Acquired　digital　images　are　often　corrupted　by　the　lack　of　camera　focus,　faulty　illumination,　or　missing　data.　An　algorithm　is　presented　for　fusion　of　multiple　corrupted　images　of　a　scene　using　the　lifting　wavelet　transform.　The　method　employs　adaptive　fusion　arithmetic　based　on　matrix　completion　and　self-adaptive　regional　variance　estimation.　Characteristics　of　the　wavelet　coefficients　are　used　to　adaptively　select　fusion　rules.　Robust　principal　component　analysis　is　applied　to　low-frequency　image　components,　and　regional　variance　estimation　is　applied　to　high-frequency　components.　Experiments　reveal　that　the　methods　are　effective　for　multi-focus,　visible-light,　and　infrared　image　fusion.　Compared　with　traditional　algorithms,　the　new　algorithm　not　only　increases　the　amount　of　preserved　information　and　clarity,　but　also　improves　robustness.