transformcoding

Transform coding is a technique used in data compression, particularly in image and audio compression. It involves applying a mathematical transformation to blocks of data, such as pixel values in an image. The goal of this transformation is to decorrelate the data, meaning to make the individual data points within the block more independent of each other. This decorrelation often results in a representation where most of the energy or important information is concentrated in a few coefficients, while many other coefficients become small or zero.

The most common transformation used in transform coding is the Discrete Cosine Transform (DCT), especially its variants like the Type-II DCT, often referred to simply as DCT. Other transformations like the Discrete Fourier Transform (DFT) or the Karhunen-Loève Transform (KLT) can also be used. After the transformation, these coefficients are typically quantized. Quantization is a lossy process that reduces the precision of the coefficients, effectively discarding less significant information. Coefficients with small magnitudes are quantized more coarsely (represented with fewer bits or even set to zero), while those with larger magnitudes are quantized more finely. This quantization step is crucial for achieving compression.

Following quantization, the transformed and quantized coefficients are then entropy coded, for example, using Huffman coding or arithmetic coding. Entropy coding exploits the statistical redundancies in the quantized coefficients to represent them more efficiently, further reducing the overall data size. When decompressing, the process is reversed: entropy decoding, dequantization, and then applying the inverse transform. This reconstructs an approximation of the original data. Transform coding is a fundamental component of many modern compression standards like JPEG for images and MPEG for video.