外文翻譯---小波變換在圖像處理中的仿真及應(yīng)用

1、<p><b>　　附錄B</b></p><p>　　Wavelet transform in image processing in simulation and Application</p><p>　　1, task significance</p><p>　　In the traditional analysis of

2、signal in frequency domain, is completely unfolded, does not contain any time frequency information, which for some applications it is appropriate, because the frequency of the signal to its information is very important

3、. But its discarded time information may be possible for some applications also is very important, so the analysis of the promotion, put forward a lot of time domain and frequency domain information signal analysis metho

4、ds, such as short Fourier tra</p><p>　　The traditional signal theory, is built on the basis of the analysis of Fourier, Fourier transform is a kind of global change, it has some limitations. In practical app

5、lication, the people start to Fourier transform are improved, thus resulting in wavelet analysis. Wavelet analysis is a new branch of mathematics, it is a universal function, Fourier analysis, harmonic analysis, numerica

6、l analysis of the most perfect crystalline; in the fields of application, especially in signal processing, image</p><p>　　Wavelet transform is a rapid development and more popular signal analysis method, the

7、 image processing is a very important application, including image compression, image denoising, image fusion, image decomposition, image enhancement. Wavelet analysis is the analysis method of thinking in the developmen

8、t and continuation. In addition to continuous wavelet, discrete wavelet transform ( CWT ) ( DWT ), and the wavelet packet ( Wavelet Packet ) and multidimensional wavelet</p><p>　　Wavelet analysis in image pr

9、ocessing applications are very important, including image compression, image denoising, image fusion, image decomposition, image enhancement. Wavelet transform is a new transform analysis method, it has inherited and dev

10、eloped the STFT localization of thought, and also overcomes the window size does not vary with frequency and other shortcomings, to provide a frequency changing with time frequency window, is a time-frequency signal anal

11、ysis and processing the ideal to</p><p>　　2, problem overview</p><p>　　( a ) the application of wavelet analysis and development</p><p>　　The application of wavelet analysis and wav

12、elet analysis theory to work closely together. Now, it has been in the information technology industry has made the achievement attract people's attention. Electronic information technology is the six new and high te

13、chnology an important field, which is an important aspect of image and signal processing. Nowadays, signal processing has become an important part of the work of contemporary science and technology, the purpose of signal

14、 processing is: accur</p><p>　　Course number processing ( image can be viewed as a two-dimensional signal ), the wavelet analysis of the many analysis for many applications, can be attributed to the signal p

15、rocessing problems. Now, for its properties with time stable signal ( stationary random process ), an ideal tool in processing is still a Fourier analysis. But in the practical application of the vast majority of signal

16、is unstable ( non stationary random process ), and is especially suitable for the unstable signal wavele</p><p>　　In fact the wavelet analysis applied field is very extensive, it includes many disciplines: m

17、athematics; signal analysis, image processing; quantum mechanics, theoretical physics; military electronic warfare and weapons computer intelligent; classification and recognition; music and language artificial synthesis

18、; medical imaging and diagnosis; seismic data processing; mechanical the fault diagnosis and so on; for example, in mathematics, it has been used in numerical analysis, structure, fast nu</p><p>　　(1) applic

19、ation of wavelet analysis in signal and image compression wavelet analysis is an important application of the. It is characterized by high compression ratio, compression speed, the compressed signal can be maintained and

20、 image feature invariant, and the transfer of anti interference. The compression method based on wavelet analysis, comparative success of wavelet packet best base method, wavelet texture model method, wavelet transform Z

21、erotree compression, wavelet transform vector comp</p><p>　　(2) the wavelet in the signal analysis are widely used. It can be used for boundary processing and filtering, time-frequency analysis, signal-noise

22、 separation and extraction of weak signal, fractal index, signal recognition and diagnosis as well as the multi-scale edge detection. </p><p>　　In conclusion, because wavelet has low entropy, multi-resolutio

23、n, decorrelation, selected medium characteristics such as flexibility, the theory of wavelet in denoising fields by many scholars, and obtained good results. But how to take certain technology to eliminate image noise wh

24、ile preserving image detail is an important topic in the image pretreatment. At present, based on wavelet analysis in image denoising image denoising technology has become an important method.</p><p>　　(b) i

