Images can be encoded much more efficiently than by pixel arrays if local regions are represented as combinations of elementary functions. Computing the coefficients on those elementary functions such that their linear combination becomes equivalent to, or closely approximates, the original image is the same operation as computing a transform. Each local image region is multiplied by each of several such elementary functions and integrated to obtain each such coefficient. The resulting coefficients usually have lower entropy than the original pixel distribution, enabling more compact coding; in addition, their values can be coarsely quantized without detrimental effect. An image is recovered from the coded coefficients by essentially an inverse transform. The most ubiquitous image compression protocol is JPEG, defined by ISO Standard 10918. It applies the Discrete Cosine Transform (DCT) to local square tiles of an image (typically 8 × 8 pixels), but the abrupt truncation of each cosine wave causes “block quantization” artifacts which become noticeable when only subsets of cosine waves are used in order to achieve compression ratios above about 30:1. JPEG2000 overcomes this problem by replacing the block DCT cosine waves with Daubechies wavelets which are smoothly attenuated instead of chopped; the resulting Discrete Wavelet Transform (DWT) is the core of JPEG2000 ISO Standard 15444. JPEG2000 also has other advanced features to allocate the coding budget inhomogeneously across an image if needed. Both protocols allow control over the compression factor (CF for JPEG2000; quality factor QF for JPEG). Despite its superior mathematical basis and performance, JPEG2000 is not as widely used as JPEG nor as freely available.

 Iris Recognition Performance Under Extreme Image Compression