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研究生：	許俊宏 Xu, Jun-Hong
論文名稱：	一小波式邊緣保留由單張影像重建超解析度影像的方法 A Wavelet-Based Edge-Preserving Method for Superresolution Reconstruction from a Single Image
指導教授：	陳進興 Chen, Chin-Hsing
學位類別：	碩士 Master
系所名稱：	電機資訊學院 - 電機工程學系 Department of Electrical Engineering
論文出版年：	2004
畢業學年度：	92
語文別：	英文
論文頁數：	78
中文關鍵詞：	內插法、小波轉換、貝氏最大事後機率估測、重建超解析度影像
外文關鍵詞：	Interpolation, Bayesian MAP Estimation, Wavelet Transform, Superresolution Reconstruction
相關次數：	點閱：104 下載：2
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　　數位影像應用極需要高解析度影像，因其能提供較多關鍵性的細節;因此如何產生一張高解析度影像成了一個重要的研究問題。感應器(sensor)製造與數位訊號處理為兩種解決問題的途徑，本論文的方法屬於後者。一張影像的解析度越高，輪廓越明顯，也就越能解釋此張影像;同樣的若影像的解析度越低，影像就會越模糊。影像的模糊現象。主要是由於失去了邊緣的資訊;因此若能正確的估出失去的邊緣資訊，就可還原其高解析度的面貌。使用訊號處理技術估測邊緣資訊，以增加原來影像的解析度，便是本論文所研究的超解析度影像重建問題。

　　本論文以單張低解析度影像重建其高解析度影像，探討的問題包括無雜訊與有雜訊兩種情形。本論文的方法將貝氏最大事後機率估測技術應用於此兩種情形，使問題變成泛函的最佳化。本論文提出利用小波轉換取代傳統高通濾波器來偵測影像的邊緣資訊，使得求解過程更能準確的保留所需要的邊緣，因此可以得到更清晰的高解析度影像。

　　實驗証明本論文所提方法產生的影像，不管是在視覺上或數值上都比零次，雙線性，和三次內插法所得的影像要好。實驗並証明提出的方法確實會比使用傳統高通濾波器於貝氏最大事後機率估測所得到的結果要好。在的情形下，論文所提出的方法，比零次內插法改善2.6dB，比雙線性內插法改善2dB，比三次內插法改善1.9db，和比使用傳統高通濾波器於貝氏最大事後機率估測的方法改善1.4dB。在的情形下，論文所提出的方法，比零次內插改善2.6dB，比雙線性內插法改善1.6dB，比三次內插法改善1.5dB，和比使用傳統高通濾波器於貝氏最大事後機率估測的方法改善0.9dB。

　　In the applications of digital images, high-resolution images are important due to the detail information they provided. Therefore, how to obtain high-resolution images has become an important issue. Manufacture of high quality sensors and digital signal processing are two solutions to the issue, this thesis deals with the latter. The higher the resolution of an image is, the more obvious the image’s contour will be, and it can be interpreted more accurately. Similarly, if an image’s resolution is low, it blurs and loses its edge information. So, if we can estimate the lost edges precisely, the high- resolution content of the blurred image will be reconstructed. How to estimate edges accurately and use them to improve the resolution of the original image, called super-resolution reconstruction, is the subject studied in this thesis.

　　The method adopted by this thesis treats estimating a high-resolution image from a low-resolution one as an ill-posed inverse problem. The inverse problems for noiseless and noisy cases were both investigated. The Bayesian MAP estimation technique was applied to both cases to cast superresolution reconstruction problems into functional optimization ones. Our proposed method uses the wavelet modulus to replace the conventional high-pass filter in the detection of the given image’s edges. This change makes the Huber function preserve edges more precisely in the estimation process, and therefore obtain a more clear high-resolution image.

　　The images reconstructed from the proposed method were shown better than the images produced by zero-order, bilinear, and cubic-B-spline interpolation in both visual and quantitative comparisons. It was also proved that the proposed method gives better result than the Bayesian MAP estimation with conventional high-pass filters. In the case of the proposed method improves over the zero-order interpolation by 2.6dB, over the bilinear interpolation by 2dB, over the cubic-B-spline interpolation by 1.9dB, and over the Bayesian MAP estimation with conventional high-pass filters by 1.4dB. In the case of the proposed method improves over the zero-order interpolation by 2.6dB, over the bilinear interpolation by 1.6dB, over the cubic-B-spline interpolation by 1.5dB, and over the Bayesian MAP estimation with conventional high-pass filters by 0.9dB.

Abstract.........................................................I
	Contents.........................................................III
	Figure Captions..................................................VI
	Table Captions...................................................X

Chapter 1 Introduction...................................................1
        1.1 Motivation...................................................1
        1.2 Related Problems.............................................2
        1.3 Recent Works.................................................2
        1.4 Thesis Organization..........................................4

Chapter 2 Markov and Gibbs Random fields.................................6 
        2.1 Definitions of Lattice.......................................6
        2.2 Markov Random Fields.........................................8
        2.3 Gibbs Random Fields..........................................9
        2.4 Equivalence of MRF and GRF...................................10

Chapter 3 Observation Model of Super Resolution..........................12
        3.1 Modeling the Problem.........................................12
        3.2 Stochastic Approach..........................................16
        3.3 Desirable A Priori Model.....................................20
          3.3.1 Influence of A Priori Model..............................20
          3.3.2 Convex Function Analysis.................................21
          3.3.3 Edge-Preserving Model....................................23
          3.3.4 Robust Statistic Huber Model.............................25
        3.4 Disadvantages of Edges Detector..............................26

Chapter 4 Comparison of Wavelet and Edges Detection 
          Techniques.....................................................29
        4.1 High-Pass Filter.............................................29
          4.1.1 Laplacian Operator.......................................29
          4.1.2 Gradient Operator........................................31
        4.2 Wavelet Transform Analysis...................................32
          4.2.1 1-D Wavelet Transform....................................32
          4.2.2 2-D Wavelet Transform....................................34
          4.2.3 Wavelet Modulus..........................................36
        4.3 Experiments with Wavelet and High-Pass Filter................37
        4.4 Conclusions of the Wavelet Modulus in Edge Detection.........40

Chapter 5 Implementation of the Wavelet-Based Edge-Preserving 
          Method for MAP Superresolution Reconstruction..................41
        5.1 Noiseless Case...............................................41
          5.1.1 Modeling the Constrained Functional......................41
          5.1.2 Gradient Projection Technique............................42
          5.1.3 Computational Aspects....................................46
        5.2 Noisy Case...................................................51
          5.2.1 Modeling the Unconstrained Functional....................51
          5.2.2 Choice of the Smoothing Parameter........................51
          5.2.3 Computational Aspects....................................52

Chapter 6 Experimental Results and Conclusions...........................55
        6.1 Experimental Results for Noiseless Cases.....................55   
          6.1.1 The Example of p=2.......................................57
          6.1.2 The Example of p=4.......................................64
          6.1.3 Discussions..............................................70
        6.2 Experimental Results for Noisy Cases.........................71
          6.2.1 The Example of p=4.......................................71
          6.2.2 Discussions..............................................74
        6.3 Conclusions..................................................74
References...............................................................76
 
                                    

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校內：2005-07-26公開
校外：2005-07-26公開

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