Modeling multiscale subbands of photographic images with fields of Gaussian scale mixtures

Siwei Lyu, Eero Simoncelli

Research output: Contribution to journalArticle

Abstract

The local statistical properties of photographic images, when represented in a multi-scale basis, have been described using Gaussian scale mixtures. Here, we use this local description as a substrate for constructing a global field of Gaussian scale mixtures (FoGSMs). Specifically, we model multi-scale subbands as a product of an exponentiated homogeneous Gaussian Markov random field (hGMRF) and a second independent hGMRF. We show that parameter estimation for this model is feasible, and that samples drawn from a FoGSM model have marginal and joint statistics similar to subband coefficients of photographic images. We develop an algorithm for removing additive Gaussian white noise based on the FoGSM model, and demonstrate denoising performance comparable with state-of-the-art methods.

Original languageEnglish (US)
Pages (from-to)693-706
Number of pages14
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Volume31
Issue number4
DOIs
StatePublished - 2009

Fingerprint

Scale Mixture
Multiscale Modeling
Gaussian Mixture
Gaussian Markov Random Field
Mixture Model
Multiscale Model
Gaussian White Noise
White noise
Denoising
Parameter estimation
Statistical property
Parameter Estimation
Substrate
Statistics
Substrates
Coefficient
Demonstrate

Keywords

  • Image denoising
  • Image statistics
  • Markov random field

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computer Vision and Pattern Recognition
  • Software
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

@article{db6a4c034115439385f013978e18f420,
title = "Modeling multiscale subbands of photographic images with fields of Gaussian scale mixtures",
abstract = "The local statistical properties of photographic images, when represented in a multi-scale basis, have been described using Gaussian scale mixtures. Here, we use this local description as a substrate for constructing a global field of Gaussian scale mixtures (FoGSMs). Specifically, we model multi-scale subbands as a product of an exponentiated homogeneous Gaussian Markov random field (hGMRF) and a second independent hGMRF. We show that parameter estimation for this model is feasible, and that samples drawn from a FoGSM model have marginal and joint statistics similar to subband coefficients of photographic images. We develop an algorithm for removing additive Gaussian white noise based on the FoGSM model, and demonstrate denoising performance comparable with state-of-the-art methods.",
keywords = "Image denoising, Image statistics, Markov random field",
author = "Siwei Lyu and Eero Simoncelli",
year = "2009",
doi = "10.1109/TPAMI.2008.107",
language = "English (US)",
volume = "31",
pages = "693--706",
journal = "IEEE Transactions on Pattern Analysis and Machine Intelligence",
issn = "0162-8828",
publisher = "IEEE Computer Society",
number = "4",

}

TY - JOUR

T1 - Modeling multiscale subbands of photographic images with fields of Gaussian scale mixtures

AU - Lyu, Siwei

AU - Simoncelli, Eero

PY - 2009

Y1 - 2009

N2 - The local statistical properties of photographic images, when represented in a multi-scale basis, have been described using Gaussian scale mixtures. Here, we use this local description as a substrate for constructing a global field of Gaussian scale mixtures (FoGSMs). Specifically, we model multi-scale subbands as a product of an exponentiated homogeneous Gaussian Markov random field (hGMRF) and a second independent hGMRF. We show that parameter estimation for this model is feasible, and that samples drawn from a FoGSM model have marginal and joint statistics similar to subband coefficients of photographic images. We develop an algorithm for removing additive Gaussian white noise based on the FoGSM model, and demonstrate denoising performance comparable with state-of-the-art methods.

AB - The local statistical properties of photographic images, when represented in a multi-scale basis, have been described using Gaussian scale mixtures. Here, we use this local description as a substrate for constructing a global field of Gaussian scale mixtures (FoGSMs). Specifically, we model multi-scale subbands as a product of an exponentiated homogeneous Gaussian Markov random field (hGMRF) and a second independent hGMRF. We show that parameter estimation for this model is feasible, and that samples drawn from a FoGSM model have marginal and joint statistics similar to subband coefficients of photographic images. We develop an algorithm for removing additive Gaussian white noise based on the FoGSM model, and demonstrate denoising performance comparable with state-of-the-art methods.

KW - Image denoising

KW - Image statistics

KW - Markov random field

UR - http://www.scopus.com/inward/record.url?scp=62249200514&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=62249200514&partnerID=8YFLogxK

U2 - 10.1109/TPAMI.2008.107

DO - 10.1109/TPAMI.2008.107

M3 - Article

C2 - 19229084

AN - SCOPUS:62249200514

VL - 31

SP - 693

EP - 706

JO - IEEE Transactions on Pattern Analysis and Machine Intelligence

JF - IEEE Transactions on Pattern Analysis and Machine Intelligence

SN - 0162-8828

IS - 4

ER -