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 steganography approach for audio files

We present a novel robust and secure steganography technique to hide images into audio files aiming at increasing the carrier medium capacity. The audio files are in the standard WAV format, which is based on the LSB algorithm while images are compressed by the GMPR technique which is based on the Discrete Cosine Transform (DCT) and high frequency minimization encoding algorithm. The method involves compression-encryption of an image file by the GMPR technique followed by hiding it into audio data by appropriate bit substitution. The maximum number of bits without significant effect on audio signal for LSB audio steganography is 6 LSBs. The encrypted image bits are hidden into variable and multiple LSB layers in the proposed method. Experimental results from observed listening tests show that there is no significant difference between the stego audio reconstructed from the novel technique and the original signal. A performance evaluation has been carried out according to quality measurement criteria of Signal-to-Noise Ratio (SNR) and Peak Signal-to-Noise Ratio (PSNR)

Joint image encryption and compression schemes based on hexa-coding

This research proposes a new image compression and encryption method depend on a modified JPEG technique combined with the Hexa-Coding algorithm. The compression algorithm starts by dividing an image into 8x8 blocks, then DCT (Discrete Cosine Transform) is applied to all blocks independently followed by uniform quantization. Additionally, the size of blocks is reduced by eliminating insignificant coefficients, and then Arithmetic coding is applied to compress residual coefficients. Finally, Hexa-encoding is applied to the compressed data to further reduce compression size as well as provide encryption. The encryption is accomplished based on five different random keys. The decompression uses a searching method called FMSA (Fast Matching Search Algorithm) which is used for decoding the previously compressed data, followed by Arithmetic decoding) to retrieve residual coefficients. These residuals are padded with zeros to rebuild the original 8x8 blocks. Finally, inverse DCT is applied to reconstruct approximately the original image. The experimental results showed that our proposed image compression and decompression has achieved up to 99% compression ratio while maintaining high visual image quality compared with the JPEG technique

Information Systems: Secure Access and Storage in the Age of Cloud Computing

Given that cloud computing is a remotely accessed service, the connection between provider and customer needs to be adequately protected against all known security risks. In order to ensure this, an open and clear specification of all standards, algorithms and security protocols adopted by the cloud provider is required. In this paper, we review current issues concerned with security threats to cloud computing and present a solution based on our unique patented compression-encryption method. The method provides highly efficient data compression where a unique symmetric key is generated as part of the compression process and is dependent on the characteristics of the data. Without the key, the data cannot be decompressed. We focus on threat prevention by cryptography that, if properly implemented, is virtually impossible to break directly. Our security by design is based on two principles: first, defence in depth, where our proposed design is such that more than one subsystem needs to be violated to get both the data and their key. Second, the principle of least privilege, where the attacker may gain access to only part of a system. The paper highlights the benefits of the solution that include high compression ratios, less bandwidth requirements, faster data transmission and response times, less storage space, and less energy consumption among others

A novel Hexa data encoding method for 2D image crypto-compression

Abstract: We proposed a novel method for 2D image compression-encryption whose quality is demonstrated through accurate 2D image reconstruction at higher compression ratios. The method is based on the DWT-Discrete Wavelet Transform where high frequency sub-bands are connected with a novel Hexadata crypto-compression algorithm at compression stage and a new fast matching search algorithm at decoding stage. The novel crypto-compression method consists of four main steps: 1) A five-level DWT is applied to an image to zoom out the low frequency sub-band and increase the number of high frequency sub-bands to facilitate the compression process; 2) The Hexa data compression algorithm is applied to each high frequency sub-band independently by using five different keys to reduce each sub-band to1/6of its original size; 3) Build a look up table of probability data to enable decoding of the original high frequency sub-bands, and 4) Apply arithmetic coding to the outputs of steps (2) and (3). At decompression stage a fast matching search algorithm is used to reconstruct all high frequency sub-bands. We have tested the technique on 2D images including streaming from videos (YouTube). Results show that the proposed crypto-compression method yields high compression ratios up to 99% with high perceptual quality images

