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By exploiting the sparsity of mode shapes, CS can also enable efficient spatial reconstruction using fewer spatially distributed sensors.
A simple spatial reconstruction algorithm was used to virtually reconstruct the place preference of replays from place cell activity while the animal briefly paused.
The spatial reconstruction of the simulated transients reflects the random occurrence of the real transients.
For the spatial reconstruction, we adopt the second order TVD limiter due to Koren (Koren 1993).
Also, a direct spatial reconstruction from non-linear measurements using a variable grid size is exhibited in [7].
It is clear that BBM generates noisy results due to the absence of spatial reconstruction smoothness (shown in blue).
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We recover third-order accurate ENO spatial reconstructions when the parameter θ j =1 in smooth regions.
Spatial reconstructions from biplane geometry evolved as important tools for morphological analyses of vessels or catheters in both cardiology and neurology domains [14 19].
Formulated on staggered meshes, the methods involve Hermite WENO (HWENO) spatial reconstructions, and Lax Wendroff type discretizations or the natural continuous extension of Runge Kutta methods in time.
By performing such new procedures in spatial reconstructions and adopting a third order TVD Runge Kutta time discretization method for solving the ordinary differential equation (ODE), the new scheme's memory occupancy is decreased and the computing efficiency is increased.
Differently from the central Hermite WENO methods we developed previously in Tao et al. (2015) [34], the spatial reconstructions, a core ingredient of the methods, are based on the zeroth-order and the first-order moments of the solution, and are implemented through a dimension-by-dimension strategy when the spatial dimension is higher than one.
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