A barcode recovery system, including: an image processor configured to determine a binary vector corresponding to a blurry barcode image by: maximizing an objective function that models the system using splines. Optimizing the objective function may be efficiently accomplished by constraining a search on each bit in the barcode image to a nearby range of influence of other bits in the barcode image. Further efficiency may be gained by enumerating the local groups of bits in graycode order and by adding or subtracting values from a precomputed inner product matrix to state variables to compute the complete objective function.