Laboratory 1 Discrete Cosine Transform and Karhunen-Loeve Transform

Block based transform coding is used to convert spatial pixel values to transform coefficients in the frequency domain. Since a linear transforms is employed in image and video compression, the energy in spatial domain is equal to the energy in the transform domain but the coefficients is compacted into the low frequency area. The convenience is that most of the energy is compacted in a few large transform coefficients. After the quantization, most of the coefficients will be zero and it can save a lot of bits to represent the original image. The reason of incorporated block transform for image compression can be simply concluded by two points: − Energy compaction: a few of basis functions are sufficient to represent a given image. − Decorrelation: coefficients in transform domain are decorrelated. Linear transform coding can be consider as using a set basis functions to represent a given image. In other words, a image X can be expand as a linear combination of some basis function si.