The Discrete Cosine Transform for Image Compression in the JPEG format

V diplomskem delu smo definirali diskretno kosinusno transformacijo in predstavili osnovno idejo njene izpeljave. Pokazali smo, kako se ta definicija razširi na dve dimenziji in da lahko dvodimenzionalno obliko izračunamo s pomočjo enodimenzionalne. Opisali smo primer algoritma za hiter izračun DCT s pomočjo že obstoječih algoritmov FFT. Podobno smo opisali primer algoritma za celoštevilski DCT, ki deluje na podlagi enostavnejše aritmetike. Poglobili smo se v najpogostejšo implementacijo JPEG-a. Opisali smo celoten postopek kodiranja originalne slike v bitni niz, ki se uporablja za shranjevanje in pošiljanje. Opisali smo potek obratnega procesa, to je dekodiranja. Nato smo na primeru dejanskega bloka ilustrirali oba procesa. Za konec smo nekaj dejanskih slik pretvorili v format JPEG z različnimi nivoji kvalitete. Izračunali smo kvaliteto teh slik in primerjali, kateri nivoji kvalitete so primerni za različne aplikacije.In this bachelor\u27s thesis, we will define the Discrete Cosine Transform (DCT) and explain the fundamental principles behind its derivation. Additionally, we will explore its two-dimensional extension and demonstrate how to compute the two-dimensional form using the one-dimensional definition. We will provide an example of an algorithm for fast DCT computation, utilizing existing Fast Fourier Transform (FFT) algorithms. Similarly, we will introduce an example of an Integer DCT algorithm that works on simpler arithmetic operations. Furthermore, we will delve into the most common implementation of JPEG compression. We will explain the encoding process, transforming the original image into a bit string for storage and transmission. We will also describe the inverse process, i.e., decoding. To illustrate these processes, we will use an example involving a block of an image. Lastly, we will convert several images into the JPEG format, varying the quality levels, and subsequently assess their quality to determine the most suitable qualities for specific applications