Applied two Stages Minimize-Matrix-Size Algorithm with DCT on DWT for Image Compression

Abstract

As the use of digital imaging is on the rise, compression of acquired digital image data is becoming more and more important to cope with the storage requirements. One of the challenges of compression is to compress images with high efficiently while preserving critical data from getting permanently lost in reconstructed images. In this research we introduce a proposed algorithm for image compression, based on the Minimize-Matrix-Size Algorithm for coding and Limited Sequential Search- Algorithm (LSS-Algorithm) for decoding. The proposed algorithm starts by using single stage Discrete Wavelet Transform, to decompose an image into four subbands; low frequency and high frequencies. Each \"n \u00d7 n\" of the low-frequency subband (LL) are transformed by using two dimensional DCT, store all DC coefficients in different matrix called DC-Matrix, and the remain AC coefficients are stored in different matrix called AC-Matrix, then applying Minimize-Matrix-size algorithm for the AC-Matrix, to convert each group of AC coefficients into single floating point value. The DC-Matrix transformed again by DWT, and apply Minimize-Matrix-Size algorithm on it. LSS-Algorithm which is represents decoding; DC-Matrix and AC-Matrix, this algorithm is used to estimate original values by using iterative method, which is depends on the probability of the data of the AC-Matrix and DC-Matrix. Our compression algorithm proved good compression ratio, and compared with JPEG and JPEG2000 depending on the PSNR and HVS.