);上海市青年科技英才揚(yáng)帆計(jì)劃項(xiàng)目(14YF1410400);上海市科委地方高校能力建設(shè)項(xiàng)目(15590501900) This work was supported by the National Natural Science Foundation of China (61402282, 61672339,41671431), the Shanghai Yang-Fan Plan (14YF1410400), and the Local University Capacity Enhancement Project of Science and Technology Commission of Shanghai Municipality (15590501900).
魏立斐(Lfwei@shou.edu.cn)
一種安全的多幀遙感圖像的外包融合去噪方案
黃冬梅1戴 亮1魏立斐1魏泉苗2吳國(guó)健1
1(上海海洋大學(xué)信息學(xué)院 上海 201306)2(國(guó)家海洋局東海分局 上海 200136) (dmhuang@shou.edu.cn)
遙感圖像去噪是圖像處理領(lǐng)域的熱門研究課題.伴隨著采集設(shè)備改進(jìn)和技術(shù)提升, 同一場(chǎng)景下的多幀圖像的融合去噪已經(jīng)成為可能.然而海量遙感圖像去噪在單機(jī)上暴露出處理速度慢、并發(fā)性差等問(wèn)題,利用云計(jì)算平臺(tái)進(jìn)行海量數(shù)據(jù)的存儲(chǔ)和處理是大勢(shì)所趨.為保護(hù)外包計(jì)算的遙感圖像的安全性,提出了一種針對(duì)多幀遙感圖像的安全外包融合去噪方案.方案利用Paillier加密算法的密文加法同態(tài)性和Johnson-Lindenstrauss轉(zhuǎn)換近似保留歐氏距離的特性,對(duì)平均圖像進(jìn)行基于動(dòng)態(tài)濾波參數(shù)的融合去噪.選用從多幅Landsat 8遙感圖像中截取多個(gè)512×512像素的圖像作為實(shí)驗(yàn)對(duì)象,搭建了Spark單機(jī)環(huán)境來(lái)模擬云環(huán)境.實(shí)驗(yàn)數(shù)據(jù)表明:提出的外包方案可以有效地保證遙感圖像的安全性;同時(shí),融合去噪方案的效果明顯優(yōu)于已有的密文去噪方案和單幀密文去噪方案,且對(duì)不同圖像、不同大小的噪聲均有很好的去噪效果.
多幀圖像;遙感;安全外包;融合去噪;Paillier同態(tài)加密;Johnson-Lindenstrauss轉(zhuǎn)換
“空天地底”立體觀測(cè)技術(shù)的高速發(fā)展,使得高精度、高頻率、大覆蓋、多模態(tài)遙感數(shù)據(jù)呈幾何級(jí)數(shù)爆炸式增長(zhǎng),已成為公認(rèn)的“大數(shù)據(jù)”[1-2].但遙感圖像在獲取、傳輸、接收、輸出等過(guò)程中往往會(huì)受到噪聲的污染[3],使得遙感圖像出現(xiàn)邊緣紋理等細(xì)節(jié)模糊,導(dǎo)致圖像質(zhì)量降低,增大了遙感圖像后期處理與分析的難度[4].因此,遙感圖像必須進(jìn)行降噪預(yù)處理[5].
遙感圖像不同于普通圖像,存在多個(gè)波段、16位深的灰度值及高分辨率的遙感圖像的文件尺寸很大,傳統(tǒng)的圖像去噪如非局部均值去噪方法[6]、基于偏微分方程的去噪方法[7-8]、基于小波的去噪方法[9]和基于稀疏表示的去噪方法[10]等,處理難度較大.伴隨著遙感圖像采集設(shè)備的改進(jìn)和技術(shù)的提升,短時(shí)間內(nèi)采集同一場(chǎng)景的多幀遙感圖像提供了更豐富的空域信息,為遙感圖像去噪提供了新的研究思路,但同時(shí)也增加了遙感圖像去噪的難度.