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1、文章编号：1009-8119（2006）01-0041-02基于小波变换的航空图像压缩技术研究蒋定定 李开端 王尚强（海军航空工程学院青岛分院，青岛266041）摘 要 航空图像的压缩是其处理的一项重要内容。本文介绍了小波变换的基本原理和图像编码、压缩的基本概念，并利用小波技术对航空图像进行压缩，效果明显。 关键词 小波变换，航空图像，编码，压缩Aviation Image Compression Research Based on Wavelet TransformJiang Dingding Li Kaiduan Wang Shangqiang(Naval Aeronautical Eng
2、ineering Academy Qingdao Branch, Qingdao 266041)Abstract Aviation image compression is an important contents of image processing. This peper introduces the basic concept for basic principle for transformation with image coding, compressedly of wavelet, and makes use of the technique of wavelet to re
3、semble proceed to compress to aviation image, and result is obvious.Keywords Transformation wavelet, The aviation image, Code, Compress1 引 言小波分析属于时频分析的一种。传统的信号分析是建立在傅立叶变换的基础上的，由于傅立叶分析使用的是一种全局的变换，要么完全在时域，要么完全在频域。无法表达信号的时频局域性质，而这种性质恰恰是非平稳信号最根本和最关键的性质。为了分析和处理非平稳信号，人们提出了一系列新的信号分析理论。其中，小波变换是一种信号的时间尺度（时间频
4、率）分析方法，它具有多分辨率分析的特点，而且在时频两域都具有表征信号局域特征的能力，是一种窗口大小固定不变但形状可变，时间窗和频率窗都可以改变的时频局部化分析方法。即在低频部分具有较高的频率分辨率和较低的时间分辨率，在高频部分具有较高的时间分辨率和较低的频率分辨率，很适合于探测正常信号中夹带的瞬态反常现象并展示其成份，被誉为分析信号的显微镜。2 小波分析基础设表示平方可积的实数空间，即能量有限的信号空间），其傅立叶变换为，当满足允许条件 (1)时，称（t）为一个基本小波或母小波。将母函数（t）经伸缩和平移后，就可以得到一个小波序列。对于连续的情况，小波序列为： (2其中a为伸缩因子，b为平移因
5、子。对于离散的情况，小波序列为： (3)常用的是二进制小波。二进制小波信号对信号的分析具有变焦距的作用，假定有一放大倍数2j，它对应为观测信号的某部分内容，如果想进一步观看信号更小的细节，可增大放大倍数即减小j值；反之，若想了解信号更粗的内容，加大j值即可。Mallat在构造正交小波基时提出了多分辨分析的概念，给出了正交小波的构造方法以及正交小波变换的快速算法，即Mallat算法。在这里以一个三层的分解进行说明，其小波分解树如图1所示。图1 小波分解树从图1可以看出，多分辨分析只是对低频部分进行进一步分解，而高频部分则不予考虑。分解具有下述关系：SA3D3D2D1。如果要进行进一步分解，则可以
6、把低频部分A3分解成低频部分A4和高频部分D4，以下再分解依此类推。3 图像压缩的基本知识对于图像来说，如果需要进行快速或实时传输以及大量存储，就需要对图像数据进行压缩。在同等的通信容量下，如果图像数据压缩后再传输，就可以传输更多的图像信息，也就可以增加通信的能力。图像压缩研究就是寻找高压缩比的方法且压缩后的图像要有合适的信噪比，在压缩传输后还要恢复信号，并且在压缩、传输、恢复的过程中，还要求图像的失真度小，便于图像的分类、识别等。图像数据往往存在各种信息的冗余,如空间冗余、信息熵冗余、视觉冗余和结构冗余等。所谓压缩就是去掉各种冗余，保留对我们有用的信息。图像压缩的过程常称为编码，图像恢复的过
7、程称为解码。根据解码后的数据下原始数据是否完全一致来分类，图像压缩方法一般划分为无失真编码与有失真编码。无失真编码方法要求在解码后得到的图像与原始图像严格相同，有失真编码方法的还原图像与原始图像存在一定的误差，但视觉效果一般是可以接受的。根据有失真编码的原理进行分类，可以预测编码、变换编码、最化编码、信息熵编码、分频带编码、结构编码等。变换编码是一种针对统一冗余进行压缩方法。所谓变换编码是将时域图像（空间）变换到系数域（频域）上进行处理的方法。因为由时域映射到频域总是通过某种变换进行的，所以称为变换编码方法。在空间上具有强相关的信号，反映在频域上是在某种特定的区域中能集中在一起，或是系数矩阵的
8、分布具有某种规律，这就可以利用这些规律频域上的最化比特数，从而达到图像压缩的目的。小波分析用于图像压缩是小波分析应用的一个重要方面。其特点是压缩比高，压缩速度快，压缩后能保持信号与图像的特征基本不变，传递过程中抗干扰。4 采用MATLAB利用二维小波对航空图像压缩一个图像作小波分解后，可得到一系列不同分辩率的子图像，不同分辩率的航空子图像的频率是不同的。高分辩率（即高频）航空子图像上大部分点的数值都接近于零，越是高频这种现象越明显。对一幅航空图像来说，表现一个目标最主要的部分是低频部分，所以一个最简单的压缩方法是利用小波分解，去掉航空图像的高频部分而只保留低频部分。本文采用MATLAB编程利用
9、小波函数实现了航空图像的压缩。第一次压缩是从原始航空图像中提取小波分解第一层的低频信息，压缩效果良好。压缩比约13.6；第二次压缩是提取第一层分解低频部分的低频部分（即小波分解第二层的低频部分），其压缩比约为112，压缩效果在视觉上较不清楚。压缩前航空图像的x大小：名 称大 小字 节x25625665536 单元阵列Cal(第一次压缩)135135145800 双阵列Ca2(第二次压缩)757545000双阵列参考文献1 赵松年, 熊小芸.子波变换与子波分析. 电子工业出版社, 1996: 82 胡昌华等.基于MATLAB的系统分析与设计一小波分析. 西安电子科技大学出版社, 1999: 9待
10、添加的隐藏文字内容3Editors note: Judson Jones is a meteorologist, journalist and photographer. He has freelanced with CNN for four years, covering severe weather from tornadoes to typhoons. Follow him on Twitter: jnjonesjr (CNN) - I will always wonder what it was like to huddle around a shortwave radio and t
11、hrough the crackling static from space hear the faint beeps of the worlds first satellite - Sputnik. I also missed watching Neil Armstrong step foot on the moon and the first space shuttle take off for the stars. Those events were way before my time.As a kid, I was fascinated with what goes on in th
12、e sky, and when NASA pulled the plug on the shuttle program I was heartbroken. Yet the privatized space race has renewed my childhood dreams to reach for the stars.As a meteorologist, Ive still seen many important weather and space events, but right now, if you were sitting next to me, youd hear my
