Topic
Hexagonal sampling
About: Hexagonal sampling is a research topic. Over the lifetime, 97 publications have been published within this topic receiving 2481 citations.
Papers published on a yearly basis
Papers
TL;DR: The well-known Whittaker-Kotel'nikov-Shannon sampling theorem for frequency-bandlimited functions of time is extended to functions of multidimensional arguments and it is shown that a function whose spectrum is restricted to a finite region of wave-number space may be reconstructed from its samples taken over a periodic lattice having suitably small repetition vectors.
Abstract: The well-known Whittaker-Kotel'nikov-Shannon sampling theorem for frequency-bandlimited functions of time is extended to functions of multidimensional arguments. It is shown that a function whose spectrum is restricted to a finite region of wave-number space may be reconstructed from its samples taken over a periodic lattice having suitably small repetition vectors. The most efficient lattice (i.e., requiring minimum sampling points per unit hypervolume) is not in general rectangular, nor is a unique reconstruction function associated with a given sampling lattice. The above results also apply to homogeneous wave-number-limited stochastic processes in the sense of a vanishing mean-square error. It is also found that, given a particular sampling lattice, the optimum (mean-square) presampling filter for nonwave-number-limited processes effects an ideal wave-number cutoff appropriate to the specified sampling lattice. Particular attention is paid to isotropic processes: minimum sampling lattices are specified up to eight-dimensional spaces, and a number of typical reconstruction functions are calculated.
697 citations
TL;DR: In this article, the authors proposed a technique that allows the authors to process the visibility samples over the hexagonal sampling grids given by Y-shaped and triangular-shaped arrays with standard rectangular FFT routines.
Abstract: In Earth observation programs there is a need of passive low frequency (L-band) measurements to monitor soil moisture and ocean salinity with high spatial resolution 10-20 km, a radiometric resolution of 1 K and a revisit time of 1-3 days. Compared to total power radiometers aperture synthesis interferometric radiometers are technologically attractive because of their reduced mass and hardware requirements. In this field it should be mentioned the one-dimensional (1D) linear interferometer ESTAR developed by NASA and MIRAS a two-dimensional (2D) Y-shaped interferometer currently under study by European Space Agency (ESA). Interferometer radiometers measure the correlation between pairs of nondirective antennas. Each complex correlation is a sample of the "visibility" function which, in the ideal case, is the spatial Fourier transform of the brightness temperature distribution. Since most receiver phase and amplitude errors can be hardware calibrated, Fourier based iterative inversion methods will be useful when antenna errors are small, their radiation voltage patterns are not too different, and mutual coupling is small. In order to minimize on-board hardware requirements-antennas, receivers and correlators-the choice of the interferometer array shape is of great importance since it determines the (u,v) sampling strategy and the minimum number of visibility samples required for a determined aliasing level. In this sense, Y-shaped and triangular-shaped arrays with equally spaced antennas are optimal. The main contribution of this paper is a technique that allows the authors to process the visibility samples over the hexagonal sampling grids given by Y-shaped and triangular-shaped arrays with standard rectangular FFT routines. Since no interpolation processes are involved, the risk of induced artifacts in the recovered brightness temperature over the wide held of view required in Earth observation missions is minimized and signal to noise ratio (SNR) is preserved.
161 citations
TL;DR: Results from using edge detection on this framework show that the computational requirement for processing a hexagonally sampled image is less than that for square sampled images, and a better qualitative performance which is due to the compact and circular nature of the hexagonal lattice.
84 citations
TL;DR: Shannon’s theory of information for communication channels is used to assess the performance of line-scan and sensor-array imaging systems and to optimize the design trade-offs involving sensitivity, spatial response, and sampling intervals.
Abstract: Shannon's theory of information for communication channels is used to assess the performance of line-scan and sensor-array imaging systems and to optimize the design trade-offs involving sensitivity, spatial response, and sampling intervals. Formulations and computational evaluations account for spatial responses typical of line-scan and sensor-array mechanisms, lens diffraction and transmittance shading, defocus blur, and square and hexagonal sampling lattices.
58 citations
TL;DR: New reconstruction methods for hexagonally sampled data are proposed that use the intrinsically 2-D nature of the lattice, and that at the same time remain practical and efficient, and rely on the quasi-interpolation paradigm to design compelling prefilters.
Abstract: The reconstruction of a continuous-domain representation from sampled data is an essential element of many image processing tasks, in particular, image resampling. Until today, most image data have been available on Cartesian lattices, despite the many theoretical advantages of hexagonal sampling. In this paper, we propose new reconstruction methods for hexagonally sampled data that use the intrinsically 2-D nature of the lattice, and that at the same time remain practical and efficient. To that aim, we deploy box-spline and hex-spline models, which are notably well adapted to hexagonal lattices. We also rely on the quasi-interpolation paradigm to design compelling prefilters; that is, the optimal filter for a prescribed design is found using recent results from approximation theory. The feasibility and efficiency of the proposed methods are illustrated and compared for a hexagonal to Cartesian grid conversion problem
48 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2022 | 1 |
| 2021 | 2 |
| 2020 | 1 |
| 2019 | 2 |
| 2018 | 1 |
| 2017 | 4 |