在短時(shí)間內(nèi)采集的同一場(chǎng)景的多幅圖像中含有噪聲的強(qiáng)度大小相近,且噪聲分布相似.多幀圖像疊加平均方法利用多幀圖像的時(shí)間域相關(guān)性,可以較好地削弱圖像中的噪聲,還原出更清晰的圖像.多幀圖像去噪如以塊為單位的多幀圖像去噪方法[11]、單/多幀圖像相結(jié)合的去噪方法[12]、基于時(shí)域疊加平均和空域非局部均值的多幀圖像去噪方法[13]、基于平均圖像的多圖非局部均值去噪方法[14]等.然而,上述遙感圖像的單機(jī)處理模式暴露出處理速度慢、并發(fā)性差等問(wèn)題,尤其對(duì)于多幀遙感圖像數(shù)據(jù)量大,更無(wú)法滿足海量遙感圖像存儲(chǔ)與處理的需求.
云計(jì)算是一個(gè)典型的分布式、并行計(jì)算模式,能提供海量存儲(chǔ)空間和計(jì)算能力.但云平臺(tái)并非完全可信[15],為了保護(hù)數(shù)據(jù)的安全與隱私,需要對(duì)數(shù)據(jù)先進(jìn)行加密再存儲(chǔ)在云平臺(tái).目前,在云環(huán)境下已經(jīng)出現(xiàn)了密文搜索[16]、密文模式匹配[17-18]、密文信號(hào)處理[19-20]、密文矩陣計(jì)算[21-22]、密文最優(yōu)化計(jì)算[23-24]等密文處理方案.然而,針對(duì)圖像外包去噪研究剛剛起步,Hu等人提出了針對(duì)單幀普通圖像的安全去噪方案[25].遙感圖像作為國(guó)家重要的戰(zhàn)略資源,對(duì)遙感圖像進(jìn)行加密,被認(rèn)為是保護(hù)遙感圖像中信息隱私的有效方式[26].現(xiàn)有的圖像外包去噪方案[25],只考慮了單幀圖像的空間域相關(guān)性,未考慮多幀圖像的時(shí)間域相關(guān)性.多圖非局部去噪[14]利用多幀圖像的時(shí)間域相關(guān)性和空間域相關(guān)性,可在非局部去噪過(guò)程中找到更多、相似程度更高的像素點(diǎn),更好地削弱圖像中的噪聲.
本文在已有工作的基礎(chǔ)上,提出了遙感圖像外包去噪的單幀去噪方案和融合去噪方案,并給出了實(shí)驗(yàn)對(duì)比結(jié)果:
1) 利用Paillier加密算法[27-28]的密文加法同態(tài)性和JL(Johnson-Lindenstrauss)轉(zhuǎn)換[29-30]近似保留歐氏距離的特性,采用雙密文策略,對(duì)密文遙感圖像進(jìn)行基于動(dòng)態(tài)濾波參數(shù)的外包去噪.
2) 基于文獻(xiàn)[14]中的融合去噪方案,提出了一種針對(duì)多幀遙感圖像的安全外包融合去噪方案,對(duì)平均圖像進(jìn)行基于動(dòng)態(tài)濾波參數(shù)的外包融合去噪.
3) 選用從多幅Landsat8遙感圖像中截取多個(gè)512×512大小的圖像作為實(shí)驗(yàn)對(duì)象,搭建了Spark單機(jī)環(huán)境來(lái)模擬云環(huán)境.實(shí)驗(yàn)數(shù)據(jù)表明:本文提出的外包方案可以有效地保證遙感圖像的安全性;同時(shí),本文的融合去噪方案明顯優(yōu)于已有的密文去噪方案[25]和單幀去噪方案,對(duì)不同大小的噪聲均有很好的去噪效果.
1.1系統(tǒng)模型
1.1.1 單幀圖像模型
對(duì)于給定的任意一幅含有噪聲的圖像可以描述為:v={v(a)|a∈A},其中A表示該圖像域.對(duì)于該圖中的任意一個(gè)像素點(diǎn)a表示為
v(a)=u(a)+n(a),
(1)
其中,v(a)為像素點(diǎn)a的測(cè)定值,u(a)為像素點(diǎn)a的原始灰度值,n(a)為該圖像在像素點(diǎn)a的噪聲值.對(duì)于圖像中任意一個(gè)像素點(diǎn)a,非局部均值去噪算法利用圖像中所有相似像素點(diǎn)的灰度值加權(quán)平均得到該點(diǎn)的估計(jì)值,表示為

