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Page 1249 of Mathematical Reviews Vol. , Issue 99b [page]

1991 Mathematical Reviews  
W. (5-ANUM-MaA; Canberra) Linear bijections and the fast Fourier transform. (English summary) Appl. Algebra Engrg. Comm. Comput. 8 (1997), no. 2, 143-163.  ...  As is known, linear bijections between data arrays (so-called index transforms) play a significant role in the construction of fast Fourier transforms (FFTs).  ... 

Algebraic theory of finite fourier transforms

Peter J. Nicholson
1971 Journal of computer and system sciences (Print)  
This results in a general decomposition formula from which all possible versions of the Fast Fourier Transform algorithm may be derived.  ...  of G, Matrix representations of the isomorphisms are derived and each is called a generalized finite Fourier transform.  ...  Kalman, who originally suggested the topic to me and who, with remarkable intuition, insisted that the algebraic approach would be fruitful. I would also thank my colleague, Professor Y.  ... 
doi:10.1016/s0022-0000(71)80014-4 fatcat:mzmeidlpkbesbivxh2wgqipddy

Algebraic Signal Processing Theory: Foundation and 1-D Time

M. Puschel, J. Moura
2008 IEEE Transactions on Signal Processing  
The mapping 8 generalizes the concept of a -transform to bijective linear mappings from a vector space of signal samples into the module .  ...  Finally, ASP provides a systematic methodology to derive fast algorithms for linear transforms.  ...  Further, in [5] and [7] , we use ASP to present concise derivations of existing and new fast algorithms for linear transforms.  ... 
doi:10.1109/tsp.2008.925261 fatcat:d5t5ig3bzfhljnmcfienw7qowu

A standard and linear fan-beam Fourier backprojection theorem [article]

Patricio Guerrero, Matheus Bernardi, Eduardo X. Miqueles
2021 arXiv   pre-print
In this work we propose a theoretical low-complexity formulation for the tomographic fan-beam backprojection in standard and linear geometries.  ...  The proposed formula is obtained from a recent backprojection theorem in the parallel case.  ...  We used the numerical library scipy [15] to compute Fast Fourier transforms, linear interpolations and Bessel coefficients.  ... 
arXiv:1812.06519v3 fatcat:kexcv2xgqnfqhapjdyyb3xetsq

Beltrami Representation and its applications to texture map and video compression [article]

Lok Ming Lui, Ka Chun Lam, Tsz Wai Wong, XianFeng Gu
2012 arXiv   pre-print
Using the Beltrami representation, the surface homeomorphism can be easily compressed by Fourier approximation, without distorting the bijectivity of the map.  ...  Conversely, given a Beltrami representation, the corresponding bijective surface map can be exactly reconstructed using the Linear Beltrami Solver introduced in this paper.  ...  We can use fast Fourier transform to compute the coefficients c j,k efficiently.  ... 
arXiv:1210.8025v1 fatcat:5gd7jg6cdbcyvdris22hme2bua

Page 3829 of Mathematical Reviews Vol. , Issue 87g [page]

1987 Mathematical Reviews  
A general procedure is presented for linear operator equations of the second kind (L— K)z = f, where L is continuous and bijective and K is compact.  ...  Summary: “In this paper, the prime factor algorithm for the evalu- ation of a one-dimensional discrete Fourier transform is generalized to the evaluation of multidimensional discrete Fourier transforms  ... 

Parallelization of the FFT on SO(3) [article]

Denis-Michael Lux, Christian Wülker, Gregory S. Chirikjian
2018 arXiv   pre-print
In this paper, a work-optimal parallelization of Kostelec and Rockmore's well-known fast Fourier transform and its inverse on the three-dimensional rotation group SO(3) is designed, implemented, and tested  ...  Using all 64 available cores, the speedup for the largest considered bandwidths 128, 256, and 512 amounted to 29.57, 36.86, and 34.36 in the forward, and 24.57, 26.69, and 24.25 in the inverse transform  ...  The fast SO(3) Fourier transform and its inverse are revisited in Subsection 2.4.  ... 
arXiv:1808.00896v1 fatcat:xiwfey77sbfz5gbanjgxlky6zq

Texture Map and Video Compression Using Beltrami Representation

Lok Ming Lui, Ka Chun Lam, Tsz Wai Wong, Xianfeng Gu
2013 SIAM Journal of Imaging Sciences  
However, Fourier compression is not possible for other representations such as 3D coordinate functions, as the bijective property (1-1 and onto) of the resulting maps cannot be guaranteed (see Figure 4  ...  Using the Beltrami representation, the surface homeomorphism can be easily compressed by Fourier approximation, without distorting the bijectivity of the map.  ...  In practice, we can use the fast Fourier transform (FFT) to compute the coefficients c m,n efficiently.  ... 
doi:10.1137/120866129 fatcat:4hm6cic2dzgihil3halxrtekui

