Sampling random signals
Download
1 / 29

Sampling Random Signals - PowerPoint PPT Presentation


  • 105 Views
  • Uploaded on

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.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Sampling Random Signals ' - rane


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

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


Introduction review of definitions and properties
IntroductionReview of Definitions and Properties

  • Filtering:

  • Wiener filter:




Hybrid wiener filter1
Hybrid Wiener Filter

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



Hybrid Wiener Filter Image scaling

Original Image

Bicubic Interpolation

Hybrid Wiener


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 !



Non-Stationary Reconstruction

Stationary Signal

Reconstructed Signal



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 Approach Non-Stationarity

[Michaeli & Eldar 08]


Simulations Synthetic Data


Simulations Synthetic Data


Simulations Synthetic 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


ad