現今，航空和光學衛星影像等等的遙感探測影像是人類生活當中不可或缺的一部份，光學衛星影像可以幫助不同的應用，像是製圖學、遙感探測和空間與時間資料的分析，因此藉由轉換影像特徵線的梯度剖面以及利用超解析度或放大影像尺度的方法提升衛星影像品質，能夠幫助其相關的應用。本論文提出改善光學衛星影像調製傳遞函數的方案，結合了梯度轉換和快速反卷積運算的優點。所提出方法之輸入是使用雙三次插值的上採樣影像，然後將較低解析度影像梯度轉換成較高解析度影像梯度。像素銳利度描述高解析度與低解析梯度之間的關係且決定影像調製傳遞函數（MTF）的性質，根據局部影像可自適應地估計銳利度，與相關文獻不同，銳利度估計中使用的局部影像大小是可調式的。之後藉由帕松重建法影像會被重建回像素強度場，此外，在影像重建的過程當中，像素位移的問題可以借助侵蝕濾波器解決。一般而言，超解析度方法是最小化能量函數與影像梯度及強度場有關的約制條件，相關文獻利用梯度下降法解決超解析度模型的最佳化問題，本論文是根據(Lin et al., 2011)所提出的方法，通過使用快速反捲積的方法來產生超解度影像，從而避免迭代和梯度下降的龐大計算時間。此研究所提出的方案可改善光學衛星影像的調製傳遞函數和空間解析度，再者，此方案能有效率的原因是基於局部銳利度估計和反卷積中使用快速傅立葉轉換。增強影像成果有較清晰的結構線和邊界。原始影像的SSIM等於0.75837，而通過結合梯度剖面和超解析度方法，增強衛星影像有最佳的SSIM值，其為0.84640如第四章所示。

Nowadays remote-sensing images, including aerial and optical satellite images, play an essential role in the life of human beings. The optical satellite images bring many benefits to cartographic drawing, remote sensing, and spatial temporal data analysis. Therefore, the improvement of satellite image quality by transforming gradient profiles of image structure lines and utilizing super-resolution or rescaling techniques is helpful to related applications. In this paper, an improved modulation transfer function (MTF) scheme for optical satellite images is proposed, which combines the advantages of gradient field transformation and super-resolution using fast deconvolution. The input to the proposed method is an image up-sampled by using bicubic interpolation, and then a lower-resolution gradient field is transferred into a higher-resolution gradient field. The relation between these two gradient fields is described by pixel sharpness which dominates the descriptions of modulation transfer functions (MTFs) of images. The sharpness can be adaptively estimated depending only on a local patch. Different from related studies, the size of local patches used in sharpness estimation is tunable. After that, the images are reconstructed back to intensity field using Poisson reconstruction. In addition, pixel shifting problem is solved with the aid of erosion filter, which is involved in the reconstruction process. Generally, super-resolution methods minimize an energy function with the constraints relating to gradient field and intensity field of an image. Related studies used gradient decent to solve the optimization in the super-resolution model. Following by (Lin et al., 2011), in the proposed method, super-resolution images are generated by using fast-deconvolution-based method to avoid time-consuming iterations and gradient decent calculations. The proposed scheme can improve modulation transfer function (MTF) and spatial resolution of optical satellite images. In addition, the proposed scheme is efficient because of local sharpness estimation and the usage of fast Fourier transform in deconvolution. The result of enhanced image has clearer structure lines and edges. The SSIM of Original image is equal to 0.75837. By combing gradient profile and super-resolution method, the enhanced satellite image will have the best SSIM value that is equal to 0.84640, which is shown in the chapter 4.

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