25、n the image processing field, wavelet transform has the following advantages:</p><p>　　(1) wavelet decomposition can cover the whole frequency domain ( provides a mathematically complete description)</p&g

26、t;<p>　　(2) wavelet transform by selecting appropriate filter, can greatly reduce or remove the correlation between different feature extraction</p><p>　　(3) wavelet transform has a" zoom" c

27、haracteristics, in the low frequency band can be used with high frequency resolution and low resolution ( width analysis window ), in the high frequency band, the available low frequency resolution and high temporal reso

28、lution ( narrow analysis window )</p><p>　　(4) wavelet transform on a fast algorithm ( Mallat algorithm )Wavelet analysis has become one of the fastest and most attract sb.'s attention on one of the subj

29、ects, or applied to the field of information involved in almost all disciplines.</p><p>　　(c) demonstration program</p><p>　　This paper based on the wavelet transform image denoising methods car

30、ried out in-depth research and analysis, the paper introduces several classic wavelet transform denoising method. The wavelet transform modulus maximum denoising method, described in detail the denoising principle and al

31、gorithm, analyzes the denoising process parameter selection problem, and gives some basis; detailed correlation of wavelet coefficient denoising method principle and algorithm; wavelet transform threshold denois</p>

32、;<p>　　In many image denoising based on wavelet transform method, is the largest use wavelet shrinkage denoising method. The traditional hard threshold function and soft threshold function de-noising method in pra

33、ctice has been widely used, and achieved good results. But the hard threshold function is discontinuous resulting reconstructed signal prone to false phenomenon of Gibbs; and the soft threshold function although the over

34、all good continuity, but the estimated value and the actual value of aggre</p><p>　　Wavelet basis function from the following3 aspects to consider.</p><p>　　(1)complex and real wavelet selection

35、Complex wavelet analysis can not only obtain the amplitude information, can also be obtained from the phase information, so the complex wavelet is suitable for the analysis and calculation of the normal signal characteri

36、stics. But the real wavelet is best used for peak or discontinuity detection.</p><p>　　(2) continuous wavelet effective support region selectionContinuous wavelet basis function in the effective support outs

37、ide the area of rapid decay. Effective support area is longer, the frequency resolution is better; effective support region is shorter, the better time resolution.</p><p>　　(3) wavelet shape selectionIf the

38、time-frequency analysis, to select a smooth continuous wavelet, because time more smooth basis functions, in the frequency domain localization characteristic. If the signal is detected, then you should try to choose and

39、signal waveform phase approximation of wavelet.</p><p>　　Wavelet transform and FFT comparison</p><p>　　Wavelet analysis, FFT analysis method of thinking in the development and extension of. Sinc

40、e its inception, has been closely related with fft. Its existence proof, wavelet construction as well as the results of analysis are dependent on Fourier analysis, the two complement. Comparing the two following differen

41、t:</p><p>　　(1) transform is the essence of the finite energy signal decomposition to orthogonal base space up; and the wavelet transform is the essence of the limited energy of the signal is decomposed by w

42、avelet function of space. Both the discrete form can realize orthogonal transformation, to meet the time frequency energy conservation law.</p><p>　　(2) transform used in the basic function only, or, with th

43、e only; wavelet analysis using wavelet function is not the only, the same engineering problems by using different wavelet function analysis the results are sometimes differ very far. The selection of wavelet function is

44、the application of wavelet analysis to the practical problem of a difficulty in wavelet analysis is a hot issue for the study, it is often through experience or continuous experiments, different analysis results were ana

45、ly</p><p>　　(3) in the frequency domain, transform has good localization ability, especially for those frequency components compared to simple deterministic signal, FFT is easy to signal into various frequen

46、cy components of the superposition and form, but in the time domain, Fourier-transform no localization ability, i.e. not from the signal FFT to see at any point in time the nearby state. Therefore, wavelet transform in t

47、he transient signal analysis with greater advantage.</p><p>　　(4) in wavelet analysis, scale larger values of equivalent transform of value is small.</p><p>　　(5) in the short-time Fourier trans

48、form, transform coefficient depends mainly on the signal in the time window inside the case, once the time window function is determined, the resolution can be defined. In wavelet transform, transform coefficients are de

49、pendent on the signal in the time window inside the case, but the time width with scale changes, so the wavelet transform has the time local analysis ability. Therefore, the wavelet transform can also be regarded as loca