(2)

1.1.2 多幀圖像模型
對(duì)于多幀圖像,如圖1所示,噪聲圖像nf1,nf2,…,nfn為短時(shí)間內(nèi)采集到的同一場(chǎng)景的多幀圖像,平均圖像nf0為多幀圖像疊加平均得到.a1,a2,…,an是時(shí)間域上對(duì)應(yīng)空間位置的像素點(diǎn),分別來(lái)自nf1,nf2,…,nfn.那么在平均圖像nf0中像素點(diǎn)a0處融合去噪后的估計(jì)值為

(3)


(4)
其中高斯公式
(5)


Fig. 1 Multi-images and average image圖1 多幀圖像及疊加平均

Fig. 2 Outsourced fusion denoising framework圖2 外包融合去噪框架圖
1.2安全模型
本文采用云平臺(tái)是誠(chéng)實(shí)且好奇(honest but curious)模型[26],即云平臺(tái)會(huì)誠(chéng)實(shí)地執(zhí)行用戶預(yù)設(shè)的計(jì)算,但是云平臺(tái)可能會(huì)窺探數(shù)據(jù)內(nèi)容.如圖2所示,用戶在上傳到云平臺(tái)前進(jìn)行遙感圖像的加密,然后云平臺(tái)基于密文遙感圖像進(jìn)行多幀遙感圖像的融合去噪,最后用戶解密云平臺(tái)返回的遙感圖像,獲得完成融合去噪后的遙感圖像.
1.3算法描述
根據(jù)Gennaro等人提出的安全外包計(jì)算的形式化定義[31],本文給出遙感圖像外包融合去噪方案的定義.方案包括4個(gè)算法:密鑰生成(KeyGen)、問(wèn)題生成(ProbGen)、問(wèn)題計(jì)算(Compute)和問(wèn)題解決(Solve).
1) 密鑰生成.KeyGen(τ)→(skPerm,skJL,pkPail,skPail).輸入一個(gè)隨機(jī)的安全參數(shù)τ,輸出隨機(jī)置換密鑰skPerm;輸出JL轉(zhuǎn)換的密鑰skJL;輸出Paillier加密的公私鑰對(duì)pkPail和skPail.
本文的方案分成密鑰生成(KeyGen)、問(wèn)題生成(ProbGen)、問(wèn)題計(jì)算(Compute)和問(wèn)題解決(Solve)四個(gè)算法.
2.1密鑰生成KeyGen
本文的遙感圖像安全外包融合去噪方案所需要的密鑰包括: 隨機(jī)置換密鑰skPerm;JL轉(zhuǎn)換的密鑰skJL=(P,ζ);Paillier加密的公鑰pkPail=(N,g)和私鑰skPail=(λ,g).
2.2問(wèn)題生成ProbGen
二是角度。俗話說(shuō),果樹(shù)豐產(chǎn)不豐產(chǎn),開(kāi)角是關(guān)鍵。拉枝是果樹(shù)生產(chǎn)中的關(guān)鍵環(huán)節(jié),枝勢(shì)越強(qiáng),拉枝角度越大。永久性主枝拉至80°~90°即可,臨時(shí)輔養(yǎng)枝角度可加大至110°以上。
2.2.1 圖像波段拆分
對(duì)于給定具有B個(gè)波段的遙感圖像Ii(i=1,2,…,n),圖像的長(zhǎng)為im_h,寬度為im_w,按波段把這n幅遙感圖像拆分成n×B個(gè)圖像.
2.2.2 圖像JL轉(zhuǎn)換

2.2.3 圖像隨機(jī)置換
為了讓云平臺(tái)計(jì)算出遙感圖像中像素塊之間的歐氏距離,需要將單波段圖像Im1,Im2,…,Im n經(jīng)過(guò)JL轉(zhuǎn)換得到的圖像EJL(Im1),EJL(Im2),…,EJL(Im n)發(fā)送到云平臺(tái),然而圖像EJL(Im1),EJL(Im2),…,EJL(Im n)中保存了明文圖像中的相鄰像素的位置信息,雖然無(wú)法推斷出該圖像各個(gè)像素點(diǎn)準(zhǔn)確的灰度值,但可以通過(guò)二值化攻擊獲得原始圖像的大概輪廓.對(duì)圖像EJL(Im1),EJL(Im2),…,EJL(Im n)進(jìn)行二值化攻擊,得到的結(jié)果如圖3(a),(b)所示,攻擊者依然能夠獲得海岸線、道路輪廓等地貌特征.


