# Discretization and solution of elliptic PDEs-a digital signal processing approach

@article{Kuo1990DiscretizationAS, title={Discretization and solution of elliptic PDEs-a digital signal processing approach}, author={C.-C. Jay Kuo and Bernard C. Levy}, journal={Proc. IEEE}, year={1990}, volume={78}, pages={1808-1842} }

A digital signal processing (DSP) approach is used to study numerical methods for discretizing and solving linear elliptic partial differential equations (PDEs). Whereas conventional PDE analysis techniques rely on matrix analysis and on a space-domain point of view to study the performance of solution methods, the DSP approach described here relies on frequency-domain analysis and on multidimensional DSP techniques. Both discretization schemes and solution methods are discussed. In the area of…

## 16 Citations

### Discrete simulation of linear multidimensional continuous systems

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To increase reconstruction speed, spatially invariant preconditioning filters that can be designed using the tomographic system response and implemented using 2-D frequency-domain filtering techniques have been applied.

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The determination of intravascular pressure fields is important to the characterization of cardiovascular pathology. We present a two-stage method that solves the inverse problem of estimating the…

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The authors have developed a technique based on a solution of the Poisson equation to unwrap the phase in magnetic resonance (MR) phase images that is robust in the presence of noise and applies to the 3-point Dixon technique for water and fat separation.

### A least squares based phase unwrapping algorithm for MRI

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The authors have developed a technique based on a solution of the Poisson equation to unwrap the phase in magnetic resonance (MR) phase images. The method is based on the assumption that the…

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### Simulation of wave propagation by multidimensional digital filters

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### Approximate Estimation of Functionals of the Solutions of Parabolic Equation under Nonlinearity in Output

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The paper focuses on the minimax estimation approach used widely with signal processing. The paper deals with the problem of minimax estimating a functional from the solution of a parabolic equation…

### Determining cardiac velocity fields and intraventricular pressure distribution from a sequence of ultrafast CT cardiac images

- PhysicsIEEE Trans. Medical Imaging
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A numerical algorithm developed by discretizing the pressure Poisson equation (PPE) can reconstruct the pressure distribution using only the velocity data and is shown to be robust in the presence of noise.

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