A　filtering　method　was　proposed　to　restore　image　corrupted　by　random　impulse　noise,　including　a　noise　detector　and　an　image　filter.　During　the　process　of　noise　detection,　a　noise　pixel　boundary　of　each　sub-window　is　detected　by　two-order　difference　of　pixels,　and　the　noise　boundary　of　the　whole　image　is　obtained　by　statistics　for　all　sub-window　noise　boundaries.　Moreover,　the　pixels　in　the　noise　boundary　are　rectified　by　the　number　of　congeneric　pixels　in　sub-window　to　reduce　the　fault　detection.　The　functional　filter　is　constructed　by　the　regular　function　of　the　image　and　the　constraints　of　noise　pixels　to　restore　noise　pixels.　This　method　is　evaluated　with　four　noise　models　and　the　simulation　results　show　that　this　method　can　obtain　the　lowest　ratio　of　miss　detection　and　fault　detection　in　the　noise　detection　with　comparisons　of　other　methods,　and　can　obtain　the　highest　peak　signal　to　noise　ratio　(PSNR)　and　performance　of　the　restoration　image　for　subjective　vision.