50、l signal singularity anal</p><p>　　(6) if the signal through the filter, wavelet transform and short time Fourier transform is different: the STFT, band-pass filter bandwidth and center frequency independent

51、; on the contrary, wavelet band-pass filter bandwidth is proportional to the center frequency.</p><p>　　(7) from the frame angle for FFT is a non-redundant orthogonal compact frame, and the wavelet transform

52、 can realize the redundant non orthogonal non tight frame.In wavelet transform in image processing is a new method of image feature analysis, especially in the details of the image processing and image feature analysis h

53、as a good effect. It has the characteristics of multi-resolution analysis, and in both time domain and frequency domain ability of characterizing local features, is a window siz</p><p>　　Three, task design&l

54、t;/p><p>　　In 1, the basic knowledge of wavelet transform</p><p>　　n mathematics, the definition of the given function localization of wavelet function. Wavelets can be defined by a finite interval

55、 function in structure, become the mother wavelet and wavelet. A set of wavelet basis function { }, by zooming and panning the basic wavelet generating, =.</p><p>　　Where a is a scaling parameter, responses

56、to specific basis function width; B for translational parameters, designated along the X axis of the translational position.Wavelet transform is a kind of signal time -- scale analysis method, it has the characteristics

57、of multi-resolution analysis in time and frequency domain, and two have ability of characterizing local features, is a kind of window size fixed but its shape is variable, the time window and frequency windows are variab

58、le time-frequency </p><p>　　Conclusion</p><p>　　Image compression for image transmission and storage, this paper still image fusion method based on wavelet fusion, analyzes technical development

59、 and the Swiss generation process, algorithm uses a simpler set partitioning and sequencing strategy, improve the coding speed, reduce the memory consumption, improve the quality of image restoration. And the analysis of

60、 2D image wavelet reconstruction, targeted not clear picture of rationalization of the fusion.</p><p>　　小波變換在圖像處理中的仿真及應(yīng)用</p><p><b>　　課題意義</b></p><p>　　在傳統(tǒng)的傅立葉分析中, 信號(hào)完全是在

61、頻域展開(kāi)的, 不包含任何時(shí)頻的信息, 這對(duì)于某些應(yīng)用來(lái)說(shuō)是很恰當(dāng)?shù)? 因?yàn)樾盘?hào)的頻率的信息對(duì)其是非常重要的。但其丟棄的時(shí)域信息可能對(duì)某些應(yīng)用同樣非常重要, 所以人們對(duì)傅立葉分析進(jìn)行了推廣, 提出了很多能表征時(shí)域和頻域信息的信號(hào)分析方法, 如短時(shí)傅立葉變換, Gabor 變換, 時(shí)頻分析, 小波變換等。而小波分析則克服了短時(shí)傅立葉變換在單分辨率上的缺陷, 具有多分辨率分析的特點(diǎn), 使其在圖像處理中得到了廣泛應(yīng)用。</p>&

62、lt;p>　　傳統(tǒng)的信號(hào)理論，是建立在Fourier分析基礎(chǔ)上的，而Fourier變換作為一種全局性的變化，其有一定的局限性。在實(shí)際應(yīng)用中人們開(kāi)始對(duì)Fourier變換進(jìn)行各種改進(jìn)，小波分析由此產(chǎn)生了。小波分析是一種新興的數(shù)學(xué)分支，它是泛函數(shù)、Fourier分析、調(diào)和分析、數(shù)值分析的最完美的結(jié)晶；在應(yīng)用領(lǐng)域，特別是在信號(hào)處理、圖像處理、語(yǔ)音處理以及眾多非線(xiàn)性科學(xué)領(lǐng)域，它被認(rèn)為是繼Fourier分析之后的又一有效的時(shí)頻分析方法。 小波

63、變換與Fourier變換相比，是一個(gè)時(shí)間和頻域的局域變換因而能有效地從信號(hào)中提取信息，通過(guò)伸縮和平移等運(yùn)算功能對(duì)函數(shù)或信號(hào)進(jìn)行多尺度細(xì)化分析（Multiscale Analysis），解決了Fourier變換不能解決的許多困難問(wèn)題。</p><p>　　小波變換是一種快速發(fā)展和比較流行的信號(hào)分析方法, 其在圖像處理中有非常重要的應(yīng)用, 包括圖像壓縮, 圖像去噪, 圖像融合, 圖像分解, 圖像增強(qiáng)等。小波分析是傅立