Fig. 3 Results of the Binarization attack before/after random permutation圖3 隨機(jī)置換前后二值化攻擊效果圖
2.2.4 圖像Paillier加密

(gN)r5modN2.
(6)
2.3問(wèn)題計(jì)算Compute
2.3.1 平均圖像計(jì)算


(7)

2.3.2 密文歐氏距離計(jì)算

dJL(a0,bj)=

(8)
2.3.3 去噪權(quán)重計(jì)算
云平臺(tái)需要對(duì)多幀遙感圖像的單個(gè)波段的圖像進(jìn)行融合去噪,然而遙感圖像中眾多的相似度低的像素點(diǎn)增加了計(jì)算量,同時(shí)也會(huì)影響融合去噪算法的去噪效果.加權(quán)核函數(shù)對(duì)融合去噪性能和效率起著至關(guān)重要的作用.本文基于余弦型高斯核函數(shù)[33],提出了一種基于自適應(yīng)濾波參數(shù)h2的融合去噪方法,其高斯函數(shù)為
fkJL(a0,bj)=
(9)
其中,h1為平滑參數(shù),h2為濾波參數(shù),且h2為集合{dJL(a0,bj)|bj∈At,1≤t≤n}中第M小的值,其中M為進(jìn)行融合去噪而選取的相似度最大的像素點(diǎn)個(gè)數(shù).
此時(shí),權(quán)重

(10)

由于Paillier加密只能處理整數(shù),w′(a0,bj)必須要轉(zhuǎn)化為一個(gè)整數(shù).權(quán)重取整轉(zhuǎn)換為

(11)

2.3.4 融合去噪計(jì)算

EPail[NL″(a0)]=
(12)
2.4問(wèn)題解決Solve
2.4.1 圖像Paillier解密
接收到云端返回的完成融合去噪的加密圖像后,用戶使用私鑰skPail對(duì)收到的遙感圖像進(jìn)行Paillier解密并計(jì)算出該圖像完成融合去噪后的結(jié)果.
在融合去噪過(guò)程中,使用w″(a0,bj)作為加權(quán)因子
w″(a0,bj)=Qw′(a0,bj)+ψ(a0,bj),
(13)
其中,ψ(a0,bj)為轉(zhuǎn)化過(guò)程中的誤差值,且|ψ(a0,bj)|<0.5.則NL″(a0)可以表示為
NL″(a0)=Q×NL′(a0)+

(14)
因此NL′(a0)可以表示為

(15)
其中,R(a0)為轉(zhuǎn)化過(guò)程中給融合去噪的結(jié)果帶來(lái)的誤差值,當(dāng)Q足夠大時(shí),R(a0)<0.5,給融合去噪結(jié)果帶來(lái)的影響非常小.因此:


(16)
2.4.2 圖像恢復(fù)

2.4.3 圖像組合
對(duì)完成去噪后B個(gè)波段的遙感圖像重新組合,即可得到完成融合去噪的遙感圖像I′.

綜上分析,本文的融合去噪方案具有良好的安全性,除了密文長(zhǎng)度和遙感圖像大小,攻擊者無(wú)法獲取到任何有用信息.
實(shí)驗(yàn)數(shù)據(jù)選用從多幅Landsat 8遙感圖像中截取多個(gè)512×512像素的圖像,采用圖像中空間分辨率為30 m的7個(gè)波段圖像(波段名為Coastal,Blue,Green,Red,NIR,SWIR1,SWIR2)作為實(shí)驗(yàn)圖像.實(shí)驗(yàn)環(huán)境為在計(jì)算機(jī)(處理器:i7-3770 3.4GHz、內(nèi)存:8 GB 1 600 MHz、編程語(yǔ)言:Java)上搭建的Spark單機(jī)環(huán)境.
Paillier加密的參數(shù)設(shè)置如下:p和q為256 b素?cái)?shù).JL轉(zhuǎn)換中參數(shù)設(shè)置如下:高斯噪聲參數(shù)ζ=0.5,維度k取值為9,12,15,18四種情況.融合去噪?yún)?shù)設(shè)置如下:濾波參數(shù)h1=384,像素塊大小S×S=5×5,進(jìn)行融合去噪的像素點(diǎn)個(gè)數(shù)M=512,權(quán)重轉(zhuǎn)換參數(shù)Q=225.
加入N(0,5122)的高斯噪聲后,遙感圖像的峰值信噪比(peak signal to noise ratio,PSNR)為42.14 dB,均方誤差(mean squared error,MSE)為262 277.00.分別運(yùn)用4種方法:基于明文的非局部均值去噪方法[6]、Hu等人的密文方法[25]、本文方案的單幅圖像去噪方法和多幀(n=3)圖像融合去噪方法對(duì)上述含有噪聲的遙感圖像進(jìn)行去噪對(duì)比.得到各個(gè)波段的PSNR值如表1所示,MSE值如表2所示.實(shí)驗(yàn)結(jié)果表明:本文的融合去噪方法優(yōu)于密文去噪方法和單幅去噪方法,且在k較大時(shí)優(yōu)于明文去噪方法.

