In this section we describe the building blocks of the image compression system. To solve the problem of adaptively compressing the image, we develop an optimization procedure that involves basis selection, quantization and lossless encoding. As illustrated in Figure 1, the image compression system consists of three stages: (1) transform or filter bank, (2) quantization or lossy compression, and (3) lossless compression. The goal of the transform/filter bank stage is to re-organize the data such that the latter stages produce good compression. A non-adaptive image compression system fixes the first stage such that its processing is not signal dependent, and thus the compression performance is tuned only by the last two stages. For example, the JPEG image compression algorithm adjusts the quantization and run-encoding of the transform data to meet the compression criteria.
Figure 1: Image compression system: stage 1 - image joint expansion and segmentation; stage 2 - selection of quantizers 
, and quantization of signal expansion coefficients; stage 3 - lossless encoding using run length encoding (rle) and entropy encoding.