Topic
Hartley transform
About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.
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TL;DR: The numerical simulations have demonstrated the validity and high security level of the image cryptosystem based on the novel transform which is similar to fractional Fourier transform and gyrator transform to some extent.
37 citations
TL;DR: In this article, the Stockwell transform of a signal is defined as a hybrid of the Gabor transform and the wavelet transform, and continuous and discrete reconstruction formulas for a signal from its Stockwell Transform are established.
Abstract: The Stockwell transform of a signal, i.e., a function in L 2(ℝ), is defined as a hybrid of the Gabor transform and the wavelet transform. The continuous and discrete reconstruction formulas for a signal from its Stockwell transform are established.
37 citations
TL;DR: The complex Fourier transform of a real function and its real Hartley transform are expressed in terms of each other, allowing translation of theorems and computer programs between the two versions, and the FHT can transform one real array of length N in half the time that it takes the FFT to process a complex array.
Abstract: The complex Fourier transform of a real function and its real Hartley transform are expressed in terms of each other, allowing translation of theorems and computer programs between the two versionsAny FFT can thus be converted, by a few indexing changes, into a Fast Hartley Transform which is equally efficient, in terms of floating point operations per real datum transformed The FHT can therefore transform one real array of length N in half the time that it takes the FFT to process a complex array of length N Several tricks to speed up both FHT and FFT are presented and a Fortran version of the FHT is supplied which delivers the result in $75\log _2 N$ multiplications and $175\log _2 N$ additions
37 citations
TL;DR: This paper shows that the Discrete Fuzzy Transform is invariant with respect to the interpolating and least-squares approximation, and defines the geometry- and confidence-driven Discrete fuzzy Transforms, which take into account the intrinsic geometry and the confidence weights associated to the data.
37 citations
TL;DR: In this article, a fast butterfly algorithm for the hyperbolic Radon transform is proposed, which reformulates the transform as an oscillatory integral operator and constructs a blockwise low-rank approximation of the kernel function.
Abstract: Generalized Radon transforms, such as the hyperbolic Radon transform, cannot be implemented as efficiently in the frequency domain as convolutions, thus limiting their use in seismic data processing. We have devised a fast butterfly algorithm for the hyperbolic Radon transform. The basic idea is to reformulate the transform as an oscillatory integral operator and to construct a blockwise low-rank approximation of the kernel function. The overall structure follows the Fourier integral operator butterfly algorithm. For 2D data, the algorithm runs in complexity O(N2 log N), where N depends on the maximum frequency and offset in the data set and the range of parameters (intercept time and slowness) in the model space. From a series of studies, we found that this algorithm can be significantly more efficient than the conventional time-domain integration.
37 citations