Author's Accepted Manuscript

Generalized signal-dependent noise model and parameter estimation for natural images

Thanh Hai Thai, Florent Retraint, Rémi Cogranne

PII: S0165-1684(15)00086-9

DOI: http://dx.doi.org/10.1016/j.sigpro.2015.02.020

Reference: SIGPRO5744

To appear in: Signal Processing

Received date: 16 June 2014

Revised date: 28 November 2014

Accepted date: 23 February 2015

Cite this article as: Thanh Hai Thai, Florent Retraint, Rémi Cogranne,

Generalized signal-dependent noise model and parameter estimation for natural images, Signal Processing, http://dx.doi.org/10.1016/j.sigpro.2015.02.020

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Signal Processing 00 (2015) 1–7

Signal Processing

Generalized Signal-Dependent Noise Model and Parameter Estimation for Natural Images

Thanh Hai Thai, Florent Retraint and, Rémi Cogranne∗∗

ICD - LM2S - University of Technology of Troyes - UMR STMR CNRS 12, rue Marie Curie - CS 42060 - 10004 Troyes cedex - France

Abstract

The goal of this paper is to propose a generalized signal-dependent noise model that is more appropriate to describe a natural image acquired by a digital camera than the conventional Additive White Gaussian Noise model widely used in image processing.

This non-linear noise model takes into account effects in the image acquisition pipeline of a digital camera. In this paper, an algorithm for estimation of noise model parameters from a single image is designed. Then the proposed noise model is applied with the Local Linear Minimum Mean Square Error filter to design an efficient image denoising method.

Keywords: Signal-Dependent Noise Model, Noise Measurement, Noise Parameter Estimation, Denoising. 1. Introduction

Noise has been studied for decades in computer vision, image processing and statistical signal processing because of its impact in various applications such as image denoising, image segmentation or edge detection. To improve performance in those applications, it is important to identify noise characteristics. Noise models proposed in the literature can be roughly divided into two groups: signal-independent and signal-dependent. A typical model for the group of signal-independent noise is the Additive White Gaussian Noise (AWGN) that is widely used in image processing. However, this signal-independent AWGN model is not relevant due to the dominant contribution of the Poisson noise corrupting a natural image acquired by imaging device [1, 2]. While signalindependent noise models assume the stationarity of noise in the whole natural image, regardless original pixel intensity, signal-dependent noise models take into account the proportional dependence of noise variance on the original pixel intensity. Signal-dependent noise models include Poisson noise or film-grain noise [3], Poisson-Gaussian noise [4, 5], heteroscedastic noise model [2, 6], and non-linear noise model [7, 8]. The signal-dependent noise model gives the noise variance as a function of pixel’s expectation. This function can be linear [4, 5, 2, 6] or non-linear [7, 8]. To identify noise characteristics or attenuate noise impact in many image processing ∗Corresponding author. ∗∗With the financial support from Champagne-Ardenne region, IDENT project.

Email address: (Rémi Cogranne ) applications, it is desirable to design an algorithm that estimates noise model parameters accurately.

Estimation of noise model parameters can be performed from a single image or multiple images. From a practical point of view, this paper mainly focuses on noise parameter estimation from a single image. Several methods have been proposed in the literature for estimation of signal-dependent noise parameters [2, 6, 7, 8]. They rely on similar basic steps but differ in details. The common methodology starts from obtaining local estimates of noise variance and image content, then performing the curve fitting to the scatter-plot based on the prior knowledge of noise model. The existing methods involve two main difficulties: influence of image content and spatial correlation of noise in a natural image. In fact, homogeneous regions where local means and variances are estimated are obtained by performing edge detection and image segmentation. However, the accuracy of those local estimates may be contaminated due to the presence of outliers (textures, details and edges) in the homogeneous regions. Moreover, because of the spatial correlation, the local estimates of noise variance can be overestimated.

Overall, the two difficulties may result in inaccurate estimation of noise parameters.

The contribution of this paper is threefold. Firstly, by modeling the main steps of the image acquisition pipeline, this paper starts from the heteroscedastic noise model [2, 6] that accurately characterizes a natural RAW image and takes into account the impact of gamma correction to develop a generalized non-linear noise model. This model has not been proposed yet in the literature. Secondly, an algorithm for estimation of noise model parameters from a single image is proposed. Finally, the

Local Linear Minimum Mean Square Error (LLMMSE) filter

T. H. Thai, F. Retraint, R. Cogranne / Signal Processing 00 (2015) 1–7 2 estimated expectation es tim at ed va ri an ce 0 0.05 0.1 0.15 0.2 0.250 0.4 0.8 1.2 1.6 2 ×10−5

Nikon D70: Estimated data

Nikon D70: Fitted data

Nikon D200: Estimated data

Nikon D200: Fitted data

Figure 1: Scatter-plot of pixels’ expectation and variance from RAW images acquired by Nikon D70 and Nikon D200 cameras [9]. that was proposed in [3] is combined with the proposed noise model to design an efficient image denoising method.