64、葉分析思想方法的發(fā)展與延拓。除了連續(xù)小波(CWT)、離散小波(DWT), 還有小波包(Wavelet Packet)和多維小波。</p><p>　　小波分析在圖像處理中有非常重要的應(yīng)用, 包括圖像壓縮, 圖像去噪, 圖像融合, 圖像分解, 圖像增強(qiáng)等。小波變換是一種新的變換分析方法，它繼承和發(fā)展了短時(shí)傅立葉變換局部化的思想，同時(shí)又克服了窗口大小不隨頻率變化等缺點(diǎn)，能夠提供一個(gè)隨頻率改變的時(shí)間一頻率窗口，是進(jìn)行信

65、號(hào)時(shí)頻分析和處理的理想工具。它的主要特點(diǎn)是通過(guò)變換能夠充分突出問(wèn)題某些方面的特征，因此，小波變換在許多領(lǐng)域都得到了成功的應(yīng)用，特別是小波變換的離散數(shù)字算法已被廣泛用于許多問(wèn)題的變換研究中。從此，小波變換越來(lái)越引進(jìn)人們的重視，其應(yīng)用領(lǐng)域來(lái)越來(lái)越廣泛。</p><p><b>　　課題綜述</b></p><p>　　（一）小波分析的應(yīng)用與發(fā)展</p>&l

66、t;p>　　小波分析的應(yīng)用是與小波分析的理論研究緊密地結(jié)合在一起的。現(xiàn)在，它已經(jīng)在科技信息產(chǎn)業(yè)領(lǐng)域取得了令人矚目的成就。電子信息技術(shù)是六大高新技術(shù)中重要的一個(gè)領(lǐng)域，它的重要方面是圖象和信號(hào)處理。現(xiàn)今，信號(hào)處理已經(jīng)成為當(dāng)代科學(xué)技術(shù)工作的重要部分，信號(hào)處理的目的就是：準(zhǔn)確的分析、診斷、編碼壓縮和量化、快速傳遞或存儲(chǔ)、精確地重構(gòu)(或恢復(fù))。從數(shù)學(xué)地角度來(lái)看，信號(hào)與圖象處理可以統(tǒng)一看作是信號(hào)處理(圖象可以看作是二維信號(hào))，在小波分析的許多

67、分析的許多應(yīng)用中，都可以歸結(jié)為信號(hào)處理問(wèn)題。現(xiàn)在，對(duì)于其性質(zhì)隨時(shí)間是穩(wěn)定不變的信號(hào)（平穩(wěn)隨機(jī)過(guò)程），處理的理想工具仍然是傅立葉分析。但是在實(shí)際應(yīng)用中的絕大多數(shù)信號(hào)是非穩(wěn)定的（非平穩(wěn)隨機(jī)過(guò)程），而特別適用于非穩(wěn)定信號(hào)的工具就是小波分析。</p><p>　　事實(shí)上小波分析的應(yīng)用領(lǐng)域十分廣泛，它包括：數(shù)學(xué)領(lǐng)域的許多學(xué)科；信號(hào)分析、圖象處理；量子力學(xué)、理論物理；軍事電子對(duì)抗與武器的智能化；計(jì)算機(jī)分類(lèi)與識(shí)別；音樂(lè)與語(yǔ)言的

68、人工合成；醫(yī)學(xué)成像與診斷；地震勘探數(shù)據(jù)處理；大型機(jī)械的故障診斷等方面；例如，在數(shù)學(xué)方面，它已用于數(shù)值分析、構(gòu)造快速數(shù)值方法、曲線(xiàn)曲面構(gòu)造、微分方程求解、控制論等。在信號(hào)分析方面的濾波、去噪聲、壓縮、傳遞等。在圖象處理方面的圖象壓縮、分類(lèi)、識(shí)別與診斷，去污等。在醫(yī)學(xué)成像方面的減少B超、CT、核磁共振成像的時(shí)間，提高分辨率等。 　　</p><p>　　（1）小波分析用于信號(hào)與圖象壓縮是小波分析應(yīng)用的一個(gè)重要方面。它

