利用擾動的方法在基底轉換上影像還原問題的探討

Abstract

在影像處理的領域中,影像還原是一個很重要的課題.一般而言,在矩陣的 表示法裡,我們可以把這樣的問題視之為反矩陣的問題.本論文即根據此概 念提出一演算法來解決影像還原問題.在本論文中,我們對這個演算法定義 一平衡函數來決定我們所欲求得解的限制條件,同時,因為經過基底轉換後 的影像訊號有較佳的收斂解,於是我們利用擾動法找出在基底轉換後平衡 函數的最小值.本論文中,我們亦將此演算法與未經基底轉換時之解作一相 對的比較.最後,我們又提出一個後等化器將經過擾動法求得的解做等化的 動作,使還原的圖片更為清晰,而完成整個影像還原的步驟. In the area of image processing, there are several algorithms proposed to solve this image restoration problems.In this thesis, a robust approach restoring the blurred image is presented. The scheme is derived based on the perturbation methodwith the concept of basis expaansion to minimize a equilibrium function which is gotten from a regularization process.The relationship of the desired solution variables and original pixel domain image signal is clearly stated in teh discretization and the concept of signal representation bya set of the weighted basis. From the basis expaansion, we can transform the signaaal from the pixel domain intothe coefficient domain and reduce the effect of the error propagation during the updating process.Thus we can achieve the effect to increase the performance of the restored image both in the convergence rate and visual system.to enhance the performance of the restored image which is passing through the perturbation methos alogorithm, an equalizeris also proposed to enhance the contrast of the restored image.Thus, the restored imaage will be clearer than the image without image enhancement.