Discrete wavelet transforms and applications

U ovom diplomskom radu je opisana diskretna wavelet transformacija (DWT), te mogućnost primjene u obradi slike. TakoĎer u radu je prvo obraĎivana teorijska podloga za uspješno opisivanje teme diplomskog rada, a kasnije se iz teorijskog znanja išlo na praktičnu primjenu istih. Poslije definiranja pojmova kontinuirana wavelet transformacija (CWT), diskretna wavelet transformacija (DWT), išlo se na definiranje algoritama za Huffmanovo i Aritmetičko kodiranje u wavelet kompresiji slike. TakoĎer je objašnjena procedura dobivanja rekonstruirane iz ulazne slike, primjenom DWT-a, IDWT-a, kvantizacije, inverzne kvantizacije i entropijskog kodiranja/dekodiranja. U praktičnom dijelu su usporeĎivana tri algoritma po omjeru kompresije i brzini kodiranja/dekodiranja. Iz rezultata je proizišlo da Huffmanov algoritam za kodiranje/dekodiranje posjeduje najveću učinkovitost, koja je rasla povećanjem razine dekompozicije (barem do treće razine). Najveći omjer kompresije postiţe algoritam aritmetičko koje čini rekurzivno kodiranje/dekodiranje. Porastom razine dekompozicije raste SNR i SSIM mjera za odreĎivanje kvalitete. U drugom dijelu su usporeĎivane slike s različitim postotkom sačuvanih wavelet koeficijenata. Za 1% posto sačuvanih wavelet koeficijenata na slici, teško je bilo uočljivo što slika zapravo predstavlja. Porastom postotka sačuvanih wavelet koeficijenata na slici, slika je posjedovala značajno više detalja. Iz objektivnih mjera za odreĎivanje kvalitete slika „lena“ je bila sličnija originalu gledano po vrijednostima za SNR i SSIM. Slika „lena“ je posjedovala veći omjer kompresije u odnosu na sliku „priroda“, te na taj način je saţeta slika „lena“ zauzimala manje memorijskog prostora.Discrete wavelet transformation (DWT) was described in this master thesis, and the possibility of applying it to the processing of digital pictures. In this thesis firstly was covered theoretical background for successfull coverage of the subject, and then it's application on pictures. After defining concepts such as Continuous wavelet transformation (CWT) and Discrete wavelet transformation (DWT), there is defining algorithms for Huffman and Arithmetic Coding in wavelet compression of pictures. It is also explained the procedure of obtaining reconstructed from the input image, using DWT, IDWT, quantization, inverse quantization and entropy coding/decoding. In practical part of thesis, three algorithms were compared by compression ratio and coding/decoding speed. From results, it is shown that Huffman algorithm for coding/decoding possesses best effectiveness which increased by enhancement of decomposion level (at least by third level). Best compression ratio achieves Arithmetic algorithm which is made of recursive coding/decoding. Increasement of level of decomposition results in increasement of SNR and SSIM criterions for assessment of quality. In second part of thesis, there are compared pictures with different percentage of preserved wavelet coefficients. For 1% of preserved wavelet coefficients of pictures, it was hard to spot what picture actually represents. By increasing percentage of wavelet coefficients, picture showed increased number of details. From objective criterion used in defining quality of picture, picture „lena“ was closest in quality to original picture using SNR and SSIM values. Picture „lena“ possesed higher compression ratio in regards to picture „priroda“, and because of that it used less memory