應用高階統計量之反濾波器於影像模型之建立及影像之復原

Abstract

本篇論文提出了一個應用高階統計量之反濾波器於影像模型之建立及影像 之復原的方法。假設一張原始影像x(m,n)通過一反濾波器v(m,n)，其輸出 為e(m,n)藉由調整反濾波器v(m,n)的係數使得J_{r,k}=|C_k|^r/|C_r|^k 為最大，我們可得到最佳的二維反濾波器 ▊(m,n)，其中r必須是偶數、 且k>r.gdsim.2､而C_k (C_r)表示輸出信號e(m,n)的k (r)階統計量 (cumulant)。因此e(m,n)信號通過一個線性非時變系統(linear time- invariant system) h(m,n)可被視為是原始影像x(m,n)的影像模型，其 中 h(m,n)是v(m,n)的穩定反濾波器(stable inverse filter)。 當影像 模型 h(m,n)已知而原始影像x(m,n)被一未知線性非時變系統g(m,n)糢糊 化了；我們可藉由前面所提到得基於高階統計量之反濾波器演算法則由糢 糊的影像中估計得e(m,n)並求得還原影像▊(m,n)=e(m,n)*h(m,n)， 其中 h(m,n)的振幅響應(the amplitude response)可以由其它內容相似又未被 破壞的影像求得，並假設它的相位響應(the phase response)為零。最後 ，提出一些實驗結果來證實我們所提出的影像模型和影像復原方法。 This thesis presents image modeling and restoration by using higher-order statistics based 2-D inverse filters. A given original image x(m,n) is processed by an optimum inverse filter v(m,n) which is designed by maximizing cumulant based criteria J_{r,k} = |C_k|^r/|C_r|^k where r is even, k>r. gdsim.2 and C_k (C_r) denotes kth-order ( rth-order ) cumulant of the output e(m,n) of the 2-D inverse filter. The original image x(m,n) can be modeled as the output of a linear shift-invariant (LSI) system h(m,n) driven by e(m,n) where h(m, n) is the stable inverse filter of v(m,n). When the image model h(m,n) is known but the original image x(m,n) is blurred by an unknown LSI system g(m,n), one can estimate e(m,n) from the blurred image using the cumulant based 2-D inverse filter criteria and then obtain the restored image ▊(m,n)=e(m, n)*h(m,n) where the amplitude response of h(m,n) can be estimated from an undegraded image which has similar contents with the original image and its phase can be chosen as zeros. Some experimental results are provided to support the proposed image modeling and restoration method.