Acquired　digital　images　are　often　corrupted　by　a　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　method　is　effective　for　multifocus,　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.　(C)　The　Authors.　Published　by　SPIE　under　a　Creative　Commons　Attribution　3.0　Unported　License.　Distribution　or　reproduction　of　this　work　in　whole　or　in　part　requires　full　attribution　of　the　original　publication,　including　its　DOI.