Advances in Engineering Advances in Engineering features breaking research judged by Advances in Engineering advisory team to be of key importance in the Engineering field. Papers are selected from over 10,000 published each week from most peer reviewed journals.
Signal Processing, Volume 93, Issue 7, July 2013, Pages 1738-1747.
Yothin Rakvongthai, Soontorn Oraintara
Department of Electrical Engineering, University of Texas at Arlington, 416 Yates St, Arlington, TX 76019, USA
Abstract
This paper proposes a method to estimate the parameters of the relative phase probability density function (RP pdf) of the complex coefficients when an image is corrupted by additive white Gaussian noise. With the complex Gaussian scale mixture (CGSM) assumption of the clean coefficients, we first introduce the relative phase mixture (RPM) pdf by deriving the pdf of the relative phase of the noisy coefficients. Along with the derived pdf, a parameter estimation method based on the maximum likelihood approach is proposed by exploiting the relationships between the pdf’s parameters and the complex covariance matrix of the corresponding complex coefficient vector. Simulation studies using simulated data are performed to show the effectiveness of the estimation method. Moreover, we use the proposed estimation method in the application of texture retrieval in a noisy environment. The results show that the proposed method can estimate the parameters of the clean vector well in the case of simulated data and that the proposed estimation method improves the retrieval accuracy rate.
Additional Information:
This work proposes a method to estimate the parameters of the relative phase probability density function (RP pdf) of the complex coefficients when an image is corrupted by additive white Gaussian noise. Based on the complex Gaussian scale mixture (CGSM) assumption of the clean coefficients, we first introduce the relative phase mixture (RPM) pdf by deriving the pdf of the relative phase of the noisy coefficients. Along with the derived pdf, a parameter estimation method based on the maximum likelihood approach is proposed by exploiting the relationships between the pdf’s parameters and the complex covariance matrix of the corresponding complex coefficient vector. Simulation studies using simulated data are performed to validate the estimation method. The results show that the proposed estimation method yields better accuracy than the methods where the noisy coefficients are assumed to be clean or where we assume that the relative phase of the noisy coefficients has the RP pdf not the RPM pdf. In addition, the results of texture retrieval in a noisy environment using the relative phase of complex coefficients are shown as an example of its applications. We have found that using the proposed method in estimating the clean parameters from a noisy texture yields higher retrieval rate than the other two methods. The retrieval results are also consistent among several complex multiresolution transforms including the dual-tree complex wavelet transform (DT-CWT).