Table 1 PSNR Results of Remote Sensing Image Denoising

Table 2 MSE Results of Remote Sensing Image Denoising
使用本文的去噪框架,分別運(yùn)用Hu等人的密文方法[25]、本文方案的單幅圖像去噪方法和多幀(n=3)圖像融合去噪方法,對(duì)不同波段的遙感圖像進(jìn)行去噪.圖4給出了去噪效果PSNR與JL轉(zhuǎn)換維度關(guān)系對(duì)比;圖5給出了去噪效果MSE與JL轉(zhuǎn)換維度關(guān)系對(duì)比;圖6給出了去噪效率對(duì)比.實(shí)驗(yàn)結(jié)果表明:本文的融合去噪方法對(duì)于不同波段的遙感圖像均有很好的去噪效果,且隨著JL轉(zhuǎn)換維度的增加,去噪效果越好;在遙感圖像幀數(shù)n=3時(shí),本文的融合去噪用時(shí)高于單幅圖像去噪,但遠(yuǎn)低于密文去噪方法[25].

Fig. 6 The comparison on outsourced denoising efficiency圖6 外包去噪效率對(duì)比圖

Fig. 4 The comparison on PSNR with different dimensions of JL transform圖4 去噪效果PSNR與JL轉(zhuǎn)換維度k關(guān)系對(duì)比圖

Fig. 5 The comparison on MSE with different dimensions of JL transform圖5 去噪效果MSE與JL轉(zhuǎn)換維度k關(guān)系對(duì)比圖
本文融合去噪方法對(duì)于多幅圖像的不同噪聲去噪效果圖如圖7所示.圖7(a1),(b1)為L(zhǎng)andsat 8遙感圖像1對(duì)應(yīng)Red波段的圖像,圖7(c1),(d1),(e1),(f1)為L(zhǎng)andsat 8遙感圖像2和遙感圖像3對(duì)應(yīng)NIR波段的圖像.第1列為原始圖像;第2列為含有不同噪聲的圖像,圖7(a2),(c2),(e2)為原始圖像加了N(0,2562)的高斯噪聲得到的其中一幅圖像,圖7(b2),(d2),(f2)為原始圖像加了N(0,5122)的高斯噪聲得到的其中一幅圖像;第3列為基于含有噪聲的明文圖像進(jìn)行非局部去噪得到的圖像[6];第4列為基于含有噪聲的密文圖像運(yùn)用本文的去噪方案基于單幅圖像去噪得到的圖像.第5列為基于含有噪聲的密文圖像運(yùn)用本文的融合去噪方案得到的圖像.實(shí)驗(yàn)結(jié)果表明:本文的融合去噪方法對(duì)于不同遙感圖像中的不同大小的噪聲都能有很好的去噪效果.
最后,實(shí)驗(yàn)給出了用于多幀融合去噪的圖像幀數(shù)n對(duì)圖像去噪效果的影響.以圖7中遙感圖像1、遙感圖像2和遙感圖像3對(duì)應(yīng)的Red波段圖像為例,實(shí)驗(yàn)設(shè)定圖像幀數(shù)n=1,2,3,4,5,噪聲大小為N(0,5122)的高斯噪聲,運(yùn)用本文的融合去噪方法進(jìn)行測(cè)試,測(cè)試結(jié)果如圖8和圖9所示.實(shí)驗(yàn)結(jié)果表明,在圖像幀數(shù)不超過(guò)5的情況下,隨著圖像幀數(shù)的增加,多幀圖像的去噪效果明顯變好.

