Pixel bit-depth increase by bit replication

In many applications, such as inverse dithering, it is necessary to increase the pixel bit-depth of images by expanding q -bit integer values to m -bit integer values ( q m > ). This paper describes a simple and efficient method that uses bit replication, instead of conventional multiplication, to achieve this expansion. First, we show that the optimal number of repetitions is given by } / { ceiling q m and that the method is equivalent to multiplication by the ideal gain when q m / is an integer. We then demonstrate that, in the case where q m / is not an integer, truncating the fraction bits to the right of the decimal point will lead to zero average error. The paper also includes two suggestions for implementing the bit-replication process, both of which have a vast complexity advantage over a multiplier. Two examples are given at the end to illustrate the bit-replication process in action.