13、foot tapping rapidly under my desk. Im anxious for the next one: a space capsule hanging from a crane in the New Mexico desert.Its like the set for a George Lucas movie floating to the edge of space.You and I will have the chance to watch a man take a leap into an unimaginable free fall from the edg
14、e of space - live.The (lack of) air up there Watch man jump from 96,000 feet Tuesday, I sat at work glued to the live stream of the Red Bull Stratos Mission. I watched the balloons positioned at different altitudes in the sky to test the winds, knowing that if they would just line up in a vertical s
15、traight line we would be go for launch.I feel this mission was created for me because I am also a journalist and a photographer, but above all I live for taking a leap of faith - the feeling of pushing the envelope into uncharted territory.The guy who is going to do this, Felix Baumgartner, must hav
16、e that same feeling, at a level I will never reach. However, it did not stop me from feeling his pain when a gust of swirling wind kicked up and twisted the partially filled balloon that would take him to the upper end of our atmosphere. As soon as the 40-acre balloon, with skin no thicker than a dr
17、y cleaning bag, scraped the ground I knew it was over.How claustrophobia almost grounded supersonic skydiverWith each twist, you could see the wrinkles of disappointment on the face of the current record holder and capcom (capsule communications), Col. Joe Kittinger. He hung his head low in mission
18、control as he told Baumgartner the disappointing news: Mission aborted.The supersonic descent could happen as early as Sunday.The weather plays an important role in this mission. Starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and li
19、mited cloud cover. The balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commerci
20、al airliners (5.6 miles/9.17 kilometers) and into the stratosphere. As he crosses the boundary layer (called the tropopause), he can expect a lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 feet (22.7 miles/36.53 kilometers). Here, Fearless Felix will unclip. He will
21、roll back the door.Then, I would assume, he will slowly step out onto something resembling an Olympic diving platform.Below, the Earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. Still, hell be traveling fast, so despite the distance, it will not be lik
22、e diving into the deep end of a pool. It will be like he is diving into the shallow end.Skydiver preps for the big jumpWhen he jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. Like hitting the top of the water, he will begin to slow as he approaches
23、the more dense air closer to Earth. But this will not be enough to stop him completely.If he goes too fast or spins out of control, he has a stabilization parachute that can be deployed to slow him down. His team hopes its not needed. Instead, he plans to deploy his 270-square-foot (25-square-meter)
24、 main chute at an altitude of around 5,000 feet (1,524 meters).In order to deploy this chute successfully, he will have to slow to 172 mph (277 kph). He will have a reserve parachute that will open automatically if he loses consciousness at mach speeds.Even if everything goes as planned, it wont. Ba
25、umgartner still will free fall at a speed that would cause you and me to pass out, and no parachute is guaranteed to work higher than 25,000 feet (7,620 meters).It might not be the moon, but Kittinger free fell from 102,800 feet in 1960 - at the dawn of an infamous space race that captured the hearts of many. Baumgartner will attempt to break that record, a feat that boggles the mind. This is one of those monumental moments I will always remember, because there is no way Id miss this.