Image Data Compression and Decompression Using Minimise Size Matrix Algorithm

Computer implemented methods of compressing and decompressing image data are described. A discrete cosine (DCT) transformation is applied to each of a plurality of pixel blocks to generate a set of DCT coefficients for each pixel block comprising a DC DCT coefficient and a plurality of AC DCT coefficients. Each set of DCT coefficients is quantised. A DC array is formed from the set of quantised DC DCT coefficients and an AC matrix is formed from the set of quantised AC DCT coefficients. The AC matrix is compressed by eliminating blocks of data having only zero values and forming a reduced AC array from blocks including non-zero values. The reduced AC array is compressed using a key to form a coded AC array. The DC array and coded AC array are arithmetically coded to form arithmetically coded data which is included in a compressed image file. The decompression method is essentially the reverse process

Image Compression for Quality 3D Reconstruction

A 3D mesh can be reconstructed from multiple viewpoint images or from a single structured light image. Lossy compression of such images by standard techniques such as JPEG at high compression ratios lead to 3D reconstruction being adversely affected by artifacts and missing vertices. In this paper we demonstrate an improved algorithm capable of high compression ratios without adversely affecting 3D reconstruction and with minimum data loss. The compression algorithm starts by applying block DCT over the input image, and the transformed data being quantized using an optimized quantization matrix. The quantized coefficients of each block are arranged as a 1D array and saved with other block’s data in a larger matrix of coefficients. The DC coefficients are subject to a first order difference whose values are referred to as residual array. The AC coefficients are reduced by eliminating zeros and saving the non-zero values in a reduced coefficients array using a mask of 0 (for a block of zeros) and 1 (for a block of non-zeros). Finally, arithmetic coding is applied to both coefficients and residual arrays. At decompression stage, the coefficients matrix is regenerated by scanning the coefficients array and examining the headers to substitute zero and non-zero data. This matrix is then added to the residual array to obtain the original DC values. The IDCT is then applied to obtain the original image. The proposed algorithm has been tested with images of varying sizes in the context of 3D reconstruction. Results demonstrate that our proposed algorithm is superior to traditional JPEG at higher compression ratios with high perceptual quality of images and the ability to reconstruct the 3D models more effectively, both for structured light images and for sequences of multiple viewpoint images

Quick sequential search algorithm used to decode high-frequency matrices

This research proposes a data encoding and decoding method based on the Matrix Minimization algorithm. This algorithm is applied to high-frequency coefficients for compression/encoding. The algorithm starts by converting every three coefficients to a single value; this is accomplished based on three different keys. The decoding/decompression uses a search method called QSS (Quick Sequential Search) Decoding Algorithm presented in this research based on the sequential search to recover the exact coefficients. In the next step, the decoded data are saved in an auxiliary array. The basic idea behind the auxiliary array is to save all possible decoded coefficients; this is because another algorithm, such as conventional sequential search, could retrieve encoded/compressed data independently from the proposed algorithm. The experimental results showed that our proposed decoding algorithm retrieves original data faster than conventional sequential search algorithms

Image Data Compression and Decompression

A compression-encryption method is described where a unique symmetric key is automatically generated as part of the compression step and it is dependent on the characteristics of the data. The file can only be decompressed with the corresponding generated key. It is the only method that can offer compression and encryption as part of the same process. Compression rates are higher than the vast majority of existing methods making it suitable for transmission over the network with reduced bandwidth requirements, massive storage reduction especially in a Cloud environment, reduced energy costs, and faster access times. The method involves a discrete cosine (DCT) transform applied to non-overlapping variable size pixel blocks to generate a set of coefficients (DC-coefficients and AC-coefficients) for each block. Each set of coefficients is quantised resulting in a DC array and an AC matrix. The AC matrix is compressed by eliminating blocks of data having only zero values and forming a reduced AC array from blocks of non-zero values. The reduced AC array is compressed by generating a unique key that is applied to each element in the array and summed over in a particular way to form a reduced, coded AC array. Both coded AC and DC arrays are subject to arithmetic coding whose outputs are included in the compressed file together with information about the unique key for that file. If the unique key is lost, the file cannot be decompressed. The decompression method is essentially the reverse process: reverse arithmetic coding, use the key to undo the sum, recover individual elements in the AC array and reconstruct the original AC matrix. These are then assembled together with the DC coefficients and the inverse DCT is applied recovering the original data