1. An image processing device which uses a representative picture having a first resolution and a plurality of reference pictures having the first resolution that are related to the representative picture to generate a target high-resolution picture having a second resolution higher than the first resolution, said image processing device comprising: a first repetition processing unit that performs positioning processing for a reference picture from among the plurality of reference pictures, said first repetition processing unit repeatedly performing the positioning processing while switching from one reference picture to another reference picture; a first determination unit that determines whether or not the positioning processing has been performed for all of the plurality of reference pictures; and a second repetition processing unit that repeats update processing for updating a value of a pixel in the target high-resolution picture after completion of the positioning processing performed by said first repetition processing unit; wherein, in the positioning processing, an amount of displacement of the reference picture from the representative picture is estimated, and based on the estimated amount of displacement, a pixel of the reference picture is positioned at a sub-pixel position in a high-resolution picture produced by enlarging the representative picture, wherein, in the update processing, the estimated value of the pixel in the target high-resolution picture is updated so that a value of an evaluation function is decreased, the evaluation function including, as a variable, a difference between a value of a pixel in the reference pictures after the positioning processing and the estimated value of the pixel in the target high-resolution picture, and wherein at least one of said first and second repetition processing units includes: a second determination unit that determines whether a pixel satisfies a completion condition from a result of one of the positioning processing and the update processing; and an exclusion unit that excludes the pixel that is determined to satisfy the completion condition from one of the positioning processing and the update processing.