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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01 Dec 2006
TL;DR: Fractional Fourier transform (FRFT) is proposed to be used in IR problems involving either linear shifts or pure rotations in the given images to be registered.
Abstract: This image registration (IR) is a fundamental task in many image processing applications such as medical diagnosis, satellite imaging, super-resolution image reconstruction etc. Fourier transform based methods have also been in use for IR purposes for both the shifted and rotated images using the phase correlation method (Brown, 1992). As fractional Fourier transform (FRFT) is a generalization of the conventional Fourier transform, it is natural to extend its use in IR applications. In this paper, the authors propose the use of the FRFT in IR problems involving either linear shifts or pure rotations in the given images to be registered. Simulation results of the proposed techniques are also presented
12 citations
06 May 2001
TL;DR: The 1-D real valued discrete Gabor transform (RDGT) is extended to the 2-D case for image representation and how to apply the discrete Hartley transform (DHT) to compute the2-D RDGT coefficients of an image and to reconstruct the original image from the coefficients efficiently is discussed.
Abstract: In this paper, we extend the 1-D real valued discrete Gabor transform (RDGT), proposed in our previous work, to the 2-D case for image representation and discuss how to apply the discrete Hartley transform (DHT) to compute the 2-D RDGT coefficients of an image and to reconstruct the original image from the coefficients efficiently. Meanwhile, as in the 1-D case, the 2-D RDGT also bears a simple relationship with the complex valued discrete Gabor transform (CDGT) so that the 2-D CDGT coefficients can be directly obtained from the 2-D RDGT coefficients, Moreover, through experiments, we shall show that the 2-D RDGT coefficients have much more degree of information decorrelation than the 2-D CDGT coefficients because both the magnitudes and the phases of the complex coefficients need to be separately quantized.
12 citations
18 Jun 1996
TL;DR: By replacing the conventional Fourier transform with the joint time-frequency transform, a 2-D range- doppler Fourier frame becomes a 3-D time-range-Doppler cube and with sampling in time, a sequence of clear 2- D range- Doppler images can be simply reconstructed without using sophisticated motion compensation.
Abstract: Conventional radar imaging systems use the Fourier transform for reconstruction of radar images. To use the Fourier transform adequately, some restrictions must be applied. Due to target's motion and manoeuvring, the reconstructed image by using Fourier transform becomes smeared. Therefore, some sophisticated motion compensation procedures must be applied to produce a clear image. However, the restrictions of Fourier transform can be lifted if a high resolution time-frequency transform can be used to retrieve the Doppler information. By replacing the conventional Fourier transform with the joint time-frequency transform, a 2-D range-Doppler Fourier frame becomes a 3-D time-range-Doppler cube. With sampling in time, a sequence of clear 2-D range-Doppler images can be simply reconstructed without using sophisticated motion compensation.
12 citations
TL;DR: In this article, the authors consider the problem of reconstruction of the singular locus of the original function given by a singular transform of the X-ray transform, and provide procedures for constructing envelopes for families of affine subspaces of R n.
12 citations
TL;DR: In this paper, the authors used the radix-4 transform for odd powers of 2 and showed that it can also be used for even powers of 4, by splitting the data sequence into two interleaved parts, applying the algorithm to each in turn, and combining the results.
Abstract: Radix-4 transforms, which have a speed advantage but have been restricted to data lengths which are powers of 4, can also be used for odd powers of 2 also by splitting the data sequence into two interleaved parts, applying the radix-4 algorithm to each in turn, and combining the results.
12 citations