In recent years , nonlinear methods have attracted more and more attention and there have been some successful cases , such as median filter , mathematical morphology , etc . as a preferred way to inverstigate nonlinear numerical problems , the continued fractions method can effectively express the gradually changing data or abrupt data , so it is meaningful to study image processing by means of the continued fractions theory and algorithms 近年來(lái)在圖像處理領(lǐng)域,利用非線性方法進(jìn)行圖像處理取得較好效果的有中值濾波、數(shù)學(xué)形態(tài)學(xué)等,非線性方法已引起越來(lái)越多研究者的重視。作為研究非線性數(shù)值問題的首選方法?連分式方法,不僅能反映數(shù)據(jù)的漸變性,也能反映數(shù)據(jù)的突變性。鑒于這些原因,本文將連分式插值和逼近引入到數(shù)字圖像處理領(lǐng)域,開展了圖像插值、圖像重建等方面的研究。