<title>Pixel bit-depth increase by bit replication</title>

Abstract

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 (m greater than q). 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 (m/q) and that the method is equivalent to multiplication by the ideal gain when m/q is an integer. We then demonstrate that, in the case where m/q 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.