Bayesian Analysis

Bayesian Multiscale Smoothing of Gaussian Noised Images

Meng Li and Subhashis Ghosal

Full-text: Open access

Abstract

We propose a multiscale model for Gaussian noised images under a Bayesian framework for both 2-dimensional (2D) and 3-dimensional (3D) images. We use a Chinese restaurant process prior to randomly generate ties among intensity values at neighboring pixels in the image. The resulting Bayesian estimator enjoys some desirable asymptotic properties for identifying precise structures in the image. The proposed Bayesian denoising procedure is completely data-driven. A conditional conjugacy property allows analytical computation of the posterior distribution without involving Markov chain Monte Carlo (MCMC) methods, making the method computationally efficient. Simulations on Shepp-Logan phantom and Lena test images confirm that our smoothing method is comparable with the best available methods for light noise and outperforms them for heavier noise both visually and numerically. The proposed method is further extended for 3D images. A simulation study shows that the proposed method is numerically better than most existing denoising approaches for 3D images. A 3D Shepp-Logan phantom image is used to demonstrate the visual and numerical performance of the proposed method, along with the computational time. MATLAB toolboxes are made available online (both 2D and 3D) to implement the proposed method and reproduce the numerical results.

Article information

Source
Bayesian Anal., Volume 9, Number 3 (2014), 733-758.

Dates
First available in Project Euclid: 5 September 2014

Permanent link to this document
https://projecteuclid.org/euclid.ba/1409921112

Digital Object Identifier
doi:10.1214/14-BA871

Mathematical Reviews number (MathSciNet)
MR3256062

Zentralblatt MATH identifier
1327.62151

Keywords
Chinese Restaurant Process MCMC-free computation 3-dimensional image

Citation

Li, Meng; Ghosal, Subhashis. Bayesian Multiscale Smoothing of Gaussian Noised Images. Bayesian Anal. 9 (2014), no. 3, 733--758. doi:10.1214/14-BA871. https://projecteuclid.org/euclid.ba/1409921112


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