69、的特點(diǎn)是壓縮比高，壓縮速度快，壓縮后能保持信號(hào)與圖象的特征不變，且在傳遞中可以抗干擾?；谛〔ǚ治龅膲嚎s方法很多，比較成功的有小波包最好基方法，小波域紋理模型方法，小波變換零樹(shù)壓縮，小波變換向量壓縮等。 　　</p><p>　?。?）小波在信號(hào)分析中的應(yīng)用也十分廣泛。它可以用于邊界的處理與濾波、時(shí)頻分析、信噪分離與提取弱信號(hào)、求分形指數(shù)、信號(hào)的識(shí)別與診斷以及多尺度邊緣檢測(cè)等。 　　</p><

70、;p>　　總之，由于小波具有低墑性、多分辨率、去相關(guān)性、選基靈活性等特點(diǎn)，小波理論在去噪領(lǐng)域受到了許多學(xué)者的重視，并獲得了良好的效果。但如何采取一定的技術(shù)消除圖像噪聲的同時(shí)保留圖像細(xì)節(jié)仍是圖像預(yù)處理中的重要課題。目前，基于小波分析的圖像去噪技術(shù)已成為圖像去噪的一個(gè)重要方法。</p><p>　?。ǘ┰趫D像處理的方面，小波變換存在以下幾個(gè)優(yōu)點(diǎn)： 　　</p><p>　　（1）小波分

71、解可以覆蓋整個(gè)頻域(提供了一個(gè)數(shù)學(xué)上完備的描述) </p><p>　　（2）小波變換通過(guò)選取合適的濾波器，可以極大的減小或去除所提取得不同特征之間的相關(guān)性 　　</p><p>　?。?）小波變換具有“變焦”特性，在低頻段可用高頻率分辨率和低時(shí) 間分辨率(寬分析窗口)，在高頻段，可用低頻率分辨率和高時(shí)間分辨率(窄分析窗口) 　　</p><p>　?。?）小波變換

72、實(shí)現(xiàn)上有快速算法(Mallat小波分解算法)</p><p>　　小波分析已經(jīng)成為發(fā)展最快和最引人注目的學(xué)科之一，幾乎涉及或者應(yīng)用到信息領(lǐng)域的所有學(xué)科。</p><p><b>　　(三)方案論證</b></p><p>　　本文對(duì)基于小波變換的圖像去噪方法進(jìn)行了深入的研究分析,首先詳細(xì)介紹了幾種經(jīng)典的小波變換去噪方法。對(duì)于小波變換模極大值去

73、噪法,詳細(xì)介紹了其去噪原理和算法,分析了去噪過(guò)程中參數(shù)的選取問(wèn)題,并給出了一些選取依據(jù);詳細(xì)介紹了小波系數(shù)相關(guān)性去噪方法的原理和算法;對(duì)小波變換閾值去噪方法的原理和幾個(gè)關(guān)鍵問(wèn)題進(jìn)行了詳細(xì)討論。最后對(duì)這些方法進(jìn)行了分析比較,討論了它們各自的優(yōu)缺點(diǎn)和適用條件,并給出了仿真實(shí)驗(yàn)結(jié)果。</p><p>　　在眾多基于小波變換的圖像去噪方法中,運(yùn)用最多的是小波閾值萎縮去噪法。傳統(tǒng)的硬閾值函數(shù)和軟閾值函數(shù)去噪方法在實(shí)際中得到

74、了廣泛的應(yīng)用,而且取得了較好的效果。但是硬閾值函數(shù)的不連續(xù)性導(dǎo)致重構(gòu)信號(hào)容易出現(xiàn)偽吉布斯現(xiàn)象;而軟閾值函數(shù)雖然整體連續(xù)性好,但估計(jì)值與實(shí)際值之間總存在恒定的偏差,具有一定的局限性。鑒于此,本文提出了一種基于小波多分辨率分析和最小均方誤差準(zhǔn)則的自適應(yīng)閾值去噪算法。該方法利用小波閾值去噪基本原理,在基于最小均方誤差算法LMS和Stein無(wú)偏估計(jì)的前提下,引出了一個(gè)具有多階連續(xù)導(dǎo)數(shù)的閾值函數(shù),利用其對(duì)閾值進(jìn)行迭代運(yùn)算,得到最優(yōu)閾值,從而得到更

