Sampling random signals
Sponsored Links
This presentation is the property of its rightful owner.
1 / 29

Sampling Random Signals PowerPoint PPT Presentation


  • 91 Views
  • Uploaded on
  • Presentation posted in: General

Sampling Random Signals. Introduction Types of Priors. Subspace priors:. Smoothness priors:. Stochastic priors:. Introduction Motivation for Stochastic Modeling. Understanding of artifacts via stationarity analysis New scheme for constrained reconstruction Error analysis.

Download Presentation

Sampling Random Signals

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Sampling Random Signals


Introduction

Types of Priors

  • Subspace priors:

  • Smoothness priors:

  • Stochastic priors:


Introduction

Motivation for Stochastic Modeling

  • Understanding of artifacts via stationarity analysis

  • New scheme for constrained reconstruction

  • Error analysis


Introduction

Review of Definitions and Properties


IntroductionReview of Definitions and Properties

  • Filtering:

  • Wiener filter:


Balakrishnan’s Sampling Theorem

[Balakrishnan 1957]


Hybrid Wiener Filter


Hybrid Wiener Filter

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


Hybrid Wiener Filter


Hybrid Wiener FilterImage scaling

Original Image

Bicubic Interpolation

Hybrid Wiener


Hybrid Wiener FilterRe-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 !


Non-Stationary Reconstruction

?

Stationary


Non-Stationary Reconstruction

Stationary Signal

Reconstructed Signal


Non-Stationary Reconstruction


Non-Stationary Reconstruction

Artifacts

Original image

Interpolation with rect

Interpolation with sinc


Non-Stationary Reconstruction

Artifacts

Nearest Neighbor

Original Image

Bicubic

Sinc


Constrained Reconstruction Kernel

Predefined interpolation filter:

Solution:

1.

2.


Constrained Reconstruction Kernel

Dense Interpolation Grid

Dense grid approximation of the optimal filter:


Our Approach

Optimal dense grid interpolation:


Our Approach

Motivation


Our ApproachNon-Stationarity

[Michaeli & Eldar 08]


SimulationsSynthetic Data


SimulationsSynthetic Data


SimulationsSynthetic Data


First Order Approximation

  • Ttriangular kernel

  • Interpolation grid:

  • Scaling factor:


Optimal Dense Grid Reconstruction

  • Ttriangular kernel

  • Interpolation grid:

  • Scaling factor:


Error Analysis

  • 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


Theoretical Analysis

  • Average MSE of the hybrid Wiener filter

  • Necessary & Sufficient conditions for linear perfect recovery

  • Necessary & Sufficient condition for our scheme to be optimal


  • Login