Showing papers on "Hartley transform published in 2021"

Color image encryption scheme based on fractional Hartley transform and chaotic substitution–permutation

Abstract: We propose a novel opto-digital method of color image encryption which utilizes compound chaotic mappings, the reality preserving fractional Hartley transformation and piecewise linear chaotic map for substitution, optical processing and permutation of image pixels, respectively. The image to be encrypted initially undergoes a chaos-based substitution in the spatial domain through the compound chaotic maps followed by a transformation to the combined time–frequency domain using the fractional Hartley transform. A reality preserving version of the fractional Hartley transform is used to eliminate the complexity associated with transform coefficients. Optical transformation of the image, in the fractional Hartley domain, is followed by a permutation through piecewise linear chaotic maps. Due to the intertwined application of optical transformation and chaos-based substitution and permutation processes, the proposed image encryption scheme possesses higher security. The input parameters (initial conditions, control parameters, and number of iterations) of chaotic maps along with fractional orders of the fractional Hartley transform collectively form the secret keys for encryption/decryption. The proposed scheme is a lossless and symmetric encryption scheme. The level of security provided in terms of high sensitivity to keys, resistivity to brute-force attack, classical attacks, differential attacks, entropy attack, noise and occlusion attack along with the elimination of complex coefficients proves its better efficacy as compared to other similar state-of-the-art schemes.

Multi-layer color image encryption using random matrix affine cipher, RP2DFrHT and 2D Arnold map

Abstract: Confidentiality, integrity, authenticity, non-repudiation and storing and transmitting images over the unsecured channel has become a challenging task nowadays. In this scenario, a robust image encryption technique over open network has grasped a great deal of attention. In this paper to meet this challenge, we have established a new multi-layer robust color image encryption using random matrix affine cipher (RMAC), reality preserving two dimensional discrete fractional Hartley transform (RP2DFrHT) and two dimensional Arnold map. The first stage of encryption is designed through RMAC. RMAC provides security in co-ordinate domain as well as in geometrical domain. So if a hacker has knowledge about all the pixels of an image, but has no information about the mechanism of co-ordinate domain he/she cannot steal any information. The second stage of encryption is obtained incorporating the concept of RP2DFrHT. The reality preserving transform eliminates the complex-valued coefficients and provides the real-valued coefficients of encrypted image. The real-valuedness of data provides convenient platform for display, storage and transmission in digital domain. The third stage of encryption is done using 2D Arnold map, which not only enhances the security but also enlarges key space. Therefore, the proposed technique provides security in geometrical, co-ordinate, frequency and time domains simultaneously. The security of our proposed technique depends upon the secret keys as well as their correct arrangements. Simulation analysis provides the complete visual results of all stages of encrypted and decrypted images. Sensitivity analysis validates that our proposed technique is highly sensitive towards its secret keys and their arrangements. Statistical analysis such as histogram analysis, MSE, PSNR, correlation coefficient, entropy analysis and resistivity of classical attacks validates the effectiveness and feasibility of our proposed work. Moreover, comparison analysis testifies that our proposed technique functions significantly well as compared to existing similar techniques.

Secure Opto-Audio Cryptosystem Using XORing Mask and Hartley Transform

Abstract: This research paper proposes a secure opto-audio cryptosystem using XORing mask and Hartley transform (HT) The digital one dimensional (1D) plainaudio data is converted into two dimensional plainaudio map (2D PAM) and after that, the 2D PAM is divided into 2D plainaudio blocks (2D PABs) The basic idea of the proposed opto-audio encryption system depends on XORing each block of the 2D PABs with a single image selected from a personal image database that can be viewed as a secret key in the proposed opto-audio cryptosystem Each block of the mixed 2D PABs is then transposed using the chaotic logistic adjusted sine map (LASM) and optically encrypted with HT The XOR and LASM are implemented digitally while HT implemented optically An additional XORing mask step helps to remove residual intelligibility from the 2D PABs, fill in speechless gaps in spoken conversations, and destroy both the pitch and format details The utilization of chaotic LASM allows efficient noise immunity A comparative study is held between the proposed opto-audio encryption system and other related audio encryption systems in terms the standard well known encryption metrics The results have confirmed the efficiency of the introduced opto-audio encryption system The proposed opto-audio encryption system security is explored from an accurate encryption point of view, and tests confirmed the superiority of the proposed opto-audio encryption system from the encryption point of view

A Novel Non-Hermitian Symmetry Orthogonal Frequency Division Multiplexing System for Visible Light Communications

