一個新式多重卡曼濾波器在影像還原上的應用

Abstract

影像還原的目的在於消除影像在錄製及傳輸上遭到破壞的影響。二維卡曼 濾波器(Kalman Filter)在影像還原的處理上較其他方法有著更多的優點 。目前已有數種型式的卡曼濾波器依效率或效果的考量被提出來；其中多 重卡曼濾波器不僅在客觀標準上有較好的結果，同時也能達到較佳的主觀 視覺品質。它採用了多個不同的影像模式，可依據影像上區域的結構作適 度的調整，因而能保留影像上邊緣部份。在本論文中，我們運用空間適應 的概念對多重卡曼濾波器加以延伸，這個新的方法可稱為空間適應型的多 種卡曼濾波器。依循這個方向，我們發展了一個新的演算法：將多重卡曼 濾波器中的非邊緣平滑模式依據影像上區域統計特性加以調適，並依此修 改影像狀態變換及卡曼濾波器的算式。同時為了減低計算複雜度，我們也 發展了兩種較快速的演算法。透過實驗證實，我們所提出的這三個演算法 不論在主觀的影像品質或客觀的訊號誤差比(SNR)上，都能達到較佳的結 果。 Image restoration is a problem on removing the effect of imperfect recording of images. Two-dimensional Kalman filtering for the image restoration has some advantages with compared to other stochastic filtering techniques. There have been several two dimensional Kalman filtering algorithms proposed for efficiency and performance consideration. The multiple model Kalman filter is the one that achieves not only good subjective but also good objective results. It utilizes the multiple image models which adapt to the local structure of images and then preserves the edge areas. In this thesis, we try to extend the multiple model Kalman filter using the concept of spatial adaptive filtering. The new approach is named spatial adaptive multiple model Kalman filter. Following the approach, a new algorithm is presented to extend the nonedge flat image model for adaptation to the local statistics of images. This new algorithm modifies the state dynamic equation of Kalman filtering. The corresponding Kalman filter equations are derived based on the modified state dynamic equation. Furthermore, to reduce the computation complexity, two fast algorithms for spatial adaptive multiple model Kalman filter are proposed. Experiments have shown the three algorithms have better objective visual quality and better subjective SNR improvement than other algorithms.