Fig. 7 The result of secure fusion denoising in remote sensing image圖7 遙感圖像安全融合去噪結(jié)果圖

Fig. 8 The comparison on PSNR with different frame number of images圖8 去噪效果PSNR與圖像幀數(shù)關(guān)系對(duì)比圖

Fig. 9 The comparison on MSE with different frame number of images圖9 去噪效果MSE與圖像幀數(shù)關(guān)系對(duì)比圖
隨著云計(jì)算技術(shù)的進(jìn)一步成熟,遙感圖像外包處理的安全性已成為學(xué)術(shù)界和工業(yè)界的關(guān)注焦點(diǎn).本文提出了一種多幀遙感圖像安全外包融合去噪框架,采用雙密文技術(shù),實(shí)現(xiàn)對(duì)加密后的遙感圖像進(jìn)行基于動(dòng)態(tài)濾波參數(shù)的融合去噪處理.實(shí)驗(yàn)結(jié)果表明,該安全外包方案可以有效地保證遙感圖像的安全性,融合去噪效果明顯優(yōu)于已有的密文去噪方案和單幀密文去噪方案,對(duì)不同圖像的不同大小的噪聲均有很好的去噪效果,且隨著多幀遙感圖像幀數(shù)的增加,去噪效果明顯變好.下一步的工作是在實(shí)際的云平臺(tái)環(huán)境下實(shí)現(xiàn)遙感圖像的安全外包去噪,并進(jìn)一步利用同一地點(diǎn)不同時(shí)相的遙感圖像進(jìn)行融合去噪.
[1] He Guojin, Wang Lizhe, Ma Yan, et al. Processing of earth observation big data: Challenges and countermeasures[J]. Chinese Science Bulletin, 2015, 60(5/6): 470-478 (in Chinese)
(何國(guó)金, 王力哲, 馬艷, 等. 對(duì)地觀測(cè)大數(shù)據(jù)處理: 挑戰(zhàn)與思考[J]. 科學(xué)通報(bào), 2015, 60(5/6): 470-478)
[2] Huang Dongmei, Geng Xia, Wei Lifei, et al. A secure query scheme on encrypted remote sensing images based on Henon mapping[J]. Journal of Software, 2016, 27(7):1729-1740 (in Chinese)
(黃冬梅, 耿霞, 魏立斐, 等. 基于Henon映射的加密遙感圖像的安全檢索方案[J]. 軟件學(xué)報(bào), 2016, 27(7): 1729-1740)
[3] Zhang Jiyao, Zhang Xie, Liu Xiao, et al. Investigation on adaptive denoising of remote sensing image[J]. Journal of Atmospheric and Environmental Optics, 2011, 6(5): 368-376 (in Chinese)
(張繼堯, 張渫, 劉曉, 等. 遙感圖像自適應(yīng)去噪方法研究[J]. 大氣與環(huán)境光學(xué)學(xué)報(bào), 2011, 6(5): 368-376)
[4] Xia Qin, Xing Shuai, Ma Dongyang, et al. An improved K-SVD-based denoising method for remote sensing images[J]. Journal of Remote Sensing, 2016, 20(3): 441-449 (in Chinese)
(夏琴, 邢帥, 馬東洋, 等. 遙感衛(wèi)星影像K-SVD稀疏表示去噪[J]. 遙感學(xué)報(bào), 2016, 20(3): 441-449)
[5] Zhou Xiaojun, Tan Wei, Zhang Liao, et al. The research of remote sensing image denoising methods[J]. Industrial Instrumentation & Automation, 2015 (3): 69-72 (in Chinese)
(周小軍, 譚薇, 張燎, 等. 遙感圖像常用去噪方法[J]. 工業(yè)儀表與自動(dòng)化裝置, 2015 (3): 69-72)
[6] Buades A, Coll B, Morel J M. A review of image denoising algorithms, with a new one[J]. Multiscale Modeling & Simulation, 2005, 4(2): 490-530
[7] Perona P, Malik J. Scale-space and edge detection using anisotropic diffusion[J]. IEEE Trans on Pattern Analysis and Machine Intelligence, 1990, 12(7): 629-639
[8] Lee S H, Seo J K. Noise removal with Gauss curvature-driven diffusion[J]. IEEE Trans on Image Processing, 2005, 14(7): 904-909
[9] Luisier F, Blu T. SURE-LET multichannel image denoising: Interscale orthonormal wavelet thresholding[J]. IEEE Trans on Image Processing, 2008, 17(4): 482-492
[10] Dou Nuo, Zhao Ruizhen, Cen Yigang, et al. Noisy image super-resolution reconstruction based on sparse representa-tion[J]. Journal of Computer Research and Development, 2015, 52(4): 943-951 (in Chinese)
(竇諾, 趙瑞珍, 岑翼剛, 等. 基于稀疏表示的含噪圖像超分辨重建方法[J]. 計(jì)算機(jī)研究與發(fā)展, 2015, 52(4): 943-951)
[11] Tico M, Vehvilainen M. Robust image fusion for image stabilization[C] //Proc of the 32nd IEEE Int Conf on Acoustics, Speech and Signal Processing. Piscataway, NJ: IEEE, 2007: 565-568
[12] Buades T, Lou Y, Morel J M, et al. A note on multi-image denoising[C] //Proc of the 2nd Int Workshop on Local and Non-Local Approximation in Image Processing. Piscataway, NJ: IEEE, 2009: 1-15
