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Sampling Random Signals PowerPoint Presentation

Sampling Random Signals

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**rane** - Follow User

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Presentation Transcript

Motivation for Stochastic Modeling

- Understanding of artifacts via stationarity analysis
- New scheme for constrained reconstruction
- Error analysis

Review of Definitions and Properties

Balakrishnan’s Sampling Theorem

[Balakrishnan 1957]

Hybrid Wiener Filter

[Huck et. al. 85], [Matthews 00], [Glasbey 01], [Ramani et al 05]

Hybrid Wiener Filter Re-sampling

- Drawbacks:
- May be hard to implement
- No explicit expression in the time domain

Re-sampling:

Constrained Reconstruction Kernel

Predefined interpolation filter:

The correction filter depends on t !

Artifacts

Original image

Interpolation with rect

Interpolation with sinc

Constrained Reconstruction Kernel

Dense Interpolation Grid

Dense grid approximation of the optimal filter:

Optimal dense grid interpolation:

Motivation

Our Approach Non-Stationarity

[Michaeli & Eldar 08]

Simulations Synthetic Data

Simulations Synthetic Data

Simulations Synthetic Data

- Ttriangular kernel
- Interpolation grid:
- Scaling factor:

Optimal Dense Grid Reconstruction

- Ttriangular kernel
- Interpolation grid:
- Scaling factor:

- Average MSE of dense grid system with predefined kernel
- Average MSE of standard system (K=1) with predefined kernel
- For K=1: optimal sampling filter for predefined interpolation kernel

- Average MSE of the hybrid Wiener filter
- Necessary & Sufficient conditions for linear perfect recovery
- Necessary & Sufficient condition for our scheme to be optimal

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