Image and signal processing with discrete signal induced heap transform

Traditional transformations like Fourier, Sine and Cosine, Wavelet, Hartley, DCT, and many other transforms are extensively used in signal and image processing in order to mathematically manipulate the signals. Transformations change or modify the signals and images in order to achieve the enhancement of the quality of the signals or images under process. In this work, the mathematical concepts, calculation methods, and applications of the discrete signal induced heap transform (DsiHT), which is a novel and high performance type of transforms, are investigated. The discrete signal induced heap transform, is fast, simple to calculate mathematically, and can be applied to different kinds of 1-D and 2-D signals of any length, like audio signals and a large class of images e.g. grayscale and color, general, and medical images. In this thesis, it is successfully presented that, the discrete signal induced heap transform can be used for filtering the frequency components of the one dimensional signals like audio signals, and also two dimensional signals and images. In addition, it is shown that DsiHT can be used for noise detection in various types of the signals. Moreover, a novel method of discrete signal induced heap transform is proposed. In this method, the median of each row or column of the image is considered as the signal generator of the DsiHT, in order to enhance the quality of the image which is under process. Numerous experimental results of enhancement of the different types of grayscale and color images, support the performance of this method.