75、好的圖像去噪效果。最后,通過(guò)仿真實(shí)驗(yàn)結(jié)果可以看到,該方法去噪效果顯著,與硬閾值、軟閾值方法相比,信噪比提高較多,同時(shí)去噪后仍能較好地保留圖像細(xì)節(jié),是一種有效的圖像去噪方法。</p><p>　　小波基函數(shù)選擇可從以下3個(gè)方面考慮。</p><p>　?。?）復(fù)值與實(shí)值小波的選擇</p><p>　　復(fù)值小波作分析不僅可以得到幅度信息，也可以得到相位信息，所以復(fù)值小波

76、適合于分析計(jì)算信號(hào)的正常特性。而實(shí)值小波最好用來(lái)做峰值或者不連續(xù)性的檢測(cè)。</p><p>　?。?）連續(xù)小波的有效支撐區(qū)域的選擇</p><p>　　連續(xù)小波基函數(shù)都在有效支撐區(qū)域之外快速衰減。有效支撐區(qū)域越長(zhǎng)，頻率分辨率越好；有效支撐區(qū)域越短，時(shí)間分辨率越好。</p><p>　?。?）小波形狀的選擇</p><p>　　如果進(jìn)行時(shí)頻分析

77、，則要選擇光滑的連續(xù)小波，因?yàn)闀r(shí)域越光滑的基函數(shù)，在頻域的局部化特性越好。如果進(jìn)行信號(hào)檢測(cè)，則應(yīng)盡量選擇與信號(hào)波形相近似的小波。</p><p>　　小波變換與傅里葉變換的比較</p><p>　　小波分析是傅里葉分析思想方法的發(fā)展和延拓。自產(chǎn)生以來(lái)，就一直與傅里葉分析密切相關(guān)。它的存在性證明，小波基的構(gòu)造以及結(jié)果分析都依賴(lài)于傅里葉分析，二者是相輔相成的。兩者相比較主要有以下不同：<

78、/p><p>　?。?）傅里葉變換的實(shí)質(zhì)是把能量有限信號(hào)分解到以為正交基的空間上去；而小波變換的實(shí)質(zhì)是把能量有限的信號(hào)分解到由小波函數(shù)所構(gòu)成的空間上去。兩者的離散化形式都可以實(shí)現(xiàn)正交變換，都滿(mǎn)足時(shí)頻域的能量守恒定律。</p><p>　?。?）傅里葉變換用到的基本函數(shù)只有 ， 或，具有唯一性；小波分析用到的小波函數(shù)則不是唯一的，同一個(gè)工程問(wèn)題用不同的小波函數(shù)進(jìn)行分析時(shí)有時(shí)結(jié)果相差甚遠(yuǎn)。小波函數(shù)

79、的選用是小波分析應(yīng)用到實(shí)際中的一個(gè)難點(diǎn)問(wèn)題也是小波分析研究的一個(gè)熱點(diǎn)問(wèn)題，目前往往是通過(guò)經(jīng)驗(yàn)或不斷的實(shí)驗(yàn)，將不同的分析結(jié)果進(jìn)行對(duì)照分析來(lái)選擇小波函數(shù)。一個(gè)重要的經(jīng)驗(yàn)就是根據(jù)待分析信號(hào)和小波函數(shù)的相似性選取，而且此時(shí)要考慮小波的消失矩、正則性、支撐長(zhǎng)度等參數(shù)。</p><p>　?。?）在頻域中，傅里葉變換具有較好的局部化能力，特別是對(duì)于那些頻率成分比較簡(jiǎn)單的確定性信號(hào)，傅里葉變換很容易把信號(hào)表示成各頻率成分的疊加

80、和的形式，但在時(shí)域中，傅里葉變換沒(méi)有局部化能力，即無(wú)法從信號(hào)的傅里葉變換中看出的在任一時(shí)間點(diǎn)附近的性態(tài)。因此，小波變換在對(duì)瞬態(tài)信號(hào)分析中擁有更大的優(yōu)勢(shì)。</p><p>　?。?）在小波分析中，尺度的值越大相當(dāng)于傅里葉變換中的值越小。</p><p>　?。?）在短時(shí)傅里葉變換中，變換系數(shù)主要依賴(lài)于信號(hào)在時(shí)間窗內(nèi)的情況，一旦時(shí)間窗函數(shù)確定，則分辨率也就確定了。而在小波變換中，變換系數(shù)雖然也