Abstract: This paper proposes a novel non-Hermitian symmetry ${2 \times 2}$ MIMO-OFDM (Multiple Input Multiple Output-Orthogonal Frequency Division Multiplexing) system based on fast Hartley transform (FHT) with unipolar encoding (referred to as HU-OFDM) for visible light communications. The new scheme uses FHT instead of FFT (fast Fourier transform) to process the complex-valued signals reducing the computational complexity and hardware cost and employs two LEDs (light-emitting diodes) to transmit the real and imaginary parts of a complex-valued OFDM signal respectively. Unipolar encoding is applied to the transmitted signal from each LED to ensure non-negative. The restrictions of Hermitian symmetry in traditional optical OFDM systems and real constellation mapping in FHT based optical OFDM systems can be removed simultaneously in the proposed system. Compared with MIMO-ACO/DCO-OFDM system, HU-OFDM has significant performance improvement along with a tremendous decrease in hardware cost and computational complexity. Compared with other non-Hermitian symmetry MIMO-OFDM systems, HU-OFDM has significant advantages in terms of power efficiency, system design flexibility, computational complexity, or hardware cost without losing reliability.

Approximate solution for integral equations involving linear Toeplitz plus Hankel parts

Abstract: We propose three approximate methods using regularization techniques and finite Hartley transforms for solving first-kind integral equations involving linear Toeplitz plus Hankel parts. Numerical examples are given for illustrating these new algorithms.

Use of Deterministic Transforms to Design Weight Matrices of a Neural Network.

Abstract: Self size-estimating feedforward network (SSFN) is a feedforward multilayer network. For the existing SSFN, a part of each weight matrix is trained using a layer-wise convex optimization approach (a supervised training), while the other part is chosen as a random matrix instance (an unsupervised training). In this article, the use of deterministic transforms instead of random matrix instances for the SSFN weight matrices is explored. The use of deterministic transforms provides a reduction in computational complexity. The use of several deterministic transforms is investigated, such as discrete cosine transform, Hadamard transform, Hartley transform, and wavelet transforms. The choice of a deterministic transform among a set of transforms is made in an unsupervised manner. To this end, two methods based on features' statistical parameters are developed. The proposed methods help to design a neural net where deterministic transforms can vary across its layers' weight matrices. The effectiveness of the proposed approach vis-a-vis the SSFN is illustrated for object classification tasks using several benchmark datasets.

A New Passage to the Reciprocity Attributes of Multidimensional IFT Through Those of the Multidimensional IHT

Abstract: This paper nonce a volitional path to the Reciprocity Attributes of the Multidimensional Complex Fourier Transform (IFT) or the Infiite Fourier Transform (IFT) finis the Multidimensional Infinite Hartley Transform (IHT). The provenances for the reciprocity attributes of multidimensional IFT are conferred out of the reciprocity attributes of the multidimensional IHT, and this is doable mainly due to the mathematical liaison betwixt the IFT and the IHT. Apres the IHT is a real transform, it is viable to deduce the reciprocity attributes for IFT throughout the whilom in multidimensions. It is quotidian run-through in signal processing and communication engineering to chance upon signals having the same fettle in the temporal- and frequency-bailiwicks, such as the Gaussian function. In such paradigms, the reciprocity attributes can be blisteringly wont for working out the onward and rearward transforms of the signals under query. In multidimensional signal processing where the outgo of perpertration is of superemeinent momentousness and the IFT is the exemplar, and where the reciprocity attributes of the IFT are to be wont, it is propounded to execute these reciprocity attributes of the IFT by using the reciprocity attributes of the IHT which have been philosophized in this paper. This props up in the penny-pinching of the utraexpensive reckoning time and disbursement by moiety of one-c as it is a well-established fact that real transforms take less time for execution than those the complex transforms. Thus, the reciprocity attributes unfolded in this paper can be used in digital video processing and in the solutions of differential equations and integral equations.

Phase congruence implementation in ImageJ using Radix-2 FFT

Abstract: Automatic edge detection in images is an area of great interest to industry and the scientific community. A problem usually experienced is that edge detectors are sensitive to the magnitude of changes in brightness. However, this disadvantage disappears when employing the technique known as phase congruency, which allows edge detection in an image regardless of its illumination level. This technique is based on phase alignment of frequency components. This principle states that the edges of an image occur when the phases of the Fourier components coincide. By using phase, the direct dependence on brightness intensity in edge detection is avoided. A difficulty of phase congruency implemented with monogenic filters is that it requires the computation of the complex Fourier transform. However, its computational cost is high. There are some approaches that seek to reduce its cost, such as the FHT, but they only allow to obtain the Fourier transform of real images. Due to this limitation, methods based on phase congruency were not available in several image processing tools, such as ImageJ, a program widely used by biologists and microscopists for the analysis of biological images, since these programs make use mainly of the Fast Hartley Transform transformation. Therefore, in this work the implementation of phase congruency for ImageJ with monogenic filters using the Fourier Radix-2 FFT transform is described. The results obtained with the proposed implementation were compared with those found with the Kovesi code in GNU Octave, showing that both implementations obtain equivalent results and even better with the proposed method when at least one side of the images is not a power of two, in which case tile-mirror is used to complete the image.