Noise-Model-Recovery

This repository provides the tool to recover the noise model from dataset, and can also be used to recover the signal from its autocorrelation.

• Assumptions
  • For deautocorrelation
  • For noise model recovery from real datasets
• Principle
• Function introduction
  • Deautocorrelation
  • Pdf recovery
  • Noise model recovery from datasets
• Example results
  • Without sampling error and signal residue
  • Simulation noise without signal residue
  • Considering signal residue
• Reference

Assumptions

For deautocorrelation

• The original pdf/signal is symmetric with respect to some vertical line.
• The signal is real-valued.

For noise model recovery from real datasets

• The signal is strongly correlated for the same pixel between adjacent time points.
• The noise follows the same distribution and temporally independent.

Principle

• See the reference.

Function introduction

Deautocorrelation

• Recover the original function from its autocorrelation in deautocorrelation.m.
• Input: autocorrelation of some function.
• Output: recovered function.

Pdf recovery

• Y = X1-X2, X1 and X2 are i.i.d.
• Recover the distribution of X from the distribution of Y in pdf_recover.m.
• By autocorrelation, the recovered function may not denote a true pdf, thus need a refine step.
• Input: distribution of Y. (Users can also assign weights for the refine step).
• Output: distribution of X.

Noise model recovery from datasets

• Recover noise model for datasets in nmr.m.
• Input: data.
• Output: distribution of noise, distribution of noise difference (Y), binSize.

Example results

Without sampling error and signal residue

Here are the example results for deautocorrelation. Some common asymmetric distributions are also tested (No sampling error and no signal residue).

Simulation noise without signal residue

Here are simulation results, the noise is generated by MATLAB, with 10^8 samples.

Considering signal residue

Take Gaussian noise as example to see the influence of signal residue, and omit the influence of sampling error. SNR, signal change rate, and the signal ratio in the whole video will all have impact on the recovered result. Here we show some results for each factor:

Reference:

Waiting for the submission.