Reconstruction of undersampled radial PatLoc imaging using total generalized variation

Florian Knoll, Gerrit Schultz, Kristian Bredies, Daniel Gallichan, Maxim Zaitsev, Jürgen Hennig, Rudolf Stollberger
2012 Magnetic Resonance in Medicine  
Results from numerical simulations and in-vivo PatLoc measurements with as few as 16 radial projections are presented, which demonstrate significant improvements in image quality with the TGV based approach  ...  It is shown that this can be realized as a Type-3 non-uniform FFT, which is implemented by a combination of a Type-1 and Type-2 non-uniform FFT.  ...  fast Fourier transform (IFFT) (25) .  ... 
doi:10.1002/mrm.24426 pmid:22847824 pmcid:PMC4878715 fatcat:fmtqttlylzejhdg3appdy2w3su

Page 4638 of Mathematical Reviews Vol. , Issue 89H [page]

1989 Mathematical Reviews  
It is applied in that form to index transformations for fast discrete Fourier transform algorithms, and examples are given.  ...  The resulting algorithms retain the ‘N log N’ behavior of the fast Fou- rier transform while reducing the size of the data to approximately an asymmetric unit.  ... 

On Fourier - Laplace transform of a class of generalized functions

Ildar Khamitovich Musin
2020 Ufimskii Matematicheskii Zhurnal  
Our main result, presented in Theorem 1, states that the Fourier-Laplace transforms of the functionals establishes an isomorphism between the strong dual space of the considered space and some space of  ...  We study the problem on describing the strong dual space for this space in terms of the Fourier-Laplace transforms of functionals. Particular cases of this problem were considered by by J.W.  ...  The first result is the Paley-Wiener-Schwartz theorem for the space ( ) obtained in [3] by a scheme from [1] . It will be applied in the proving that the Fourier-Laplace transform is bijective.  ... 
doi:10.13108/2020-12-4-78 fatcat:exmderagknhbfhscfrtn56zpwi

Chirp transforms and Chirp series

Guangbin Ren, Qiuhui Chen, Paula Cerejeiras, Uwe Kaehle
2011 Journal of Mathematical Analysis and Applications  
Qian and the non-harmonic Fourier series which originated from the celebrated work of Paley and Wiener, we introduce an integral version of the non-harmonic Fourier series, called Chirp transform.  ...  As an integral transform with kernel e iφ(t)θ (ω) , the Chirp transform is an unitary isometry from L 2 (R, dφ) onto L 2 (R, dθ) and it can be explicitly defined in terms of generalized Hermite polynomials  ...  Acknowledgments The research is partially supported by the  ... 
doi:10.1016/j.jmaa.2010.07.037 fatcat:ltw2ezp3gneuhm5sjzfnvsu5ku

The automorphisms of convolution algebras of C∞ functions

Palle E.T Jørgensen
1978 Journal of Mathematical Analysis and Applications  
The continuous automorphisms and spectra of these algebras are described completely. We show that the algebra of Cm-functions of infmitly fast exponential decay at cc, .  ...  We find the automorphisms and the spectra of several different topological convolution algebras of Cm-functions on the real line.  ...  The minimal requirement on the algebra 21 in question is that for every f E 21, the Fourier transform f"extends to an entire analytic function, and that the corresponding linear functionals f-f([) are  ... 
doi:10.1016/0022-247x(78)90018-5 fatcat:lh3cl2tokfegdmvk2lsyronbnu

The fast Fourier transform and fast wavelet transform for patterns on the torus

Ronny Bergmann
2013 Applied and Computational Harmonic Analysis  
Despite the fast Fourier techniques itself, there is also the advantage of this transform to be parallelized efficiently, yielding faster versions than the one-dimensional Fourier transform.  ...  We introduce a fast Fourier transform on regular d-dimensional lattices.  ...  The fast Fourier transform on P(M) This section is devoted to derive a fast Fourier transform on P(M) using its characterisation obtained in the previous section.  ... 
doi:10.1016/j.acha.2012.07.007 fatcat:6kzvnejpurd6pohif4wmex7him

Trumpets: Injective Flows for Inference and Inverse Problems [article]

Konik Kothari, AmirEhsan Khorashadizadeh, Maarten de Hoop, Ivan Dokmanić
2021 arXiv   pre-print
They retain many of the advantages of the standard flows such as training based on maximum likelihood and a fast, exact inverse of the generator.  ...  Since Trumpets are injective and have fast inverses, they can be effectively used for downstream Bayesian inference.  ...  ID and AK were supported by the European Research Council Starting Grant 852821-SWING.  ... 
arXiv:2102.10461v1 fatcat:b6ct3l2vn5axlgl5fxieozynbe
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