# Generalized Fourier-Bessel operator and almost-periodic interpolation and approximation

@article{Gauthier2016GeneralizedFO, title={Generalized Fourier-Bessel operator and almost-periodic interpolation and approximation}, author={J. P. Gauthier and Dario Prandi}, journal={ArXiv}, year={2016}, volume={abs/1612.00056} }

We consider functions f of two real variables, given as trigonometric functions over a finite set F of frequencies. This set is assumed to be closed under rotations in the frequency plane of angle 2kπ M for some integer M. Firstly, we address the problem of evaluating these functions over a similar finite set E in the space plane and, secondly, we address the problems of interpolating or approximating a function g of two variables by such an f over the grid E. In particular, for this aim, we…

## 3 Citations

### A semidiscrete version of the Petitot model as a plausible model for anthropomorphic image reconstruction and pattern recognition

- MathematicsArXiv
- 2017

Based upon this semi-discrete model, improvements are improved on previous image-reconstruction algorithms and a pattern-recognition theory is developed that leads also to very efficient algorithms in practice.

### Dario Prandi's CV

- Education
- 2020

Education Philosophiae Doctor (Ph.D.), École Polytechnique, Palaiseau 2010–2013 Subject of the dissertation: Geometry and analysis of control-affine systems: motion planning, heat and Schrödinger…

### Enhancing Fresh Produce Yield Forecasting Using Vegetation Indices from Satellite Images

- Environmental Science2022 IEEE International Conference on Systems, Man, and Cybernetics (SMC)
- 2022

Developing fresh produce yield forecasting service is essential for estimating fair prices to protect against overpriced agricultural commodities and minimize the bid ask spread which not only…

## References

SHOWING 1-10 OF 29 REFERENCES

### Approximation of multivariate periodic functions by trigonometric polynomials based on rank-1 lattice sampling

- Mathematics, Computer ScienceJ. Complex.
- 2015

### Fast Fourier Transforms for Nonequispaced Data, II

- Computer Science
- 1995

A group of algorithms generalizing the fast Fourier transform to the case of noninteger frequencies and nonequispaced nodes on the interval [-π, π] is presented, and it turns out that the scheme of Dutt et al. is preferable for the forward problem, while the method introduced here is considerably more efficient for the inverse one.

### Fast evaluation of trigonometric polynomials from hyperbolic crosses

- Computer ScienceNumerical Algorithms
- 2006

This paper proposes an algorithm for the fast Fourier transform on hyperbolic cross points for nonequispaced spatial knots in two and three dimensions that is based on the NFFT and an appropriate partitioning of the hyperBolic cross.

### An algorithm for the machine calculation of complex Fourier series

- Computer Science
- 1965

Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.

### Hypoelliptic Diffusion and Human Vision: A Semidiscrete New Twist

- MathematicsSIAM J. Imaging Sci.
- 2014

A semidiscrete alternative to the theory of neurogeometry of vision, due to Citti, Petitot, and Sarti, working on the group of translations and discrete rotations of $SE(2,N)$.

### Efficient numerical methods in non-uniform sampling theory

- Computer Science
- 1995

A new ``second generation" reconstruction algorithm for irregular sampling, i.e. for the problem of recovering a band-limited function from its non-uniformly sampled values, is presented.

### Is the fast Hankel transform faster than quadrature

- Geology
- 2012

The fast Hankel transform (FHT) implemented with digital filters has been the algorithm of choice in EM geophysics for a few decades. However, other disciplines have predominantly relied on methods…

### Anthropomorphic Image Reconstruction via Hypoelliptic Diffusion

- MathematicsSIAM J. Control. Optim.
- 2012

A model of geometry of vision due to Petitot, Citti, and Sarti is studied, and a mathematical proof of several important facts for this model is provided.

### Generalized Fourier Descriptors with Applications to Objects Recognition in SVM Context

- Computer ScienceJournal of Mathematical Imaging and Vision
- 2007

The development of the general theory of generalized Fourier-descriptors, with several new results, about their completeness in particular, lead to simple formulas for motion-invariants of images, that are “complete” in a certain sense, and are used in the first part of the paper.

### Is computing with the finite Fourier transform pure or applied mathematics

- Mathematics
- 1979

Let me begin with my view of a bit of history. Before the Second World War mathematics in the United States was a servant of the needs of others and mathematicians taught service courses. Indeed,…