Image compression based on 2D Discrete Fourier Transform and matrix minimization algorithm

In the present era of the internet and multimedia, image compression techniques are essential to improve image and video performance in terms of storage space, network bandwidth usage, and secure transmission. A number of image compression methods are available with largely differing compression ratios and coding complexity. In this paper we propose a new method for compressing high-resolution images based on the Discrete Fourier Transform (DFT) and Matrix Minimization (MM) algorithm. The method consists of transforming an image by DFT yielding the real and imaginary components. A quantization process is applied to both components independently aiming at increasing the number of high frequency coefficients. The real component matrix is separated into Low Frequency Coefficients (LFC) and High Frequency Coefficients (HFC). Finally, the MM algorithm followed by arithmetic coding is applied to the LFC and HFC matrices. The decompression algorithm decodes the data in reverse order. A sequential search algorithm is used to decode the data from the MM matrix. Thereafter, all decoded LFC and HFC values are combined into one matrix followed by the inverse DFT. Results demonstrate that the proposed method yields high compression ratios over 98% for structured light images with good image reconstruction. Moreover, it is shown that the proposed method compares favorably with the JPEG technique based on compression ratios and image quality

A Novel Method for Image and Video Compression based on Two-Level DCT with Hexadata Coding

In this paper a novel method for 2D image compression is proposed and demonstrated through high quality reconstruction with compression ratios up to 99%. The proposed novel algorithm is based on a two-level Discrete Cosine Transform (DCT) followed by Hexadata coding and arithmetic coding at compression stage. The novel method consists of four main steps:1) A two-level DCT is applied to an image to reinforce the low frequency coefficients and increase the number of high frequency coefficients to facilitate the compression process; 2) The Hexadata coding algorithm is applied to each high frequency matrix separately through five different keys to reduce each matrix to 1/6 of their original size; 3) Build a probability table of original high-frequency data required in the decoding step; and 4) Apply arithmetic coding to compress each of the outputs of steps (2) and (3). At decompression stage, arithmetic decoding and a Fast Matching Search Algorithm (FMS-Algorithm) decodes the high frequency coefficients of step (2) using the probability table of step (3). Finally, two level inverse DCT is applied to decode the high frequency coefficients to reconstruct the image. The technique is demonstrated on still images including video streaming from YouTube. The results show that the proposed method yields high compression ratios up to 99% with better perceptual quality of reconstructed images as compared with the popular JPEG method