After each dominant pass, a subordinate pass is then performed on the subordinate list which contains all pixel values previously found to be significant. The subordinate pass performs pixel value quantization which achieves compression by telling the decoder with a symbol roughly what the pixel value is instead of exactly what the pixel value is. Since the initial threshold is one-half the maximum magnitude of all pixel values for the first dominant pass, then in the first subordinate pass only two ranges are specified in which a significant pixel value could lie: the upper half of the range between the maximum pixel value and the initial threshold, or the lower half of the same range. A pixel value in the upper half of the range gets coded with the symbol upper (for upper part of the range), while a pixel value in the lower half gets coded with the symbol lower. A pixel value found to be in a particular range is quantized, from the decoders viewpoint, to the midpoint of that range. Upon subsequent subordinate passes the threshold has been cut in half and so there are twice as many ranges as the last subordinate pass plus two new ranges corresponding to the new lower threshold. By reading the subordinate symbol corresponding to a significant pixel and knowing the threshold, the decoder is able to determine the range in which the pixel lies and reconstructs the pixel value to the midpoint of that range. Thus from the decoders viewpoint the rough estimate of a significant pixel's value is getting more refined and accurate as more subordinate passes are made. So, the subordinate passes quantize pixel values to a two symbol alphabet which then get encoded by using an adaptive arithmetic coder as described by Witten, Neal, and Cleary, thus achieving compression.