[13] Yang Jingyu, Gan Ziqiao, Wu Zhaoyang, et al. Estimation of signal-dependent noise level function in transform domain via a sparse recovery model[J]. IEEE Trans on Image Processing, 2015, 24(5): 1561-1572
[14] Wang Na. Multi-image denoising using nonlocal information[D].Xi’an: Xidian University, 2014 (in Chinese)
(王娜. 多圖非局部去噪算法研究[D]. 西安: 西安電子科技大學(xué), 2014)
[15] Wu Jiyi, Shen Qianli, Zhang Jianlin, et al. Cloud computing: Cloud security to trusted cloud[J]. Journal of Computer Research and Development, 2011, 48(1): 229-233 (in Chinese)
(吳吉義, 沈千里, 章劍林, 等. 云計(jì)算: 從云安全到可信云[J]. 計(jì)算機(jī)研究與發(fā)展, 2011, 48(1): 229-233)
[16] Wang Kaixuan, Li Yuxi, Zhou Fucai, et al. Multi-keyword fuzzy search over encrypted data[J]. Journal of Computer Research and Development, 2017, 54(2): 348-360 (in Chinese)
(王愷璇, 李宇溪, 周福才, 等. 面向多關(guān)鍵字的模糊密文搜索方法[J]. 計(jì)算機(jī)研究與發(fā)展, 2017, 54(2): 348-360)
[17] Zhou Jun, Cao Zhenfu, Dong Xiaolei. PPOPM: More efficient privacy preserving outsourced pattern matching[C] //Proc of the 21st European Symp on Research in Computer Security. Berlin: Springer, 2016: 135-153
[18] Li Dongmei, Dong Xiaolei, Cao Zhenfu. Secure and privacy-preserving pattern matching in outsourced computing[J]. Security and Communication Networks, 2016, 9(16): 3444-3451
[19] Zhang Xinpeng. Lossy compression and iterative reconstruction for encrypted image[J]. IEEE Trans on Information Forensics and Security, 2011, 6(1): 53-58
[20] Zhang Xinpeng, Long Jing, Wang Zichi, et al. Lossless and reversible data hiding in encrypted images with public-key cryptography[J]. IEEE Trans on Circuits and Systems for Video Technology, 2016, 26(9): 1622-1631
[21] Seitkulov Y N. New methods of secure outsourcing of scientific computations[J]. The Journal of Supercomputing, 2013, 65(1): 469-482
[22] Hu Xing, Tang Chunming. Secure outsourced computation of the characteristic polynomial and eigenvalues of matrix[J]. Journal of Cloud Computing, 2015, 4(1): 1-6
[23] Hong Yuan, Vaidya J. An inference-proof approach to privacy-preserving horizontally partitioned linear programs[J]. Optimization Letters, 2014, 8(1): 267-277
[24] Ferdush J, Mehzabin T, Hashem M M A. Securely outsourcing of large scale linear fractional programming problem to public cloud[C] //Proc of the 5th Int Conf on Informatics, Electronics and Vision. Piscataway, NJ: IEEE, 2016: 373-378
[25] Hu Xianjun, Zhang Weiming, Li Ke, et al. Secure nonlocal denoising in outsourced images[J]. ACM Trans on Multimedia Computing, Communications, and Applications, 2016, 12(3): 40-63
[26] Cao Zhenfu, Dong Xiaolei, Zhou Jun, et al. Research advances on big data security and privacy preserving[J]. Journal of Computer Research and Development, 2016, 53(10): 2137-2151 (in Chinese)
(曹珍富, 董曉蕾, 周俊, 等. 大數(shù)據(jù)安全與隱私保護(hù)研究進(jìn)展[J]. 計(jì)算機(jī)研究與發(fā)展, 2016, 53(10): 2137-2151)
[27] Paillier P. Public-key cryptosystems based on composite degree residuosity classes[C] //Proc of the 18th Int Conf on the Theory and Applications of Cryptographic Techniques. Berlin: Springer, 1999: 223-238
[28] Bai Jian, Yang Yatao, Li Zichen. The homomorphism and efficiency analysis of Paillier cryptosystem[J]. Journal of Beijing Elrctronic Science and Technology Institute, 2012,20(4):1-5 (in Chinese)
(白健, 楊亞濤, 李子臣. Paillier公鑰密碼體制同態(tài)特性及效率分析[J]. 北京電子科技學(xué)院學(xué)報(bào), 2012, 20(4): 1-5)
[29] Johnson W B, Lindenstrauss J. Extensions of Lipschitz mappings into a Hilbert space[J]. Contemporary Mathematics, 1984, 26(1): 189-206
