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

The probability that the product of two elements of finite group algebra is zero

Let $\mathbb{F}_qG$ be a finite group algebra. We denote by $P(\mathbb{F}_qG)$ the probability that the product of two elements of $\mathbb{F}_qG$ be zero. In this paper, the general formula for computing the $P(\mathbb{F}_qG)$ are established for the cyclic groups $C_n$, the Quaternion group $Q_8$ and the symmetric group $S_3$, for some cases

Genus One Almost Simple Groups of Lie Rank Two

In this paper, we assume that $G$ is a finite group with socle $PSL(3,q)$ and $G$ acts on the projective points of 2-dimensional projective geometry $PG(2,q)$, $q$ is a prime power. By using a new method, we show that $G$ possesses no genus one group if $q>13$. Furthermore, we study the connectedness of the Hurwitz space $\mathcal{H}^{in}_{r}(G)$ for a given group $G$, genus one and $q\leq 13$

Diagonally implicit Runge-Kutta method of order four with minimum phase-lag for solving first order linear ODEs

In this paper we derived a new diagonally implicit Runge-Kutta method of order four with minimum phase-lag for solving first order linear ordinary differential equation. The stability polynomial of the method is obtained and the stability region is presented. A set of problems are tested upon and numerical results proved that the method is more accurate compared to other well known methods in the scientific literature

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

RESIDENTIAL BUILDING DEVELOPMENT PROCESS IN KURDISTAN REGION GOVERNMENT

Nowadays, Residential buildings have become the most important part of real-estate markets in (KRG). The layout of housing in Kurdistan has transformed the face of major cities across the Region. Rapid changes since 2003, have witnessed copious architectural structures and large housing projects that have reshaped the landscape of its cities. The aim of this study is to study the housing developing policy in KRG. The objectives of the study are to evaluate the KRG's housing development policy and to investigate the types of house and the price range preferred by the potential buyer. The study focus on private residential building development projects and it is carried out by questionnaires and interviews. The respondents are the house buyers and the developers. A total of 100 questionnaires were distributed to the respondents and 78 questionnaires were returned duly answered. The data collected is analyzed using the SPSS (Statistical Package for the Social Sciences) and Average Index. The results of research indicated that the KRG’s housing development policy covers the ownership of the project land, full repatriation of project investment and profits allowed, import of spare parts tax exempt up to 15% of project cost and the employment of foreign workers allowed. Moreover, the types of house preferred by the house buyers are of double storey type and to be of corner lot. The price range preferred by the potential buyers are between (40,000 to 100,000) USD

Finite groups of small genus

For a finite group $G$, the Hurwitz space $H$$^i$$_r$$_,$$^n$$_g$ ($G$) is the space of genus $g$ covers of the Riemann sphere with $r$ branch points and the monodromy group $G$. Let ε$_r$($G$) = {($x$$_1$,...,$x$$_r$) : $G$ = $\langle$$x$$_1$,...,$x$$_r$$\rangle$, Π$^r$$_i$$_=$$_1$ $x$$_i$ = 1, $x$$_i$ ϵ $G$#, $i$ = 1,...,$r$}. The connected components of $H$$^i$$_r$$_,$$^n$$_g$($G$) are in bijection with braid orbits on ε$_r$($G$). In this thesis we enumerate the connected components of $H$$^i$$_r$$_,$$^n$$_g$($G$) in the cases where $g$ $\leq$ 2 and $G$ is a primitive affine group. Our approach uses a combination of theoretical and computational tools. To handle the most computationally challenging cases we develop a new algorithm which we call the Projection-Fiber algorithm

Classification of All Primitive Groups of Degrees Four and Five

Let be a compact Riemann surface of genus and be indecomposable meromorphic function of Riemann sphere by . Isomorphisms of such meromorphic functions are in one to one correspondence with conjugacy classes of tuples of permutations in such that and a subgroup of . Our goal of this work is to give a classification in the case where is of genus 1 and the subgroup is a primitive subgroup of or . We present the ramification types for genus 1 to complete such a classification. Furthermore, we show that the subgroups and of do not possesses primitive genus 1 systems