Image Compression: Combination of Discrete Transformation and Matrix Reduction - Mardin A, Anwer; Anwar, Dalya Abdullah; Anwer, Shereen Abdullah (International Journal of Computer Sciences and Engineering, 2025)
nowadays, compressing large data using different compression methods increase rapidly. This explains the recent importance and popularity of compressing data of multimedia applications as well as wavelet transforms in this field. Wavelet transforms tend to benefit of block-based transforms, including the Discrete Cosine Trans-form (DCT). DCT is responsible for displaying blocking artifacts while wavelets have compact support and can offer a DCT an adaptable substitute to DCT. The popularity of single-wavelets, formed through converting and expanding of single approximation functions as well as detail functions, offered high multi-resolution function-approximation bases. This paper discusses the idea of the image compression using two levels DWT with two-dimensional DCT on every 8x8 block. Hence, the low-frequency sub-band is reduced. The DC-Column stores the DC-coefficients. As a result of using Huffman coding the DC-Column will be coded. Meanwhile the other AC-Coefficient has to be quantized in order to gain additional zeros, allowing it to be converted easily to bits through the Huffman coding. HL2, HH2, as well as LH2 are other high-frequencies coefficients that are coded using the Minimize-Matrix-Size Algorithm. The mentioned proposed algorithm converts the three high-frequency coefficients into a single real number. Nevertheless, the use of the proposed algorithm; one-dimensional-array that has many real values will be reduced and will be converted it to many bits. The results of the compression algorithm are based on Mean Square Error ( MSE).