[30] Indyk P, Motwani R. Approximate nearest neighbors: Towards removing the curse of dimensionality[C] //Proc of the 30th Annual ACM Symp on Theory of Computing. New York: ACM, 1998: 604-613
[31] Gennaro R, Gentry C, Parno B. Non-interactive verifiable computing: Outsourcing computation to untrusted workers[C] //Proc of Annual Cryptology Conf. Berlin: Springer, 2010: 465-482
[32] Deng R H, Ding Xuhua, Wu Yongdong, et al. Efficient block-based transparent encryption for H.264/SVC bitstreams[J]. Multimedia Systems, 2014, 20(2): 165-178
[33] Liu Xiaoming, Tian Yu, He Hui, et al. Improved non-local means algorithm for image denoising[J]. Computer Engineering, 2012, 38(4): 199-201 (in Chinese)
(劉曉明, 田雨, 何徽, 等. 一種改進(jìn)的非局部均值圖像去噪算法[J]. 計(jì)算機(jī)工程, 2012, 38(4): 199-201)
ASecureOutsourcedFusionDenoisingSchemeinMultipleEncryptedRemoteSensingImages
Huang Dongmei1, Dai Liang1, Wei Lifei1, Wei Quanmiao2, and Wu Guojian1
1(CollegeofInformation,ShanghaiOceanUniversity,Shanghai201306)2(EastChinaSeaBranch,StateOceanicAdministration,Shanghai200136)
Remote sensing image denoising is a hot research topic in the field of image processing. The improvement of remote sensing image acquisition equipment and technology has made it possible to collect multiple images from the same scene in a short period of time. However, the processing huge number of the remote sensing images on the ordinary computers has caused the low processing capability and poor concurrency. It is a trend to store and compute the big data outsourced to the cloud. To protect the security of outsourced remote sensing images, the article presents a secure outsourced fusion denoising scheme in multiple encrypted remote sensing images to implement the fusion denoising based on dynamic filtering parameters. In the schemes, the ciphertext from Johnson-Lindenstrauss transform is used to weight calculatation as well as the plaintext and the ciphertext from Paillier homomorphic encryption is used to fusion denoise by the linear calculation of ciphertext. The experiments use several 512×512 pixels remote sensing images based on the Spark alone-server environment to simulate the cloud platform. The experimental results show that the outsourcing schemes can effectively ensure the security of the remote sensing images and get better denoising quality with different sizes of noise than the existing schemes.
multiple images; remote sensing; secure outsourcing; fusion denoising; Paillier homomorphic encryption; Johnson-Lindenstrauss transform
TP309

HuangDongmei, born in 1964. Professor, PhD supervisor. Senior member of CCF. Her main research interests include big data, remote sensing and decision support system.

DaiLiang, born in 1993. Master candidate. Student member of CCF. His main research interests include remote sensing and information security (dailiang 19931020@163.com).

WeiLifei, born in 1982. PhD. Member of CCF. His main research interests include information security and cryptography.

WeiQuanmiao, born in 1964. Deputy director of the East China Sea Branch of State Oceanic Administration. His main research interests include database and ocean assistant decision-making system (qmwei@eastsea.gov.cn).

WuGuojian, born in 1993. Master candidate. Student member of CCF. His main research interests include remote sensing and information security (wuguojian 19930913@163.com).