Evolution of the Discrete Cosine Transform Using Genetic Programming

Compression of 2 dimensional data is important for the efficient transmission, storage and manipulation of Images. The most common technique used for lossy image compression relies on fast application of the Discrete Cosine Transform (DCT). The cosine transform has been heavily researched and many efficient methods have been determined and successfully applied in practice; this paper presents a novel method for evolving a DCT algorithm using genetic programming. We show that it is possible to evolve a very close approximation to a 4 point transform. In theory, an 8 point transform could also be evolved using the same technique. A Brief Overview of the DCT The cosine transform translates a set of data points from the spatial domain to the frequency domain using Cosine basis functions[6]. The DCT has found a wide range of application in signal processing, data compression, telecommunication, image processing, feature extraction and filtering. The DCT is a very important translation method in multimedia application. This is because the DCT as an approximation to the Karhunen-Loéve transform for first-order Markov stationary random data. DCT algorithms can be classified into three categories based on their approach. a) indirect computation, b) direct factorization, c) recursive computation. [11]. A two-dimensional DCT can be obtained by first applying a 1-D DCT over the rows followed by a 1-D DCT to the columns of the input data matrix. A great detail research of DCT is introduced in [17]. The expression of a 2-D DCT is based on the following: T i j c i j S m n m i N n j N n N