Hartley transform

About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.

Mellin transform for boehmians

Abstract: A suitable Boehmian space is constructed to extend the distributional Mellin transform. Mellin transform of a Boehmian is defined as a quotient of analytic functions. We prove that the generalized Mellin transform has all its usual properties. We also discuss the relation between the Mellin transform and the Laplace transform in the context of Boehmians.

The Radon transform of functions of matrix argument

Abstract: The monograph contains a systematic treatment of a circle of problems in analysis and integral geometry related to inversion of the Radon transform on the space of real rectangular matrices. This transform assigns to a function $f$ on the matrix space the integrals of $f$ over the so-called matrix planes, the linear manifolds determined by the corresponding matrix equations. Different inversion methods are discussed. They rely on close connection between the Radon transform, the Fourier transform, the Garding-Gindikin fractional integrals, and matrix modifications of the Riesz potentials. A special emphasis is made on new higher rank phenomena, in particular, on possibly minimal conditions under which the Radon transform is well defined and can be explicitly inverted. Apart of the space of Schwartz functions, we also employ $L^p$-spaces and the space of continuous functions. Many classical results for the Radon transform on $R^n$ are generalized to the higher rank case.

Optical Double Image Hiding in the Fractional Hartley Transform Using Structured Phase Filter and Arnold Transform

Abstract: To maintain the security of the image encryption and to protect the image from intruders, a new asymmetric cryptosystem based on fractional Hartley Transform (FrHT) and the Arnold transform (AT) is proposed. AT is a method of image cropping and edging in which pixels of the image are reorganized. In this cryptosystem we have used AT so as to extent the information content of the two original images onto the encrypted images so as to increase the safety of the encoded images. We have even used Structured Phase Mask (SPM) and Hybrid Mask (HM) as the encryption keys. The original image is first multiplied with the SPM and HM and then transformed with direct and inverse fractional Hartley transform so as to obtain the encrypted image. The fractional orders of the FrHT and the parameters of the AT correspond to the keys of encryption and decryption methods. If both the keys are correctly used only then the original image would be retrieved. Recommended method helps in strengthening the safety of DRPE by growing the key space and the number of parameters and the method is robust against various attacks. By using MATLAB 8.3.0.52 (R2014a) we calculate the strength of the recommended cryptosystem. A set of simulated results shows the power of the proposed asymmetric cryptosystem.

Gegenbauer Transforms via the Radon Transform

Abstract: Use is made of the Radon transform on even dimensional spaces and Gegenbauer functions of the second kind to obtain a general Gegenbauer transform pair. In the two-dimensional limit the pair reduces to a Chebyshev transform pair.

On Computation of the Hadamard Transform and the R Transform in Ordered Form

Abstract: This correspondence describes an improved computational algorithm for the Hadamard transform and the R transform. By performing the computation "in place", the number of storage locations is minimized and the speed is increased. The transformed coefficients are in the order of increasing sequency.