Image processing algorithms employing two-dimensional Karhunen-Loeve Transform

Abstract

In the fields of image processing and pattern recognition there is an important problem of acquiring, gathering, storing and processing large volumes of data. The most frequently used solution making these data reduced is a compression, which in many cases leads also to the speeding-up further computations. One of the most frequently employed approaches is an image handling by means of Principal Component Analysis and Karhunen-Loeve Transform, which are well known statistical tools used in many areas of applied science. Their main property is the possibility of reducing the volume of data required for its optimal representation while preserving its specific characteristics.The paper presents selected image processing algorithms such as compression, scrambling (coding) and information embedding (steganography) and their realizations employing the twodimensional Karhunen-Loeve Transform (2DKLT), which is superior to the standard, onedimensional KLT since it represents images respecting their spatial properties. The principles of KLT and 2DKLT as well as sample implementations and experiments performed on the standard benchmark datasets are presented. The results show that the 2DKLT employed in the above applications gives obvious advantages in comparison to certain standard algorithms, such as DCT, FFT and wavelets.