81、是依賴(lài)于信號(hào)在時(shí)間窗內(nèi)的情況，但時(shí)間寬度是隨尺度的變化而變化的，所以小波變換具有時(shí)間局部分析的能力。因此，小波變換也可以看成是信號(hào)局部奇異性分析的有效工具。</p><p>　?。?）若用信號(hào)通過(guò)濾波器來(lái)解釋?zhuān)〔ㄗ儞Q與短時(shí)傅里葉變換不同之處在于：對(duì)短時(shí)傅里葉變換來(lái)說(shuō)，帶通濾波器的帶寬與中心頻率無(wú)關(guān)。</p><p>　　從框架角度來(lái)說(shuō)傅里葉變換是一種非冗余的正交緊框架，而小波變換卻可以實(shí)

82、現(xiàn)冗余的非正交非緊框架。 </p><p>　　總之小波變換是圖像處理中圖像特征分析的新方法，特別是在圖像細(xì)節(jié)的處理及圖像特征分析上具有良好的效果。它具有多分辨率分析的特點(diǎn)，且在時(shí)域和頻域都具有表征信號(hào)局部特征的能力，是一種窗口大小固定不變但形狀可變，時(shí)間窗和頻率窗都可變的時(shí)域局部化分析方法。即在低頻部分具有較高的頻率分辨率和較低的時(shí)間分辨率，在高頻部分具有較高的時(shí)間分辨率和較低的頻率分辨率。對(duì)于大部分信息集中在

83、低頻的圖像信號(hào)的分析而言，它具有明顯的優(yōu)勢(shì)。因此，小波分析其中一個(gè)巨大優(yōu)勢(shì)就是能體現(xiàn)信號(hào)的時(shí)域的局部性質(zhì)。</p><p><b>　　課題設(shè)計(jì)</b></p><p>　　1、小波變換基本知識(shí)</p><p>　　在數(shù)學(xué)上，小波定義為對(duì)給定函數(shù)局部化的函數(shù)。小波可由一個(gè)定義在有限區(qū)間的函數(shù)來(lái)構(gòu)造，成為母小波或基本小波。一組小波基函數(shù){}，可通

84、過(guò)縮放和平移基本小波來(lái)生成，=。</p><p>　　其中a為縮放參數(shù)，反應(yīng)特定基函數(shù)的寬度；b為平移參數(shù)，指定沿x軸平移的位置。</p><p>　　小波變換是一種信號(hào)的時(shí)間———尺度分析方法,它具有多分辨率分析的特點(diǎn),而且在時(shí)頻兩域都具有表征信號(hào)局部特征的能力,是一種窗口大小固定不變但其形狀可變,時(shí)間窗和頻率窗都可變的時(shí)頻局部化分析方法。即在低頻部分具有較高的頻率分辨率和時(shí)間分辨率,在

85、高頻部分具有較高的時(shí)間分辨率和較低的頻率分辨率,很適合探測(cè)正常信號(hào)中夾帶的瞬態(tài)反?，F(xiàn)象并展示其成分,因此被譽(yù)為分析信號(hào)的顯微鏡。小波分析是把信號(hào)分解成低頻a1 和高頻d1兩部分,在分解中,低頻a1 中失去的信息由高頻d1 捕獲。在下一層的分解中, 又將a1 分解成低頻a2 和高頻d2 兩部分,低頻a2 中失去的信息由高頻d2 捕獲,如此類(lèi)推下去,可以進(jìn)行更深層次的分解。二維小波函數(shù)是通過(guò)一維小波函數(shù)經(jīng)過(guò)張量積變換得到的,二維小波函數(shù)分解

86、是把尺度j 的低頻部分分解成四部分:尺度j + 1 的低頻部分和三個(gè)方向(水平、垂直、斜線(xiàn)) 的高頻部分。設(shè)輸入圖像為PA , Hx ( Z) , Gx ( Z) , Hy ( Z) , Gy ( Z) 分別為行方向和列方向的高通濾波器和低通濾波器。</p><p><b>　　結(jié)論</b></p><p>　　圖像的壓縮有利于圖像的傳輸和儲(chǔ)存，本文對(duì)靜止圖像的融合方